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  VOCEDplus

  VOCEDplus is a free international research database about tertiary education, maintained and developed by staff at the c (NCVER) in Adelaide, South Australia. The focus of the database content is the relation of post-compulsory education and training to workforce needs, skills development, and social inclusion. == Structure == The content of the VOCEDplus database encompasses vocational education and training (VET), higher education, lifelong learning, informal learning, VET in schools, adult and community education, apprenticeships/traineeships, international education, providers of education and training, and workforce development. It is international in scope and contains over 84,000 English language records, many with links to full text documents. VOCEDplus contains extensive Australian materials and includes a wide range of international information, covering outcomes of tertiary education in the shape of published research, practice, policy, and statistics. Entries are included for the following types of publications: reports; annual reports; papers; discussion papers; occasional papers; working papers; books; book chapters; conference papers; conference proceedings; journals; journal articles; policy documents; published statistics; theses; podcasts; and teaching and training materials. Each database entry contains standard bibliographic information and an abstract. Many entries include full text access via the publisher's website or a digitised copy. == History == === 1989-1997 === In the early years VOCEDplus was known as VOCED. The original database was produced by a network of clearinghouses across Australia with the aim of sharing activities in the technical and further education (TAFE) sector. VOCED was produced in hardcopy and an electronic version was distributed on diskette. === 1997-2001 === 1997 - the first web version of VOCED was made available from the National Centre for Vocational Education Research (NCVER) organisational website 1998 - a major project to upgrade the database and expand its international coverage commenced 2001 - creation of VOCED's own website 2001 - VOCED endorsed as the UNESCO international database for technical and vocational education and training (TVET) research information === 2001-2009 === Many changes to the database and website occurred during this period with a focus on continuous improvement to meet the needs of users and utilise emerging technologies. 2006 - materials produced for two adult literacy and learning programs funded by the Australian Department of Education, Employment and Workplace Relations (DEEWR) - the Workplace English Language and Learning (WELL) Programme and the Adult Literacy National Project (ALNP) included in VOCED 2007 - the Australian clearinghouse network transferred most of the hardcopy collections to NCVER, to form a centralised repository of resources 2009 - materials produced by Reframing the Future (RTF) a vocational education and training workforce development initiative of the Australian, State and Territory Governments included in VOCED === 2009-2014 === A major rebuild of the database and website was undertaken during this period to take advantage of the potential of new technologies to provide improved services and incorporate Web 2.0 technologies (RSS feeds, and share and bookmark tools). 2009 - scope expanded to more fully encompass the higher education sector 2011 - launch of VOCEDplus with the name change representing the enhanced features and extended focus 2012 - a major retrospective digitisation project commenced and by the end of the 2012-2013 financial year a total of 9,328 publications (593,534 pages/microfiche frames) had been digitised, ensuring these publications are available electronically for free === 2014-2019 === A number of significant curated content products were released during this period. 2015 - release of a refreshed look to adopt the new NCVER branding plus a number of search enhancements (Guided search, Expert search, and Glossary search) were added 2015 - first in the series of 'Focus on...' pages released 2016 - launch of the 'Pod Network', a convenient and efficient platform that allows instant access to research and a multitude of resources on a range of subjects 2017 - completion of the 'Pod Network', consisting of 20 Pods (on broad subjects including Apprenticeships and traineeships, Foundation skills, Teaching and learning, Career development, and Students) and 74 Podlets (on narrow topics including Online learning, Social media, VET in schools, STEM skills, and Adult literacy) 2018 - launch of the 'Timeline of Australian VET Policy Initiatives' and the 'VET Knowledge Bank' which contains a suite of products capturing Australia's diverse, complex and ever-changing VET system 2019 - after an internal review, a refreshed, streamlined version of the 'Pod Network' was released, consisting of 13 Pods and 20 Podlets 2019 - launch of the 'VET Practitioner Resource' which contains a range of information to support VET practitioners in their work and is organised into three sections: (1) Teaching, training and assessment: standards, guidance, research and good practice resources to inform daily work; (2) Practitioners as researchers: information for undertaking practitioner-led research; and (3) The VET workforce: information about VET teachers and trainers, and the professional development needs of the VET workforce 2019 - VOCEDplus celebrated 30 years of providing information to the tertiary education sector and the homepage was refreshed to make it more modern and easier to use === 2020- === VOCEDplus continued to be accessible throughout the COVID-19 pandemic. 2020-2021 - the VET Knowledge Bank added a dedicated page, 'COVID-19 announcements', that showcases the measures introduced by the Australian, state and territory governments to mitigate the impact of the pandemic and promote economic recovery 2020-2024 - published research about the effects of the pandemic on education and training, providers, students, labour markets, employment and employees was collected and made permanently available in the database 2024 - VOCEDplus celebrated 35 years of providing information to the tertiary education sector. The homepage was refreshed and a number of enhancements and new features were implemented including a new My Profile feature, improvements to My Selection, accessible search history and saved searches, enhanced search functionality, and improved navigation.

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  Visual Turing Test

  The Visual Turing Test is “an operator-assisted device that produces a stochastic sequence of binary questions from a given test image”. The query engine produces a sequence of questions that have unpredictable answers given the history of questions. The test is only about vision and does not require any natural language processing. The job of the human operator is to provide the correct answer to the question or reject it as ambiguous. The query generator produces questions such that they follow a “natural story line”, similar to what humans do when they look at a picture. == History == Research in computer vision dates back to the 1960s when Seymour Papert first attempted to solve the problem. This unsuccessful attempt was referred to as the Summer Vision Project. The reason why it was not successful was because computer vision is more complicated than what people think. The complexity is in alignment with the human visual system. Roughly 50% of the human brain is devoted in processing vision, which indicates that it is a difficult problem. Later there were attempts to solve the problems with models inspired by the human brain. Perceptrons by Frank Rosenblatt, which is a form of the neural networks, was one of the first such approaches. These simple neural networks could not live up to their expectations and had certain limitations due to which they were not considered in future research. Later with the availability of the hardware and some processing power the research shifted to image processing which involves pixel-level operations, like finding edges, de-noising images or applying filters to name a few. There was some great progress in this field but the problem of vision which was to make the machines understand the images was still not being addressed. During this time the neural networks also resurfaced as it was shown that the limitations of the perceptrons can be overcome by Multi-layer perceptrons. Also in the early 1990s convolutional neural networks were born which showed great results on digit recognition but did not scale up well on harder problems. The late 1990s and early 2000s saw the birth of modern computer vision. One of the reasons this happened was due to the availability of key, feature extraction and representation algorithms. Features along with the already present machine learning algorithms were used to detect, localise and segment objects in Images. While all these advancements were being made, the community felt the need to have standardised datasets and evaluation metrics so the performances can be compared. This led to the emergence of challenges like the Pascal VOC challenge and the ImageNet challenge. The availability of standard evaluation metrics and the open challenges gave directions to the research. Better algorithms were introduced for specific tasks like object detection and classification. Visual Turing Test aims to give a new direction to the computer vision research which would lead to the introduction of systems that will be one step closer to understanding images the way humans do. == Current evaluation practices == A large number of datasets have been annotated and generalised to benchmark performances of difference classes of algorithms to assess different vision tasks (e.g., object detection/recognition) on some image domain (e.g., scene images). One of the most famous datasets in computer vision is ImageNet which is used to assess the problem of object level Image classification. ImageNet is one of the largest annotated datasets available and has over one million images. The other important vision task is object detection and localisation which refers to detecting the object instance in the image and providing the bounding box coordinates around the object instance or segmenting the object. The most popular dataset for this task is the Pascal dataset. Similarly there are other datasets for specific tasks like the H3D dataset for human pose detection, Core dataset to evaluate the quality of detected object attributes such as colour, orientation, and activity. Having these standard datasets has helped the vision community to come up with well performing algorithms for all these tasks. The next logical step is to create a larger task encompassing of these smaller subtasks. Having such a task would lead to building systems that would understand images, as understanding images would inherently involve detecting objects, localising them and segmenting them. == Details == The Visual Turing Test (VTT) unlike the Turing test has a query engine system which interrogates a computer vision system in the presence of a human co-ordinator. It is a system that generates a random sequence of binary questions specific to the test image, such that the answer to any question k is unpredictable given the true answers to the previous k − 1 questions (also known as history of questions). The test happens in the presence of a human operator who serves two main purposes: removing the ambiguous questions and providing the correct answers to the unambiguous questions. Given an Image infinite possible binary questions can be asked and a lot of them are bound to be ambiguous. These questions if generated by the query engine are removed by the human moderator and instead the query engine generates another question such that the answer to it is unpredictable given the history of the questions. The aim of the Visual Turing Test is to evaluate the Image understanding of a computer system, and an important part of image understanding is the story line of the image. When humans look at an image, they do not think that there is a car at ‘x’ pixels from the left and ‘y’ pixels from the top, but instead they look at it as a story, for e.g. they might think that there is a car parked on the road, a person is exiting the car and heading towards a building. The most important elements of the story line are the objects and so to extract any story line from an image the first and the most important task is to instantiate the objects in it, and that is what the query engine does. === Query engine === The query engine is the core of the Visual Turing Test and it comprises two main parts : Vocabulary and Questions ==== Vocabulary ==== Vocabulary is a set of words that represent the elements of the images. This vocabulary when used with appropriate grammar leads to a set of questions. The grammar is defined in the next section in a way that it leads to a space of binary questions. The vocabulary V {\displaystyle {\mathcal {V}}} consist of three components: Types of Objects T {\displaystyle {\mathcal {T}}} Type-dependent attributes of objects A ( t ) {\displaystyle {\mathcal {A}}(t)} Type-dependent relationships between two objects R ( t , t ′ ) {\displaystyle {\mathcal {R}}(t,t')} For Images of urban street scenes the types of objects include people, vehicle and buildings. Attributes refer to the properties of these objects, for e.g. female, child, wearing a hat or carrying something, for people and moving, parked, stopped, one tire visible or two tires visible for vehicles. Relationships between each pair of object classes can be either “ordered” or “unordered”. The unordered relationships may include talking, walking together and the ordered relationships include taller, closer to the camera, occluding, being occluded etc. Additionally all of this vocabulary is used in context of rectangular image regions w \in W which allow for the localisation of objects in the image. An extremely large number of such regions are possible and this complicates the problem, so for this test, regions at specific scales are only used which include 1/16 the size of image, 1/4 the size of image, 1/2 the size of image or larger. ==== Questions ==== The question space is composed of four types of questions: Existence questions: The aim of the existence questions is to find new objects in the image that have not been uniquely identified previously. They are of the form : Qexist = 'Is there an instance of an object of type t with attributes A partially visible in region w that was not previously instantiated?' Uniqueness questions: A uniqueness question tries to uniquely identify an object to instantiate it. Quniq = 'Is there a unique instance of an object of type t with attributes A partially visible in region w that was not previously instantiated?' The uniqueness questions along with the existence questions form the instantiation questions. As mentioned earlier instantiating objects leads to other interesting questions and eventually a story line. Uniqueness questions follow the existence questions and a positive answer to it leads to instantiation of an object. Attribute questions: An attribute question tries to find more about the object once it has been instantiated. Such questions can query about a single attribute, conjunction of two attributes or disjunction of two attributes. Qatt(ot) = {'Does object ot have attribute a?' , 'Does object

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  Live Transcribe

  Live Transcribe is a mobile app for real-time captioning, developed by Google for the Android operating system. Development on the application began in partnership with Gallaudet University. It was publicly released as a free beta for Android 5.0+ on the Google Play Store on February 4, 2019. As of early 2023 it had been downloaded over 500 million times. == Development == Researchers Dimitri Kanevsky, Sagar Savla and Chet Gnegy at Google developed the app in collaboration with researchers at Gallaudet University, an American university for the education of the deaf and hard of hearing. The app uses machine learning to generate captions, similar to YouTube's auto-generated captions. In August 2019, Google made Live Transcribe an open-source project. == Features == The app uses speech recognition to generate live captions in over 80 languages with varying accuracy. The app, which requires connection to the Internet to function, is available to download on the Google Play Store. A later update to the app displayed information on sounds such as clapping, laughter, music, applause, and whistling. In May 2020, the app started supporting transcription in Albanian, Burmese, Estonian, Macedonian, Mongolian, Punjabi, and Uzbek, supporting 70 languages. In March 2022, the app was updated with support to transcribe offline, without Internet connection, so long as the appropriate language pack has been installed. The offline mode is only available for devices with 6GB of RAM and certain Google Pixel devices.

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  VLLM

  vLLM is an open-source software framework for inference and serving of large language models and related multimodal models. Originally developed at the University of California, Berkeley's Sky Computing Lab, the project is centered on PagedAttention, a memory-management method for transformer key–value caches, and supports features such as continuous batching, distributed inference, quantization, and OpenAI-compatible APIs. According to a project maintainer, the "v" in vLLM originally referred to "virtual", inspired by virtual memory. == History == vLLM was introduced in 2023 by researchers affiliated with the Sky Computing Lab at UC Berkeley. Its core ideas were described in the 2023 paper Efficient Memory Management for Large Language Model Serving with PagedAttention, which presented the system as a high-throughput and memory-efficient serving engine for large language models. In 2025, the PyTorch Foundation announced that vLLM had become a Foundation-hosted project. PyTorch's project page states that the University of California, Berkeley contributed vLLM to the Linux Foundation in July 2024. In January 2026, TechCrunch reported that the creators of vLLM had launched the startup Inferact to commercialize the project, raising $150 million in seed funding. == Architecture == According to its 2023 paper, vLLM was designed to improve the efficiency of large language model serving by reducing memory waste in the key–value cache used during transformer inference. The paper introduced PagedAttention, an algorithm inspired by virtual memory and paging techniques in operating systems, and described vLLM as using block-level memory management and request scheduling to increase throughput while maintaining similar latency. The project documentation and repository describe support for continuous batching, chunked prefill, speculative decoding, prefix caching, quantization, and multiple forms of distributed inference and serving. PyTorch has described vLLM as a high-throughput, memory-efficient inference and serving engine that supports a range of hardware back ends, including NVIDIA and AMD GPUs, Google TPUs, AWS Trainium, and Intel processors.

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  Cobocards

  CoboCards is a web application for creation, study and sharing of flashcards. They also provide mobile application for Android and iOS mobile devices, to help study of flashcards on the move. Based on the freemium model, CoboCards provides users a free account with two card sets compared to paid subscription with premium features such as unlimited card sets, Leitner system based trainer and collaborative learning. == History == CoboCards is a project of Jamil Soufan and Tamim Swaid. Tamim Swaid has developed the concept and interface of a collaboratively usable e-learning platform in his diploma thesis at the University of Applied Sciences in February 2007. In January 2010 they founded the CoboCards GmbH (limited company) together with Ali Yildirim. CoboCards is supported by its strategic partners Prof. Schroeder (RWTH Aachen University), Prof. Oliver Wrede (University for Applied Sciences Aachen) and Prof. Klaus Gasteier (University of Arts Berlin). With the idea of creating and studying flashcards online and offering an active control of learning progress they won the start2grow business idea competition in September 2009 (€25.000 ). Additionally CoboCards was funded by German Authorities with approximately €100.000 .

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  Automatic acquisition of sense-tagged corpora

  The knowledge acquisition bottleneck is perhaps the major impediment to solving the word-sense disambiguation (WSD) problem. Unsupervised learning methods rely on knowledge about word senses, which is barely formulated in dictionaries and lexical databases. Supervised learning methods depend heavily on the existence of manually annotated examples for every word sense, a requisite that can so far be met only for a handful of words for testing purposes, as it is done in the Senseval exercises. == Existing methods == Therefore, one of the most promising trends in WSD research is using the largest corpus ever accessible, the World Wide Web, to acquire lexical information automatically. WSD has been traditionally understood as an intermediate language engineering technology which could improve applications such as information retrieval (IR). In this case, however, the reverse is also true: Web search engines implement simple and robust IR techniques that can be successfully used when mining the Web for information to be employed in WSD. The most direct way of using the Web (and other corpora) to enhance WSD performance is the automatic acquisition of sense-tagged corpora, the fundamental resource to feed supervised WSD algorithms. Although this is far from being commonplace in the WSD literature, a number of different and effective strategies to achieve this goal have already been proposed. Some of these strategies are: acquisition by direct Web searching (searches for monosemous synonyms, hypernyms, hyponyms, parsed gloss' words, etc.), Yarowsky algorithm (bootstrapping), acquisition via Web directories, and acquisition via cross-language meaning evidences. == Summary == === Optimistic results === The automatic extraction of examples to train supervised learning algorithms reviewed has been, by far, the best explored approach to mine the web for word-sense disambiguation. Some results are certainly encouraging: In some experiments, the quality of the Web data for WSD equals that of human-tagged examples. This is the case of the monosemous relatives plus bootstrapping with Semcor seeds technique and the examples taken from the ODP Web directories. In the first case, however, Semcor-size example seeds are necessary (and only available for English), and it has only been tested with a very limited set of nouns; in the second case, the coverage is quite limited, and it is not yet clear whether it can be grown without compromising the quality of the examples retrieved. It has been shown that a mainstream supervised learning technique trained exclusively with web data can obtain better results than all unsupervised WSD systems which participated at Senseval-2. Web examples made a significant contribution to the best Senseval-2 English all-words system. === Difficulties === There are, however, several open research issues related to the use of Web examples in WSD: High precision in the retrieved examples (i.e., correct sense assignments for the examples) does not necessarily lead to good supervised WSD results (i.e., the examples are possibly not useful for training). The most complete evaluation of Web examples for supervised WSD indicates that learning with Web data improves over unsupervised techniques, but the results are nevertheless far from those obtained with hand-tagged data, and do not even beat the most-frequent-sense baseline. Results are not always reproducible; the same or similar techniques may lead to different results in different experiments. Compare, for instance, Mihalcea (2002) with Agirre and Martínez (2004), or Agirre and Martínez (2000) with Mihalcea and Moldovan (1999). Results with Web data seem to be very sensitive to small differences in the learning algorithm, to when the corpus was extracted (search engines change continuously), and on small heuristic issues (e.g., differences in filters to discard part of the retrieved examples). Results are strongly dependent on bias (i.e., on the relative frequencies of examples per word sense). It is unclear whether this is simply a problem of Web data, or an intrinsic problem of supervised learning techniques, or just a problem of how WSD systems are evaluated (indeed, testing with rather small Senseval data may overemphasize sense distributions compared to sense distributions obtained from the full Web as corpus). In any case, Web data has an intrinsic bias, because queries to search engines directly constrain the context of the examples retrieved. There are approaches that alleviate this problem, such as using several different seeds/queries per sense or assigning senses to Web directories and then scanning directories for examples; but this problem is nevertheless far from being solved. Once a Web corpus of examples is built, it is not entirely clear whether its distribution is safe from a legal perspective. === Future === Besides automatic acquisition of examples from the Web, there are some other WSD experiments that have profited from the Web: The Web as a social network has been successfully used for cooperative annotation of a corpus (OMWE, Open Mind Word Expert project), which has already been used in three Senseval-3 tasks (English, Romanian and Multilingual). The Web has been used to enrich WordNet senses with domain information: topic signatures and Web directories, which have in turn been successfully used for WSD. Also, some research benefited from the semantic information that the Wikipedia maintains on its disambiguation pages. It is clear, however, that most research opportunities remain largely unexplored. For instance, little is known about how to use lexical information extracted from the Web in knowledge-based WSD systems; and it is also hard to find systems that use Web-mined parallel corpora for WSD, even though there are already efficient algorithms that use parallel corpora in WSD.

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  EXAPT

  EXAPT (a portmanteau of "Extended Subset of APT") is a production-oriented programming language that allows users to generate NC programs with control information for machining tools and facilitates decision-making for production-related issues that may arise during various machining processes. EXAPT was first developed to address industrial requirements. Through the years, the company created additional software for the manufacturing industry. Today, EXAPT offers a suite of SAAS products and services for the manufacturing industry. The trade name, EXAPT, is most commonly associated with the CAD/CAM-System, production data, and tool management software of the German company EXAPT Systemtechnik GmbH based in Aachen, DE. == General == EXAPT is a modularly built programming system for all NC machining operations as Drilling Turning Milling Turn-Milling Nibbling Flame-, laser-, plasma- and water jet cutting Wire eroding Operations with industrial robots Due to the modular structure, the main product groups, EXAPTcam and EXAPTpdo, are gradually expandable and permit individual software for the manufacturing industry used individually and also in a compound with an existing IT environment. == Functionality == EXAPTcam meets the requirements for NC planning, especially for the cutting operations such as turning, drilling, and milling up to 5-axis simultaneous machining. Thereby new process technologies, tool, and machine concepts are constantly involved. In the NC programming data from different sources such as 3D CAD models, drawings or tables can flow in. The possibilities of NC programming reaches from language-oriented to feature-oriented NC programming. The integrated EXAPT knowledge database and intelligent and scalable automatisms support the user. The EXAPT NC planning also covers the generation of production information as clamping and tool plans, presetting data or time calculations. The realistic simulation possibilities of NC planning and NC control data provide with production reliability. EXAPTpdo (EXAPT ProductionsDataOrganization) provides a neutrally applicable technology platform for the information compound of the NC planning - to the shop floor. This applies to all NC production data that are necessary for the set-up of NC machines, for the provision, presetting, and stocking of manufacturing resources and provided by EXAPTpdo in a central database. Besides classical functions of the tool management system (TMS) as the management of cutting tools, measuring, testing and clamping devices the technology data management and tool lifecycle management (TLM) is also included. System-supported "where-used lists" helps to handle the manufacturing resource cycle by secured requirement determination and requirement fulfillment. Unnecessary transports and unplanned dispositive adjustments are dropped, stocks are reduced, set-up times reduced and the throughput is increased. EXAPTpdo synchronizes involved systems within the value chain. Stock systems, MES systems or ERP systems (e.g. from the purchasing or production areas) do not work in isolation from each other but they interact with each other. EXAPTpdo provides the base to Smart Factory, for more flexibility in production and faster communication. == History == With the foundation of the EXAPT-Verein in 1967 as spin-off of the universities Aachen, Berlin and Stuttgart the further development "EXAPT (EXtended Subset of APT)" of the programming language "APT (Automatically Programmed Tool)" was focused and so the first milestone for the EXAPT history was set. In the same year the system EXAPT 1 for drilling and simple milling tasks became available. 1969 The industrial application of EXAPT 2 for the programming of NC machines with 2-axis linear and path control begins. In the following year, the development of the EXAPT modular system starts. 1972 BASIC-EXAPT is provided for the universal, homogeneous programming of all NC tasks. The support is made by the EXAPT applications consultancy. 1973 EXAPT 1.1 is provided for the programming of straight-cut and continuous-path controlled drilling and milling machines and machining centers. At the Hanover Fair (IHA 73) the interactive access to a mainframe via a time-sharing terminal for the part program entry and correction is presented and starts the replacement of the punch card. 1974 The possibilities for the use of process computers for the NC data transfer are leveled out. EXAPT offers the possibility of the result simulation when using plotters with display of tool paths and tools in assignment to the workpiece. In April 1975, the EXAPT NC Systemtechnik GmbH was founded with the aim, of enabling entry into the NC technique for small and medium-sized companies by a complete product and service program. In the following year, the system portfolio is extended with further system modules and service programs and the provision of postprocessors. 1978 The development activities on the EXAPT module system started in 1970 are completed. Using modern software techniques, the different system parts BASIC-EXAPT, EXAPT 1, EXAPT 1.1, and EXAPT 2 are composed of a total system. System support and applications consultancy become a new working focus. From the beginning to the middle of the 1980s Beside new portable software modules for CAD/CAM applications (e. g. CAPEX, NESTEX, CADEX, CADCPL), the first version of the EXAPT DNC system and extensions of the EXAPT NC programming system for the machining of sculptured surfaces are presented. 1988 EXAPT expands the software product range by systems for tool data management (BMO) and production data management (FDO). EXAPT trains more than 1,300 course participants including company-specific courses. 1992 The first version of the completely new product generation EXAPTplus is presented and the agency in Dresden is opened. 1993 The company name "EXAPT NC Systemtechnik GmbH" is changed to "EXAPT Systemtechnik GmbH." EXAPTplus is presented on PC under Windows NT at the EMO '93. The decentralization of the use of EXAPT systems expands the range of applications. In the following year, EXAPT-DNC is executable under Windows on a customary PC. Special hardware is not needed and so it can be used in compound with the database-supported EXAPT production data management system (FDO). 1995 EXAPTplus is also ready for complex application cases such as machining of tubes at extrusion tools. EXAPT-CADI provides the transfer of 2D CAD data to EXAPTplus. With the new office Gießen the marketing is strengthened. In the following year the EXAPT NC editor is developed for the direct processing of NC control data with tool path display and visualization of the tools. In the course of the market entry of more comfortable 3D CAD systems for the solid modelling of components a detailed evaluation of current systems is made in 1997. It is decided to use SolidWorks as a reference system for the solid-oriented NC planning with EXAPT. 1998 The first solution for the transfer of geometry data between SolidWorks and EXAPTplus is generated. The EXAPT organization systems are (beside SQL) also executable under Oracle now. The use of client server solutions supports the data flow in the production. 1999 AFR functions are provided in connection with EXAPTsolid to support a workpiece modelling for NC. The millennium capability is ensured for all EXAPT systems. AFR is a ground-breaking for the integration of third-party products. 2002 EXAPT-BMG is developed for the generation and visualization of tools with additional functions for the assembly from components. The acquisition of tools with their geometric and technological presentation offers extensive support of the NC planning with EXAPT systems. 2003 EXAPTpdo is available to optimize the process chains in production planning and production execution optimally regarding the increasing requirements of changing production conditions. 2004 Diverse system extensions are made in EXAPTplus, EXAPTsolid, EXAPT NC editor, EXAPTpdo for the complete machining on turning/milling centres with result reliability because of more extensive simulation based on realNC (Tecnomatix), for the use of new complex tool systems and the compound use between ERP systems as SAP and intelligent CNC systems. In the following year, EXAPTpdo is extended for the cross-order set-up optimization and provision of manufacturing re-sources especially for single and small series production with connection to purchase and physical portfolio management. 2006 The EXAPT systems are available for extended use as an information platform for production, the time management, and similar requirements. EXAPTsolid is extended for the feature-oriented milling operation and machine simulation. The NC programming of complex machine tools, e.g. three-turret-turning/milling centers is supported by EXAPT systems, as well as the use of multi-functional tools. 2007 A module for 3-5-axis simultaneous milling machining is presented.

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  Latent semantic mapping

  Latent semantic mapping (LSM) is a data-driven framework to model globally meaningful relationships implicit in large volumes of (often textual) data. It is a generalization of latent semantic analysis. In information retrieval, LSA enables retrieval on the basis of conceptual content, instead of merely matching words between queries and documents. LSM was derived from earlier work on latent semantic analysis. There are 3 main characteristics of latent semantic analysis: Discrete entities, usually in the form of words and documents, are mapped onto continuous vectors, the mapping involves a form of global correlation pattern, and dimensionality reduction is an important aspect of the analysis process. These constitute generic properties, and have been identified as potentially useful in a variety of different contexts. This usefulness has encouraged great interest in LSM. The intended product of latent semantic mapping, is a data-driven framework for modeling relationships in large volumes of data. Mac OS X v10.5 and later includes a framework implementing latent semantic mapping.

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  ROCm

  ROCm is an Advanced Micro Devices (AMD) software stack for graphics processing unit (GPU) programming. ROCm spans several domains, including general-purpose computing on graphics processing units (GPGPU), high performance computing (HPC), and heterogeneous computing. It offers several programming models: HIP (GPU-kernel-based programming), OpenMP (directive-based programming), and OpenCL. ROCm is free, libre and open-source software (except the GPU firmware blobs), and it is distributed under various licenses. The name initially stood for Radeon Open Compute platform; however, due to Open Compute being a registered trademark, the name no longer functions as an acronym. == Background == The first GPGPU software stack from ATI/AMD was Close to Metal, which became Stream. ROCm was launched around 2016 with the Boltzmann Initiative. ROCm stack builds upon previous AMD GPU stacks; some tools trace back to GPUOpen and others to the Heterogeneous System Architecture (HSA). === Heterogeneous System Architecture Intermediate Language === HSAIL was aimed at producing a middle-level, hardware-agnostic intermediate representation that could be JIT-compiled to the eventual hardware (GPU, FPGA...) using the appropriate finalizer. This approach was dropped for ROCm: now it builds only GPU code, using LLVM, and its AMDGPU backend that was upstreamed, although there is still research on such enhanced modularity with LLVM MLIR. == Programming abilities == ROCm as a stack ranges from the kernel driver to the end-user applications. AMD has introductory videos about AMD GCN hardware, and ROCm programming via its learning portal. One of the best technical introductions about the stack and ROCm/HIP programming, remains, to date, to be found on Reddit. == Hardware support == ROCm is primarily targeted at discrete professional GPUs, but consumer GPUs and APUs of the same architecture as a supported professional GPU are known to work with ROCm. For example, all professional GPUs of the RDNA 2 architecture are officially supported by ROCm 5.x; users report that Consumer RDNA2 units such as the Radeon 6800M APU and the Radeon 6700XT GPU also work. === Professional-grade GPUs === === Consumer-grade GPUs === == Software ecosystem == === Machine learning === Various deep learning frameworks have a ROCm backend: PyTorch TensorFlow ONNX MXNet CuPy MIOpen Caffe Iree (which uses LLVM Multi-Level Intermediate Representation (MLIR)) llama.cpp === Supercomputing === ROCm is gaining significant traction in the top 500. ROCm is used with the Exascale supercomputers El Capitan and Frontier. Some related software is to be found at AMD Infinity hub. === Other acceleration & graphics interoperation === As of version 3.0, Blender can now use HIP compute kernels for its renderer cycles. === Other languages === ==== Julia ==== Julia has the AMDGPU.jl package, which integrates with LLVM and selects components of the ROCm stack. Instead of compiling code through HIP, AMDGPU.jl uses Julia's compiler to generate LLVM IR directly, which is later consumed by LLVM to generate native device code. AMDGPU.jl uses ROCr's HSA implementation to upload native code onto the device and execute it, similar to how HIP loads its own generated device code. AMDGPU.jl also supports integration with ROCm's rocBLAS (for BLAS), rocRAND (for random number generation), and rocFFT (for FFTs). Future integration with rocALUTION, rocSOLVER, MIOpen, and certain other ROCm libraries is planned. === Software distribution === ==== Official ==== Installation instructions are provided for Linux and Windows in the official AMD ROCm documentation. ROCm software is currently spread across several public GitHub repositories. Within the main public meta-repository, there is an XML manifest for each official release: using git-repo, a version control tool built on top of Git, is the recommended way to synchronize with the stack locally. AMD starts distributing containerized applications for ROCm, notably scientific research applications gathered under AMD Infinity Hub. AMD distributes itself packages tailored to various Linux distributions. ==== Third-party ==== There is a growing third-party ecosystem packaging ROCm. Linux distributions are officially packaging (natively) ROCm, with various degrees of advancement: Arch Linux, Gentoo, Debian, Fedora , GNU Guix, and NixOS. There are Spack packages. == Components == There is one kernel-space component, ROCk, and the rest - there is roughly a hundred components in the stack - is made of user-space modules. The unofficial typographic policy is to use: uppercase ROC lowercase following for low-level libraries, i.e. ROCt, and the contrary for user-facing libraries, i.e. rocBLAS. AMD is active developing with the LLVM community, but upstreaming is not instantaneous, and as of January 2022, is still lagging. AMD still officially packages various LLVM forks for parts that are not yet upstreamed – compiler optimizations destined to remain proprietary, debug support, OpenMP offloading, etc. === Low-level === ==== ROCk – Kernel driver ==== ==== ROCm – Device libraries ==== Support libraries implemented as LLVM bitcode. These provide various utilities and functions for math operations, atomics, queries for launch parameters, on-device kernel launch, etc. ==== ROCt – Thunk ==== The thunk is responsible for all the thinking and queuing that goes into the stack. ==== ROCr – Runtime ==== The ROC runtime is a set of APIs/libraries that allows the launch of compute kernels by host applications. It is AMD's implementation of the HSA runtime API. It is different from the ROC Common Language Runtime. ==== ROCm – CompilerSupport ==== ROCm code object manager is in charge of interacting with LLVM intermediate representation. === Mid-level === ==== ROCclr Common Language Runtime ==== The common language runtime is an indirection layer adapting calls to ROCr on Linux and PAL on windows. It used to be able to route between different compilers, like the HSAIL-compiler. It is now being absorbed by the upper indirection layers (HIP and OpenCL). ==== OpenCL ==== ROCm ships its installable client driver (ICD) loader and an OpenCL implementation bundled together. As of January 2022, ROCm 4.5.2 ships OpenCL 2.2, and is lagging behind competition. ==== HIP – Heterogeneous Interface for Portability ==== The AMD implementation for its GPUs is called HIPAMD. There is also a CPU implementation mostly for demonstration purposes. ==== HIPCC ==== HIP builds a `HIPCC` compiler that either wraps Clang and compiles with LLVM open AMDGPU backend, or redirects to the NVIDIA compiler. ==== HIPIFY ==== HIPIFY is a source-to-source compiling tool. It translates CUDA to HIP and reverse, either using a Clang-based tool, or a sed-like Perl script. ==== GPUFORT ==== Like HIPIFY, GPUFORT is a tool compiling source code into other third-generation-language sources, allowing users to migrate from CUDA Fortran to HIP Fortran. It is also in the repertoire of research projects, even more so. === High-level === ROCm high-level libraries are usually consumed directly by application software, such as machine learning frameworks. Most of the following libraries are in the General Matrix Multiply (GEMM) category, which GPU architecture excels at. The majority of these user-facing libraries comes in dual-form: hip for the indirection layer that can route to Nvidia hardware, and roc for the AMD implementation. ==== rocBLAS / hipBLAS ==== rocBLAS and hipBLAS are central in high-level libraries, it is the AMD implementation for Basic Linear Algebra Subprograms. It uses the library Tensile privately. ==== rocSOLVER / hipSOLVER ==== This pair of libraries constitutes the LAPACK implementation for ROCm and is strongly coupled to rocBLAS. === Utilities === ROCm developer tools: Debug, tracer, profiler, System Management Interface, Validation suite, Cluster management. GPUOpen tools: GPU analyzer, memory visualizer... External tools: radeontop (TUI overview) == Comparison with competitors == ROCm competes with other GPU computing stacks: Nvidia CUDA and Intel OneAPI. === Nvidia CUDA === Nvidia's CUDA is closed-source, whereas AMD ROCm is open source. There is open-source software built on top of the closed-source CUDA, for instance RAPIDS. CUDA is able to run on consumer GPUs, whereas ROCm support is mostly offered for professional hardware such as AMD Instinct and AMD Radeon Pro. Nvidia provides a C/C++-centered frontend and its Parallel Thread Execution (PTX) LLVM GPU backend as the Nvidia CUDA Compiler (NVCC). === Intel OneAPI === All the oneAPI corresponding libraries are published on its GitHub Page. ==== Unified Acceleration Foundation (UXL) ==== Unified Acceleration Foundation (UXL) is a new technology consortium that are working on the continuation of the OneAPI initiative, with the goal to create a new open standard accelerator software ecosystem, related open standards and specification projects through Working Groups and Specia

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  Document mosaicing

  Document mosaicing is a process that stitches multiple, overlapping snapshot images of a document together to produce one large, high resolution composite. The document is slid under a stationary, over-the-desk camera by hand until all parts of the document are snapshotted by the camera's field of view. As the document slid under the camera, all motion of the document is coarsely tracked by the vision system. The document is periodically snapshotted such that the successive snapshots are overlap by about 50%. The system then finds the overlapped pairs and stitches them together repeatedly until all pairs are stitched together as one piece of document. The document mosaicing can be divided into four main processes. Tracking Feature detecting Correspondences establishing Images mosaicing. == Tracking (simple correlation process) == In this process, the motion of the document slid under the camera is coarsely tracked by the system. Tracking is performed by a process called simple correlation process. In the first frame of snapshots, a small patch is extracted from the center of the image as a correlation template. The correlation process is performed in the four times size of the patch area of the next frame. The motion of the paper is indicated by the peak in the correlation function. The peak in the correlation function indicates the motion of the paper. The template is resampled from this frame and the tracking continues until the template reaches the edge of the document. After the template reaches the edge of the document, another snapshot is taken and the tracking process performs repeatedly until the whole document is imaged. The snapshots are stored in an ordered list to facilitate pairing the overlapped images in later processes. == Feature detecting for efficient matching == Feature detection is the process of finding the transformation that aligns one image with another. There are two main approaches for feature detection. Feature-based approach : Motion parameters are estimated from point correspondences. This approach is suitable for the case that there is plenty supply of stable and detectable features. Featureless approach : When the motion between the two images is small, the motion parameters are estimated using optical flow. On the other hand, when the motion between the two images is large, the motion parameters are estimated using generalised cross-correlation. However, this approach requires a computationally expensive resources. Each image is segmented into a hierarchy of columns, lines, and words to match the organised sets of features across images. Skew angle estimation and columns, lines and words finding are the examples of feature detection operations. === Skew angle estimation === Firstly, the angle that the rows of text make with the image raster lines (skew angle) is estimated. It is assumed to lie in the range of ±20°. A small patch of text in the image is selected randomly and then rotated in the range of ±20° until the variance of the pixel intensities of the patch summed along the raster lines is maximised. To ensure that the found skew angle is accurate, the document mosaic system performs calculation at many image patches and derive the final estimation by finding the average of the individual angles weighted by the variance of the pixel intensities of each patch. === Columns, lines and words finding === In this operation, the de-skewed document is intuitively segmented into a hierarchy of columns, lines and words. The sensitivity to illumination and page coloration of the de-skewed document can be removed by applying a Sobel operator to the de-skewed image and thresholding the output to obtain the binary gradient, de-skewed image. The operation can be roughly separated into 3 steps: column segmentation, line segmentation and word segmentation. Columns are easily segmented from the binary gradient, de-skewed images by summing pixels vertically. Baselines of each row are segmented in the same way as the column segmentation process but horizontally. Finally, individual words are segmented by applying the vertical process at each segmented row. These segmentations are important because the document mosaic is created by matching the lower right corners of words in overlapping images pair. Moreover, the segmentation operation can organize the list of images in the context of a hierarchy of rows and column reliably. The segmentation operation involves a considerable amount of summing in the binary gradient, de-skewed images, which done by construct a matrix of partial sums whose elements are given by p i y = ∑ u = 1 i ∑ v = 1 j b u v {\displaystyle p_{iy}=\sum _{u=1}^{i}\sum _{v=1}^{j}b_{uv}} The matrix of partial sums is calculated in one pass through the binary gradient, de-skewed image. ∑ u = u 1 u 2 ∑ v = v 1 v 2 b u v = p u 2 v 2 + p u 1 v 1 − p u 1 v 2 − p u 2 v 1 {\displaystyle \sum _{u=u_{1}}^{u_{2}}\sum _{v=v_{1}}^{v_{2}}b_{uv}=p_{u_{2}v_{2}}+p_{u_{1}v_{1}}-p_{u_{1}v_{2}}-p_{u_{2}v_{1}}} == Correspondences establishing == The two images are now organized in hierarchy of linked lists in following structure : image=list of columns row=list of words column=list of row word=length (in pixels) At the bottom of the structure, the length of each word is recorded for establishing correspondence between two images to reduce to search only the corresponding structures for the groups of words with the matching lengths. === Seed match finding === A seed match finding is done by comparing each row in image1 with each row in image2. The two rows are then compared to each other by every word. If the length (in pixel) of the two words (one from image1 and one from image2) and their immediate neighbours agree with each other within a predefined tolerance threshold (5 pixels, for example), then they are assumed to match. The row of each image is assumed a match if there are three or more word matches between the two rows. The seed match finding operation is terminated when two pairs of consecutive row match are found. === Match list building === After finishing a seed match finding operation, the next process is to build the match list to generate the correspondences points of the two images. The process is done by searching the matching pairs of rows away from the seed row. == Images mosaicing == Given the list of corresponding points of the two images, finding the transformation of the overlapping portion of the images is the next process. Assuming a pinhole camera model, the transformation between pixels (u,v) of image 1 and pixels (u0, v0) of image 2 is demonstrated by a plane-to-plane projectivity. [ s u ′ s v ′ s ] = [ p 11 p 12 p 13 p 21 p 22 p 23 p 31 p 32 1 ] [ u v 1 ] E q .1 {\displaystyle \left[{\begin{array}{c}su'\\sv'\\s\end{array}}\right]=\left[{\begin{array}{ccc}p_{11}&p_{12}&p_{13}\\p_{21}&p_{22}&p_{23}\\p_{31}&p_{32}&1\end{array}}\right]\left[{\begin{array}{c}u\\v\\1\end{array}}\right]\qquad Eq.1} The parameters of the projectivity is found from four pairs of matching points. RANSAC regression technique is used to reject outlying matches and estimate the projectivity from the remaining good matches. The projectivity is fine-tuned using correlation at the corners of the overlapping portion to obtain four correspondences to sub-pixel accuracy. Therefore, image1 is then transformed into image2's coordinate system using Eq.1. The typical result of the process is shown in Figure 5. === Many images coping === Finally, the whole page composition is built up by mapping all the images into the coordinate system of an "anchor" image, which is normally the one nearest the page center. The transformations to the anchor frame are calculated by concatenating the pair-wise transformations found earlier. The raw document mosaic is shown in Figure 6. However, there might be a problem of non-consecutive images that are overlap. This problem can be solved by performing Hierarchical sub-mosaics. As shown in Figure 7, image1 and image2 are registered, as are image3 and image4, creating two sub-mosaics. These two sub-mosaics are later stitched together in another mosaicing process. == Applied areas == There are various areas that the technique of document mosaicing can be applied to such as : Text segmentation of images of documents Document Recognition Interaction with paper on the digital desk Video mosaics for virtual environments Image registration techniques == Relevant research papers == Huang, T.S.; Netravali, A.N. (1994). "Motion and structure from feature correspondences: A review". Proceedings of the IEEE. 82 (2): 252–268. doi:10.1109/5.265351. D.G. Lowe. [1] Perceptual Organization and Visual Recognition. Kluwer Academic Publishers, Boston, 1985. Irani, M.; Peleg, S. (1991). "Improving resolution by image registration". CVGIP: Graphical Models and Image Processing. 53 (3): 231–239. doi:10.1016/1049-9652(91)90045-L. S2CID 4834546. Shivakumara, P.; Kumar, G. Hemantha; Guru, D. S.; Nagabhushan, P. (2006). "

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  Image analysis

  Image analysis or imagery analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques. Image analysis tasks can be as simple as reading bar coded tags or as sophisticated as identifying a person from their face. Computers are indispensable for the analysis of large amounts of data, for tasks that require complex computation, or for the extraction of quantitative information. On the other hand, the human visual cortex is an excellent image analysis apparatus, especially for extracting higher-level information, and for many applications — including medicine, security, and remote sensing — human analysts still cannot be replaced by computers. For this reason, many important image analysis tools such as edge detectors and neural networks are inspired by human visual perception models. == Digital == Digital Image Analysis or Computer Image Analysis is when a computer or electrical device automatically studies an image to obtain useful information from it. Note that the device is often a computer but may also be an electrical circuit, a digital camera or a mobile phone. It involves the fields of computer or machine vision, and medical imaging, and makes heavy use of pattern recognition, digital geometry, and signal processing. This field of computer science developed in the 1950s at academic institutions such as the MIT A.I. Lab, originally as a branch of artificial intelligence and robotics. It is the quantitative or qualitative characterization of two-dimensional (2D) or three-dimensional (3D) digital images. 2D images are, for example, to be analyzed in computer vision, and 3D images in medical imaging. The field was established in the 1950s—1970s, for example with pioneering contributions by Azriel Rosenfeld, Herbert Freeman, Jack E. Bresenham, or King-Sun Fu. == Techniques == There are many different techniques used in automatically analysing images. Each technique may be useful for a small range of tasks, however there still aren't any known methods of image analysis that are generic enough for wide ranges of tasks, compared to the abilities of a human's image analysing capabilities. Examples of image analysis techniques in different fields include: 2D and 3D object recognition, image segmentation, motion detection e.g. Single particle tracking, video tracking, optical flow, medical scan analysis, 3D Pose Estimation. == Deep learning == Since the early 2010s, deep learning methods have substantially advanced the field of image analysis. In 2012, a deep convolutional neural network (CNN) known as AlexNet achieved a significant reduction in error rates on the ImageNet large-scale image classification benchmark, demonstrating the effectiveness of deep learning for visual recognition tasks. Subsequent architectures such as ResNet introduced residual connections that enabled training of much deeper networks, further improving accuracy across image analysis tasks. Real-time object detection became practical with frameworks such as YOLO (You Only Look Once), which unified detection and classification into a single network pass. In 2020, the Vision Transformer (ViT) demonstrated that transformer architectures, originally developed for natural language processing, could achieve competitive results on image classification when applied directly to sequences of image patches. More recently, foundation models trained on large-scale datasets have enabled zero-shot generalisation across image analysis tasks. The Segment Anything Model (SAM), trained on over one billion masks, can segment arbitrary objects in images without task-specific fine-tuning. These advances have made image analysis techniques increasingly accessible through browser-based tools and open-source implementations. == Applications == The applications of digital image analysis are continuously expanding through all areas of science and industry, including: anatomy, allows for precise measurements, visualization, and statistical analysis of anatomical structures. assay micro plate reading, such as detecting where a chemical was manufactured. astronomy, such as calculating the size of a planet. automated species identification (e.g. plant and animal species) defense error level analysis filtering machine vision, such as to automatically count items in a factory conveyor belt. materials science, such as determining if a metal weld has cracks. medicine, such as detecting cancer in a mammography scan. metallography, such as determining the mineral content of a rock sample. microscopy, such as counting the germs in a swab. automatic number plate recognition; optical character recognition, such as automatic license plate detection. remote sensing, such as detecting intruders in a house, and producing land cover/land use maps. robotics, such as to avoid steering into an obstacle. security, such as detecting a person's eye color or hair color. == Object-based == Object-based image analysis (OBIA) involves two typical processes, segmentation and classification. Segmentation helps to group pixels into homogeneous objects. The objects typically correspond to individual features of interest, although over-segmentation or under-segmentation is very likely. Classification then can be performed at object levels, using various statistics of the objects as features in the classifier. Statistics can include geometry, context and texture of image objects. Over-segmentation is often preferred over under-segmentation when classifying high-resolution images. Object-based image analysis has been applied in many fields, such as cell biology, medicine, earth sciences, and remote sensing. For example, it can detect changes of cellular shapes in the process of cell differentiation.; it has also been widely used in the mapping community to generate land cover. When applied to earth images, OBIA is known as geographic object-based image analysis (GEOBIA), defined as "a sub-discipline of geoinformation science devoted to (...) partitioning remote sensing (RS) imagery into meaningful image-objects, and assessing their characteristics through spatial, spectral and temporal scale". The international GEOBIA conference has been held biannually since 2006. OBIA techniques are implemented in software such as eCognition or the Orfeo toolbox.

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  Stixel

  In computer vision, a stixel (portmanteau of "stick" and "pixel") is a superpixel representation of depth information in an image, in the form of a vertical stick that approximates the closest obstacles within a certain vertical slice of the scene. Introduced in 2009, stixels have applications in robotic navigation and advanced driver-assistance systems, where they can be used to define a representation of robotic environments and traffic scenes with a medium level of abstraction. == Definition == One of the problems of scene understanding in computer vision is to determine horizontal freespace around the camera, where the agent can move, and the vertical obstacles delimiting it. An image can be paired with depth information (produced e.g. from stereo disparity, lidar, or monocular depth estimation), allowing a dense tridimensional reconstruction of the observed scene. One drawback of dense reconstruction is the large amount of data involved, since each pixel in the image is mapped to an element of a point cloud. Vision problems characterised by planar freespace delimited by mostly vertical obstacles, such as traffic scenes or robotic navigation, can benefit from a condensed representation that allows to save memory and processing time. Stixels are thin vertical rectangles representing a slice of a vertical surface belonging to the closest obstacle in the observed scene. They allow to dramatically reduce the amount of information needed to represent a scene in such problems. A stixel is characterised by three parameters: vertical coordinate of the bottom, height of the stick, and depth. Stixels have fixed width, with each stixel spanning over a certain number of image columns, allowing downsampling of the horizontal image resolution. In the original formulation, each column of the image would contain at most one stixel, and later extensions were developed to allow multiple stixels on each column, allowing to represent multiple objects at different distances. == Stixel estimation == The input to stixel estimation is a dense depth map, that can be computed from stereo disparity or other means. The original approach computes an occupancy grid that can be segmented to estimate the freespace, with dynamic programming providing an efficient method to find an optimal segmentation. Alternative approaches can be used instead of occupancy grid mapping, such as manifold-based methods. The freespace boundary provides the base points of the obstacles at closest longitudinal distance, however multiple objects at different distances might appear in each column of the image. To fully define the obstacles, their height should be estimated, and this is accomplished by segmenting the depth of the object from the depth of the background. A membership function over the pixels can be defined based on the depth value, where the membership represents the confidence of a pixel belonging to the closest vertical obstacle or to the background, and a cut separating the obstacles from the background can again be computed effectively with dynamic programming. Once both the freespace and the obstacle height are known, the stixels can be estimated by fusing the information over the columns spanned by each stixel, and finally a refined depth of the stixel can be estimated via model fitting over the depth of the pixels covered by the stixel, possibly paired with confidence information (e.g. disparity confidence produced by methods such as semi-global matching).

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  Learnable function class

  In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg ⁡ min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg ⁡ min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg ⁡ min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.

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  Image moment

  In image processing, computer vision and related fields, an image moment is a certain particular weighted average (moment) of the image pixels' intensities, or a function of such moments, usually chosen to have some attractive property or interpretation. Image moments are useful to describe objects after segmentation. Simple properties of the image which are found via image moments include area (or total intensity), its centroid, and information about its orientation. == Raw moments == For a 2D continuous function f(x,y) the moment (sometimes called "raw moment") of order (p + q) is defined as M p q = ∫ − ∞ ∞ ∫ − ∞ ∞ x p y q f ( x , y ) d x d y {\displaystyle M_{pq}=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }x^{p}y^{q}f(x,y)\,dx\,dy} for p,q = 0,1,2,... Adapting this to scalar (grayscale) image with pixel intensities I(x,y), raw image moments Mij are calculated by M i j = ∑ x ∑ y x i y j I ( x , y ) {\displaystyle M_{ij}=\sum _{x}\sum _{y}x^{i}y^{j}I(x,y)\,\!} In some cases, this may be calculated by considering the image as a probability density function, i.e., by dividing the above by ∑ x ∑ y I ( x , y ) {\displaystyle \sum _{x}\sum _{y}I(x,y)\,\!} A uniqueness theorem states that if f(x,y) is piecewise continuous and has nonzero values only in a finite part of the xy plane, moments of all orders exist, and the moment sequence (Mpq) is uniquely determined by f(x,y). Conversely, (Mpq) uniquely determines f(x,y). In practice, the image is summarized with functions of a few lower order moments. === Examples === Simple image properties derived via raw moments include: Area (for binary images) or sum of grey level (for greytone images): M 00 {\displaystyle M_{00}} Centroid: { x ¯ , y ¯ } = { M 10 M 00 , M 01 M 00 } {\displaystyle \{{\bar {x}},\ {\bar {y}}\}=\left\{{\frac {M_{10}}{M_{00}}},{\frac {M_{01}}{M_{00}}}\right\}} == Central moments == Central moments are defined as μ p q = ∫ − ∞ ∞ ∫ − ∞ ∞ ( x − x ¯ ) p ( y − y ¯ ) q f ( x , y ) d x d y {\displaystyle \mu _{pq}=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }(x-{\bar {x}})^{p}(y-{\bar {y}})^{q}f(x,y)\,dx\,dy} where x ¯ = M 10 M 00 {\displaystyle {\bar {x}}={\frac {M_{10}}{M_{00}}}} and y ¯ = M 01 M 00 {\displaystyle {\bar {y}}={\frac {M_{01}}{M_{00}}}} are the components of the centroid. If ƒ(x, y) is a digital image, then the previous equation becomes μ p q = ∑ x ∑ y ( x − x ¯ ) p ( y − y ¯ ) q f ( x , y ) {\displaystyle \mu _{pq}=\sum _{x}\sum _{y}(x-{\bar {x}})^{p}(y-{\bar {y}})^{q}f(x,y)} The central moments of order up to 3 are: μ 00 = M 00 , μ 01 = 0 , μ 10 = 0 , μ 11 = M 11 − x ¯ M 01 = M 11 − y ¯ M 10 , μ 20 = M 20 − x ¯ M 10 , μ 02 = M 02 − y ¯ M 01 , μ 21 = M 21 − 2 x ¯ M 11 − y ¯ M 20 + 2 x ¯ 2 M 01 , μ 12 = M 12 − 2 y ¯ M 11 − x ¯ M 02 + 2 y ¯ 2 M 10 , μ 30 = M 30 − 3 x ¯ M 20 + 2 x ¯ 2 M 10 , μ 03 = M 03 − 3 y ¯ M 02 + 2 y ¯ 2 M 01 . {\displaystyle {\begin{aligned}\mu _{00}&=M_{00},&\mu _{01}&=0,\\\mu _{10}&=0,&\mu _{11}&=M_{11}-{\bar {x}}M_{01}=M_{11}-{\bar {y}}M_{10},\\\mu _{20}&=M_{20}-{\bar {x}}M_{10},&\mu _{02}&=M_{02}-{\bar {y}}M_{01},\\\mu _{21}&=M_{21}-2{\bar {x}}M_{11}-{\bar {y}}M_{20}+2{\bar {x}}^{2}M_{01},&\mu _{12}&=M_{12}-2{\bar {y}}M_{11}-{\bar {x}}M_{02}+2{\bar {y}}^{2}M_{10},\\\mu _{30}&=M_{30}-3{\bar {x}}M_{20}+2{\bar {x}}^{2}M_{10},&\mu _{03}&=M_{03}-3{\bar {y}}M_{02}+2{\bar {y}}^{2}M_{01}.\end{aligned}}} It can be shown that: μ p q = ∑ m p ∑ n q ( p m ) ( q n ) ( − x ¯ ) ( p − m ) ( − y ¯ ) ( q − n ) M m n {\displaystyle \mu _{pq}=\sum _{m}^{p}\sum _{n}^{q}{p \choose m}{q \choose n}(-{\bar {x}})^{(p-m)}(-{\bar {y}})^{(q-n)}M_{mn}} Central moments are translational invariant. === Examples === Information about image orientation can be derived by first using the second order central moments to construct a covariance matrix. μ 20 ′ = μ 20 / μ 00 = M 20 / M 00 − x ¯ 2 μ 02 ′ = μ 02 / μ 00 = M 02 / M 00 − y ¯ 2 μ 11 ′ = μ 11 / μ 00 = M 11 / M 00 − x ¯ y ¯ {\displaystyle {\begin{aligned}\mu '_{20}&=\mu _{20}/\mu _{00}=M_{20}/M_{00}-{\bar {x}}^{2}\\\mu '_{02}&=\mu _{02}/\mu _{00}=M_{02}/M_{00}-{\bar {y}}^{2}\\\mu '_{11}&=\mu _{11}/\mu _{00}=M_{11}/M_{00}-{\bar {x}}{\bar {y}}\end{aligned}}} The covariance matrix of the image I ( x , y ) {\displaystyle I(x,y)} is now cov ⁡ [ I ( x , y ) ] = [ μ 20 ′ μ 11 ′ μ 11 ′ μ 02 ′ ] . {\displaystyle \operatorname {cov} [I(x,y)]={\begin{bmatrix}\mu '_{20}&\mu '_{11}\\\mu '_{11}&\mu '_{02}\end{bmatrix}}.} The eigenvectors of this matrix correspond to the major and minor axes of the image intensity, so the orientation can thus be extracted from the angle of the eigenvector associated with the largest eigenvalue towards the axis closest to this eigenvector. It can be shown that this angle Θ is given by the following formula: Θ = 1 2 arctan ⁡ ( 2 μ 11 ′ μ 20 ′ − μ 02 ′ ) {\displaystyle \Theta ={\frac {1}{2}}\arctan \left({\frac {2\mu '_{11}}{\mu '_{20}-\mu '_{02}}}\right)} The above formula holds as long as: μ 20 ′ − μ 02 ′ ≠ 0 {\displaystyle \mu '_{20}-\mu '_{02}\neq 0} The eigenvalues of the covariance matrix can easily be shown to be λ i = μ 20 ′ + μ 02 ′ 2 ± 4 μ ′ 11 2 + ( μ ′ 20 − μ ′ 02 ) 2 2 , {\displaystyle \lambda _{i}={\frac {\mu '_{20}+\mu '_{02}}{2}}\pm {\frac {\sqrt {4{\mu '}_{11}^{2}+({\mu '}_{20}-{\mu '}_{02})^{2}}}{2}},} and are proportional to the squared length of the eigenvector axes. The relative difference in magnitude of the eigenvalues are thus an indication of the eccentricity of the image, or how elongated it is. The eccentricity is 1 − λ 2 λ 1 . {\displaystyle {\sqrt {1-{\frac {\lambda _{2}}{\lambda _{1}}}}}.} == Moment invariants == Moments are well-known for their application in image analysis, since they can be used to derive invariants with respect to specific transformation classes. The term invariant moments is often abused in this context. However, while moment invariants are invariants that are formed from moments, the only moments that are invariants themselves are the central moments. Note that the invariants detailed below are exactly invariant only in the continuous domain. In a discrete domain, neither scaling nor rotation are well defined: a discrete image transformed in such a way is generally an approximation, and the transformation is not reversible. These invariants therefore are only approximately invariant when describing a shape in a discrete image. === Translation invariants === The central moments μi j of any order are, by construction, invariant with respect to translations. === Scale invariants === Invariants ηi j with respect to both translation and scale can be constructed from central moments by dividing through a properly scaled zero-th central moment: η i j = μ i j μ 00 ( 1 + i + j 2 ) {\displaystyle \eta _{ij}={\frac {\mu _{ij}}{\mu _{00}^{\left(1+{\frac {i+j}{2}}\right)}}}\,\!} where i + j ≥ 2. Note that translational invariance directly follows by only using central moments. === Rotation invariants === As shown in the work of Hu, invariants with respect to translation, scale, and rotation can be constructed: I 1 = η 20 + η 02 {\displaystyle I_{1}=\eta _{20}+\eta _{02}} I 2 = ( η 20 − η 02 ) 2 + 4 η 11 2 {\displaystyle I_{2}=(\eta _{20}-\eta _{02})^{2}+4\eta _{11}^{2}} I 3 = ( η 30 − 3 η 12 ) 2 + ( 3 η 21 − η 03 ) 2 {\displaystyle I_{3}=(\eta _{30}-3\eta _{12})^{2}+(3\eta _{21}-\eta _{03})^{2}} I 4 = ( η 30 + η 12 ) 2 + ( η 21 + η 03 ) 2 {\displaystyle I_{4}=(\eta _{30}+\eta _{12})^{2}+(\eta _{21}+\eta _{03})^{2}} I 5 = ( η 30 − 3 η 12 ) ( η 30 + η 12 ) [ ( η 30 + η 12 ) 2 − 3 ( η 21 + η 03 ) 2 ] + ( 3 η 21 − η 03 ) ( η 21 + η 03 ) [ 3 ( η 30 + η 12 ) 2 − ( η 21 + η 03 ) 2 ] {\displaystyle I_{5}=(\eta _{30}-3\eta _{12})(\eta _{30}+\eta _{12})[(\eta _{30}+\eta _{12})^{2}-3(\eta _{21}+\eta _{03})^{2}]+(3\eta _{21}-\eta _{03})(\eta _{21}+\eta _{03})[3(\eta _{30}+\eta _{12})^{2}-(\eta _{21}+\eta _{03})^{2}]} I 6 = ( η 20 − η 02 ) [ ( η 30 + η 12 ) 2 − ( η 21 + η 03 ) 2 ] + 4 η 11 ( η 30 + η 12 ) ( η 21 + η 03 ) {\displaystyle I_{6}=(\eta _{20}-\eta _{02})[(\eta _{30}+\eta _{12})^{2}-(\eta _{21}+\eta _{03})^{2}]+4\eta _{11}(\eta _{30}+\eta _{12})(\eta _{21}+\eta _{03})} I 7 = ( 3 η 21 − η 03 ) ( η 30 + η 12 ) [ ( η 30 + η 12 ) 2 − 3 ( η 21 + η 03 ) 2 ] − ( η 30 − 3 η 12 ) ( η 21 + η 03 ) [ 3 ( η 30 + η 12 ) 2 − ( η 21 + η 03 ) 2 ] . {\displaystyle I_{7}=(3\eta _{21}-\eta _{03})(\eta _{30}+\eta _{12})[(\eta _{30}+\eta _{12})^{2}-3(\eta _{21}+\eta _{03})^{2}]-(\eta _{30}-3\eta _{12})(\eta _{21}+\eta _{03})[3(\eta _{30}+\eta _{12})^{2}-(\eta _{21}+\eta _{03})^{2}].} These are well-known as Hu moment invariants. The first one, I1, is analogous to the moment of inertia around the image's centroid, where the pixels' intensities are analogous to physical density. The first six, I1 ... I6, are reflection symmetric, i.e. they are unchanged if the image is changed to a mirror image. The last one, I7, is reflection antisymmetric (changes sign under reflection), which enables it to distinguish mirror images of otherwise identical im

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  Connected-component labeling

  Connected-component labeling (CCL), connected-component analysis (CCA), blob extraction, region labeling, blob discovery, or region extraction is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component labeling is not to be confused with segmentation. Connected-component labeling is used in computer vision to detect connected regions in binary digital images, although color images and data with higher dimensionality can also be processed. When integrated into an image recognition system or human-computer interaction interface, connected component labeling can operate on a variety of information. Blob extraction is generally performed on the resulting binary image from a thresholding step, but it can be applicable to gray-scale and color images as well. Blobs may be counted, filtered, and tracked. Blob extraction is related to but distinct from blob detection. == Overview == A graph, containing vertices and connecting edges, is constructed from relevant input data. The vertices contain information required by the comparison heuristic, while the edges indicate connected 'neighbors'. An algorithm traverses the graph, labeling the vertices based on the connectivity and relative values of their neighbors. Connectivity is determined by the medium; image graphs, for example, can be 4-connected neighborhood or 8-connected neighborhood. Following the labeling stage, the graph may be partitioned into subsets, after which the original information can be recovered and processed . == Definition == The usage of the term connected-component labeling (CCL) and its definition is quite consistent in the academic literature, whereas connected-component analysis (CCA) varies both in terminology and in its definition of the problem. Rosenfeld et al. define connected components labeling as the “[c]reation of a labeled image in which the positions associated with the same connected component of the binary input image have a unique label.” Shapiro et al. define CCL as an operator whose “input is a binary image and [...] output is a symbolic image in which the label assigned to each pixel is an integer uniquely identifying the connected component to which that pixel belongs.” There is no consensus on the definition of CCA in the academic literature. It is often used interchangeably with CCL. A more extensive definition is given by Shapiro et al.: “Connected component analysis consists of connected component labeling of the black pixels followed by property measurement of the component regions and decision making.” The definition for connected-component analysis presented here is more general, taking the thoughts expressed in into account. == Algorithms == The algorithms discussed can be generalised to arbitrary dimensions, albeit with increased time and space complexity. === One component at a time === This is a fast and very simple method to implement and understand. It is based on graph traversal methods in graph theory. In short, once the first pixel of a connected component is found, all the connected pixels of that connected component are labelled before going onto the next pixel in the image. This algorithm is part of Vincent and Soille's watershed segmentation algorithm, other implementations also exist. In order to do that a linked list is formed that will keep the indexes of the pixels that are connected to each other, steps (2) and (3) below. The method of defining the linked list specifies the use of a depth or a breadth first search. For this particular application, there is no difference which strategy to use. The simplest kind of a last in first out queue implemented as a singly linked list will result in a depth first search strategy. It is assumed that the input image is a binary image, with pixels being either background or foreground and that the connected components in the foreground pixels are desired. The algorithm steps can be written as: Start from the first pixel in the image. Set current label to 1. Go to (2). If this pixel is a foreground pixel and it is not already labelled, give it the current label and add it as the first element in a queue, then go to (3). If it is a background pixel or it was already labelled, then repeat (2) for the next pixel in the image. Pop out an element from the queue, and look at its neighbours (based on any type of connectivity). If a neighbour is a foreground pixel and is not already labelled, give it the current label and add it to the queue. Repeat (3) until there are no more elements in the queue. Go to (2) for the next pixel in the image and increment current label by 1. Note that the pixels are labelled before being put into the queue. The queue will only keep a pixel to check its neighbours and add them to the queue if necessary. This algorithm only needs to check the neighbours of each foreground pixel once and doesn't check the neighbours of background pixels. The pseudocode is: algorithm OneComponentAtATime(data) input : imageData[xDim][yDim] initialization : label = 0, labelArray[xDim][yDim] = 0, statusArray[xDim][yDim] = false, queue1, queue2; for i = 0 to xDim do for j = 0 to yDim do if imageData[i][j] has not been processed do if imageData[i][j] is a foreground pixel do check its four neighbors(north, south, east, west) : if neighbor is not processed do if neighbor is a foreground pixel do add it to queue1 else update its status to processed end if labelArray[i][j] = label (give label) statusArray[i][j] = true (update status) while queue1 is not empty do For each pixel in the queue do : check its four neighbors if neighbor is not processed do if neighbor is a foreground pixel do add it to queue2 else update its status to processed end if give it the current label update its status to processed remove the current element from queue1 copy queue2 into queue1 end While increase the label end if else update its status to processed end if end if end if end for end for === Two-pass === Relatively simple to implement and understand, the two-pass algorithm, (also known as the Hoshen–Kopelman algorithm) iterates through 2-dimensional binary data. The algorithm makes two passes over the image: the first pass to assign temporary labels and record equivalences, and the second pass to replace each temporary label by the smallest label of its equivalence class. The input data can be modified in situ (which carries the risk of data corruption), or labeling information can be maintained in an additional data structure. Connectivity checks are carried out by checking neighbor pixels' labels (neighbor elements whose labels are not assigned yet are ignored), or say, the north-east, the north, the north-west and the west of the current pixel (assuming 8-connectivity). 4-connectivity uses only north and west neighbors of the current pixel. The following conditions are checked to determine the value of the label to be assigned to the current pixel (4-connectivity is assumed) Conditions to check: Does the pixel to the left (west) have the same value as the current pixel? Yes – We are in the same region. Assign the same label to the current pixel No – Check next condition Do both pixels to the north and west of the current pixel have the same value as the current pixel but not the same label? Yes – We know that the north and west pixels belong to the same region and must be merged. Assign the current pixel the minimum of the north and west labels, and record their equivalence relationship No – Check next condition Does the pixel to the left (west) have a different value and the one to the north the same value as the current pixel? Yes – Assign the label of the north pixel to the current pixel No – Check next condition Do the pixel's north and west neighbors have different pixel values than current pixel? Yes – Create a new label id and assign it to the current pixel The algorithm continues this way, and creates new region labels whenever necessary. The key to a fast algorithm, however, is how this merging is done. This algorithm uses the union-find data structure which provides excellent performance for keeping track of equivalence relationships. Union-find essentially stores labels which correspond to the same blob in a disjoint-set data structure, making it easy to remember the equivalence of two labels by the use of an interface method E.g.: findSet(l). findSet(l) returns the minimum label value that is equivalent to the function argument 'l'. Once the initial labeling and equivalence recording is completed, the second pass merely replaces each pixel label with its equivalent disjoint-set representative element. A faster-scanning algorithm for connected-region extraction is presented below. On the first pass: Iterate through each element of the data by column, then by row (Raster Scanning) If the element is not the background Get the neighboring elements of the current element If there are no neighbors, uniquely

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