Human rights and encryption refers to the ways in which digital encryption affects human rights. Encryption can be used as both a detriment and a boon to human rights; for example, encryption can be used to enforce digital rights management for video games. This kind of video game licensing can render software unusable long term and represents the erosion of consumer rights. At the same time, encryption is fundamental part of internet security. Asymmetrical encryption is used extensively online for authentication, providing users confidence their internet traffic is not being misdirected. Encryption is also used to obfuscate information as it travels from end-to-end over the internet, preventing eavesdropping and tampering. Encryption can also provide anonymity, which is an important consideration for freedom of expression. Despite its drawbacks, encryption is essential for a free, open, and trustworthy internet. == Background == === Human rights === Human rights are moral principles or norms for human behaviour that are regularly protected as legal rights in national and international law. They are commonly understood as inalienable, fundamental rights "to which a person is inherently entitled simply because they are a human being". Those rights are "inherent in all human beings" regardless of their nationality, location, language, religion, ethnic origin, or any other status. They are applicable everywhere and at every time and are universal and egalitarian. === Cryptography === Cryptography is a long-standing subfield of both mathematics and computer science. It can generally be defined as "the protection of information and computation using mathematical techniques." Encryption and cryptography are closely interlinked, although "cryptography" has a broader meaning. For example, a digital signature is "cryptography", but not technically "encryption". == Overview == Under international human rights law, freedom of expression is recognized as a human right under Article 19 of the Universal Declaration of Human Rights (UDHR) and the International Covenant on Civil and Political Rights (ICCPR). In Article 19 of the UDHR states that "everyone shall have the right to hold opinions without interference" and "everyone shall have the right to freedom of expression; this right shall include freedom to seek, receive and impart information and ideas of all kinds, regardless of frontiers, either orally, in writing or in print, in the form of art, or through any other media of his choice". Since the 1970s, the availability of digital computing and the invention of public-key cryptography have made encryption more widely available. (Previously, encryption techniques were the domain of nation-state actors.) Cryptographic techniques are also used to protect the anonymity of communicating actors and privacy more generally. The availability and use of encryption continue to lead to complex, important, and highly contentious legal policy debates. Some government agencies have made statements or proposals to lessen such usage and deployment due to hurdles it presents for government access. The rise of commercial end-to-end encryption services have pushed towards more debates around the use of encryption and the legal status of cryptography in general. Encryption, as defined above, is a set of cryptographic techniques to protect information. The normative value of encryption, however, is not fixed but varies with the type and purpose of the cryptographic methods used. Traditionally, encryption (cipher) techniques were used to ensure the confidentiality of communications and prevent access to information and communications by others and intended recipients. Cryptography can also ensure the authenticity of communicating parties and the integrity of communications contents, providing a key ingredient for enabling trust in the digital environment. There is a growing awareness within human rights organizations that encryption plays an important role in realizing a free, open, and trustworthy Internet. UN Special Rapporteur on the promotion and protection of the right to freedom of opinion and expression David Kaye observed, during the Human Rights Council in June 2015, that encryption and anonymity deserve a protected status under the rights to privacy and freedom of expression: "Encryption and anonymity, today's leading vehicles for online security, provide individuals with a means to protect their privacy, empowering them to browse, read, develop and share opinions and information without interference and enabling journalists, civil society organizations, members of ethnic or religious groups, those persecuted because of their sexual orientation or gender identity, activists, scholars, artists and others to exercise the rights to freedom of opinion and expression." == Encryption in media and communication == In the context of media and communication, two types of encryption in media and communication can be distinguished: It could be used as a result of the choice of a service provider or deployed by Internet users. Client-side encryption tools and technologies are relevant for marginalized communities, journalists and other online media actors practicing journalism as a way of protecting their rights. It could prevent unauthorized third party access, but the service provider implementing it would still have access to the relevant user data. End-to-end encryption is an encryption technique that refers to encryption that also prevents service providers themselves from having access to the user's communications. The implementation of these forms of encryption has sparked the most debate since the start of the 21st century. === Service providers deployed techniques to prevent unauthorized third-party access. === Among the most widely deployed cryptographic techniques is the securitization of communications channel between internet users and specific service providers from man-in-the-middle attacks, access by unauthorized third parties. Given the breadth of nuances involved, these cryptographic techniques must be run jointly by both the service user and the service provider in order to work properly. They require service providers, including online news publisher(s) or social network(s), to actively implement them into service design. Users cannot deploy these techniques unilaterally; their deployment is contingent on active participation by the service provider. The TLS protocol, which becomes visible to the normal internet user through the HTTPS header, is widely used for securing online commerce, e-government services and health applications as well as devices that make up networked infrastructures, e.g., routers, cameras. However, although the standard has been around since 1990, the wider spread and evolution of the technology has been slow. As with other cryptographic methods and protocols, the practical challenges related to proper, secure and (wider) deployment are significant and have to be considered. Many service providers still do not implement TLS or do not implement it well. In the context of wireless communications, the use of cryptographic techniques that protect communications from third parties are also important. Different standards have been developed to protect wireless communications: 2G, 3G and 4G standards for communication between mobile phones, base stations and base stations controllers; standards to protect communications between mobile devices and wireless routers ('WLAN'); and standards for local computer networks. One common weakness in these designs is that the transmission points of the wireless communication can access all communications e.g., the telecommunications provider. This vulnerability is exacerbated when wireless protocols only authenticate user devices, but not the wireless access point. Whether the data is stored on a device, or on a local server as in the cloud, there is also a distinction between 'at rest'. Given the vulnerability of cellphones to theft for instance, particular attention may be given to limiting service provided access. This does not exclude the situation that the service provider discloses this information to third parties like other commercial entities or governments. The user needs to trust the service provider to act in their interests. The possibility that a service provider is legally compelled to hand over user information or to interfere with particular communications with particular users, remains. === Privacy-enhancing Technologies === There are services that specifically market themselves with claims not to have access to the content of their users' communication. Service Providers can also take measures that restrict their ability to access information and communication, further increasing the protection of users against access to their information and communications. The integrity of these Privacy Enhancing Technologies (PETs), depends on delicate design decisions as well as the
Smart data capture
Smart data capture (SDC), also known as 'intelligent data capture' or 'automated data capture', describes the branch of technology concerned with using computer vision techniques like optical character recognition (OCR), barcode scanning, object recognition and other similar technologies to extract and process information from semi-structured and unstructured data sources. IDC characterize smart data capture as an integrated hardware, software, and connectivity strategy to help organizations enable the capture of data in an efficient, repeatable, scalable, and future-proof way. Data is captured visually from barcodes, text, IDs and other objects - often from many sources simultaneously - before being converted and prepared for digital use, typically by artificial intelligence-powered software. An important feature of SDC is that it focuses not just on capturing data more efficiently but serving up easy-to-access, actionable insights at the instant of data collection to both frontline and desk-based workers, aiding decision-making and making it a two-way process. Smart data capture automates and accelerates capture, applying insights in real time and automating processes based on extracted input. Smart data capture is designed to be repeatable and scalable to reduce low-level manual tasks and eliminate human error. To achieve this goal, smart data capture solutions are often made available using specialist software installed on commodity hardware such as smartphones. However, some solutions may rely on specialized hardware such as dedicated scanning devices, wearables or shop floor robots. == Differences from OCR == Optical character recognition applications are typically concerned with the actual data capture process; they are intended to faithfully reproduce text, words, letters and symbols from a printed document. Smart data capture is multimodal, capable of extracting data from a wider range of semi-structured and unstructured sources, going beyond basic text recognition to offer a wider scope of applications. By extending functionality to provide actionable insights at the point of capture, SDC is also a two-way process (capture-display), while OCR is more commonly one-way (capture only), primarily used for data input. Smart data capture solutions typically have two parts: Data capture (which includes OCR, barcode scanning, object recognition) Functionality that then uses this data to provide actionable insights at the point of capture. == Applications == Smart data capture can be applied to almost any industry and application that requires visual information capture and interpretation. This may include: Retail Warehouse inventory control Logistics, handling and shipping Manufacturing Field service Healthcare Transport and travel Fraud detection
User-defined function
A user-defined function (UDF) is a function provided by the user of a program or environment, in a context where the usual assumption is that functions are built into the program or environment. UDFs are usually written for the requirement of its creator. == BASIC language == In some old implementations of the BASIC programming language, user-defined functions are defined using the "DEF FN" syntax. More modern dialects of BASIC are influenced by the structured programming paradigm, where most or all of the code is written as user-defined functions or procedures, and the concept becomes practically redundant. == COBOL language == In the COBOL programming language, a user-defined function is an entity that is defined by the user by specifying a FUNCTION-ID paragraph. A user-defined function must return a value by specifying the RETURNING phrase of the procedure division header and they are invoked using the function-identifier syntax. See the ISO/IEC 1989:2014 Programming Language COBOL standard for details. As of May 2022, the IBM Enterprise COBOL for z/OS 6.4 (IBM COBOL) compiler contains support for user-defined functions. == Databases == In relational database management systems, a user-defined function provides a mechanism for extending the functionality of the database server by adding a function, that can be evaluated in standard query language (usually SQL) statements. The SQL standard distinguishes between scalar and table functions. A scalar function returns only a single value (or NULL), whereas a table function returns a (relational) table comprising zero or more rows, each row with one or more columns. User-defined functions in SQL are declared using the CREATE FUNCTION statement. For example, a user-defined function that converts Celsius to Fahrenheit (a temperature scale used in USA) might be declared like this: Once created, a user-defined function may be used in expressions in SQL statements. For example, it can be invoked where most other intrinsic functions are allowed. This also includes SELECT statements, where the function can be used against data stored in tables in the database. Conceptually, the function is evaluated once per row in such usage. For example, assume a table named Elements, with a row for each known chemical element. The table has a column named BoilingPoint for the boiling point of that element, in Celsius. The query would retrieve the name and the boiling point from each row. It invokes the CtoF user-defined function as declared above in order to convert the value in the column to a value in Fahrenheit. Each user-defined function carries certain properties or characteristics. The SQL standard defines the following properties: Language - defines the programming language in which the user-defined function is implemented; examples include SQL, C, C# and Java. Parameter style - defines the conventions that are used to pass the function parameters and results between the implementation of the function and the database system (only applicable if language is not SQL). Specific name - a name for the function that is unique within the database. Note that the function name does not have to be unique, considering overloaded functions. Some SQL implementations require that function names are unique within a database, and overloaded functions are not allowed. Determinism - specifies whether the function is deterministic or not. The determinism characteristic has an influence on the query optimizer when compiling a SQL statement. SQL-data access - tells the database management system whether the function contains no SQL statements (NO SQL), contains SQL statements but does not access any tables or views (CONTAINS SQL), reads data from tables or views (READS SQL DATA), or actually modifies data in the database (MODIFIES SQL DATA). User-defined functions should not be confused with stored procedures. Stored procedures allow the user to group a set of SQL commands. A procedure can accept parameters and execute its SQL statements depending on those parameters. A procedure is not an expression and, thus, cannot be used like user-defined functions. Some database management systems allow the creation of user defined functions in languages other than SQL. Microsoft SQL Server, for example, allows the user to use .NET languages including C# for this purpose. DB2 and Oracle support user-defined functions written in C or Java programming languages. === SQL Server 2000 === There are three types of UDF in Microsoft SQL Server 2000: scalar functions, inline table-valued functions, and multistatement table-valued functions. Scalar functions return a single data value (not a table) with RETURNS clause. Scalar functions can use all scalar data types, with exception of timestamp and user-defined data types. Inline table-valued functions return the result set of a single SELECT statement. Multistatement table-valued functions return a table, which was built with many TRANSACT-SQL statements. User-defined functions can be invoked from a query like built‑in functions such as OBJECT_ID, LEN, DATEDIFF, or can be executed through an EXECUTE statement like stored procedures. Performance Notes: User-defined functions are subroutines made of one or more Transact-SQL statements that can be used to encapsulate code for reuse. It takes zero or more arguments and evaluates a return value. Has both control-flow and DML statements in its body similar to stored procedures. Does not allow changes to any Global Session State, like modifications to database or external resource, such as a file or network. Does not support output parameter. DEFAULT keyword must be specified to pass the default value of parameter. Errors in UDF cause UDF to abort which, in turn, aborts the statement that invoked the UDF. === Apache Hive === Apache Hive defines, in addition to the regular user-defined functions (UDF), also user-defined aggregate functions (UDAF) and table-generating functions (UDTF). Hive enables developers to create their own custom functions with Java. === Apache Doris === Apache Doris, an open-source real-time analytical database, allows external users to contribute their own UDFs written in C++ to it.
CityEngine
ArcGIS CityEngine is a commercial 3D modeling program. Developed by Esri R&D Center Zurich (formerly Procedural Inc.), it specializes in the generation of 3D urban environments to support the creation of detailed large-scale 3D city models. Unlike traditional 3D modeling methodology, which uses computer-aided design (CAD) tools and techniques, CityEngine takes a procedural modeling approach which shapes generation via a rules-based system. Due to its integration with the wider ArcGIS platform, CityEngine can also be used with geographic information system (GIS) datasets. CityEngine can be used for urban planning and architecture, graphics visualization, game development, entertainment, and archeology. CityEngine can be used to visualize the building information modeling (BIM) data of buildings in a larger urban context, making for more realistic construction projects. == History and releases == === Software history === ArcGIS CityEngine, originally named Esri CityEngine, was developed at Swiss technology university ETH Zurich by Pascal Mueller, the co-founder and CEO of Procedural Inc. While researching for his PhD at the ETH Computer Vision Lab, Mueller invented a number of techniques for procedural modeling of 3D architecture that make up the foundation of CityEngine. CityEngine publically debuted at the 2001 SIGGRAPH conference; since then, additional research papers have been published that have contributed to CityEngine and its features. The first commercial version of CityEngine was released in 2008. In 2007, Procedural Inc. was founded and separated from ETH Zurich, the top-ranking technology university in Switzerland. In the summer of 2011, Procedural Inc. was acquired by Esri Inc., becoming Esri R&D Center Zurich. Esri CityEngine was renamed to ArcGIS CityEngine in June 2020 to offically make it a part of the ArcGIS software suite. === Releases === === Licensing and pricing === ArcGIS CityEngine is included in the Professional and Professional Plus tiers of ArcGIS Online. Pricing may vary by region and distributors. In the US, the professional tier costs US$2,200 per year; in the UK, it is £4,200 per year (excluding VAT). CityEngine can be purchased elsewhere via a local Esri partner. . Once purchased, users can download and obtain license details from the MyEsri portal. == Features == CGA (computer generated architecture) parametric modeling rules to control mass, geometry assets, proportions, or texturing of buildings or streets on a citywide scale Select a target location and import geo-referenced satellite imagery and 3D terrain of the location to more quickly build accurate urban environments through OpenStreetMap integration Interactively control specific street or building parameters, such as height or age Import/export geo-spatial/vector data with industry-standard formats such as Esri Shapefile, File Geodatabase, and OpenStreetMap, as well as file formats for WebGL, KMZ, Collada, Autodesk FBX, Autodesk Maya, 3DS, Wavefront OBJ, RenderMan RIB, Alembic, e-on software's Vue, Universal Scene Description USD, Khronos Group GLTF, Unreal Engine, and Unreal Datasmith Script and generate rules-based reports to show socioeconomic figures (e.g., Gross Floor Area (GFA) and Floor Area Ratio (FAR)) to analyze their urban design proposals. VR viewing of modeled environments with Samsung Gear VR Use a variety of materials through the Esri materials library == Procedural modeling == ArcGIS CityEngine uses a procedural modeling approach to automatically generate models through a predefined rule set. The rules are defined through a CGA shape grammar system, enabling the creation of complex parametric models. Users can change or add the shape grammar as needed. Urban environments can be modeled within CityEngine by starting with creating a street network (either from the street drawing tool or with data imported from map data). Then, lots may be subdivided as many times as specified, resulting in a map of multiple lots and streets. CityEngine can then be instructed to start generating the buildings using defined procedural modeling rules. At this point, the city model can be re-designed and adjusted by changing the parameters or the shape grammar. === Geodesign === Though CityEngine is not an analytical tool like GIS, discussions about geodesign often mention the use of ArcGIS CityEngine. As it can be used to enhance 3D shape generation in ArcGIS, ArcGIS CityEngine is a critical product to improve the applicability of geodesign by using geospatial information to design or analyze a city. == Applications == === Urban design and planning === Garsdale Design used ArcGIS CityEngine in the creation of city master plans in Iraq before 2013, both to model existing historic areas and also model future plans. Larger companies like Foster+Partners and HOK Architects have also used CityEngine in their urban planning projects. === Urban and environmental studies === Because its primary feature is building informative city models, some urban researchers use CityEngine to compare land-use planning schemes, for example in very dense global cities such as Hong Kong and Seoul. Environmental scientists can also utilize the instant 3D model generation in CityEngine, which can make for more convenient informative research than modeling a city by creating each building individually. === Game development === CityEngine can be used as a tool in the creation of video games that require detailed 3D environments to assign interactive scripts. === Movie industry === Zootopia (also known outside of the US as Zootopolis), which won the 2016 Academy Award for Best Animated Feature Film, used CityEngine to model the city in its movie. multi-scaling city, the designers used CityEngine due to its rule-based system. CityEngine was also used to create Big Hero 6's San-Fransokyo. === Military === Due to its integration with the Esri product suite and its ability to process geospatial data to create 3D scenes/maps, CityEngine can be used within military/defense organizations. == List of movies and TV shows using CityEngine == Studios and companies rarely state what software they use in their pipelines. When CityEngine is mentioned as a tool in production, it's often in a small reference in a larger article. Movies only claimed to use CityEngine by a single Esri employee Presented at FMX 2025 workshop == Ports == ArcGIS CityEngine is built on top of Eclipse IDE, and has therefore able to be used on Windows and Linux operating systems. Support for macOS was stopped in March 2021. == Plugins and extensions == ArcGIS CityEngine currently works with a number of third party 3D modeling, rendering, and analytical software products via its SDK and API; these currently are: ArcGIS CityEngine for ArcGIS Urban: ArcGIS Urban Suite Puma: ArcGIS CityEngine for Rhinoceros 3D Palladio: ArcGIS CityEngine for Houdini Serlio: ArcGIS CityEngine for Maya PyPRT: ArcGIS CityEngine for Python ArcGIS CityEngine provides a Python scripting interface built on Jython (current version 2.7.0) which allows users to create their own tools and functionality. == Publications ==
Lossless join decomposition
In database design, a lossless join decomposition is a decomposition of a relation r {\displaystyle r} into relations r 1 , r 2 {\displaystyle r_{1},r_{2}} such that a natural join of the two smaller relations yields back the original relation. This is central in removing redundancy safely from databases while preserving the original data. Lossless join can also be called non-additive. == Definition == A relation r {\displaystyle r} on schema R {\displaystyle R} decomposes losslessly onto schemas R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} if π R 1 ( r ) ⋈ π R 2 ( r ) = r {\displaystyle \pi _{R_{1}}(r)\bowtie \pi _{R_{2}}(r)=r} , that is r {\displaystyle r} is the natural join of its projections onto the smaller schemas. A pair ( R 1 , R 2 ) {\displaystyle (R_{1},R_{2})} is a lossless-join decomposition of R {\displaystyle R} or said to have a lossless join with respect to a set of functional dependencies F {\displaystyle F} if any relation r ( R ) {\displaystyle r(R)} that satisfies F {\displaystyle F} decomposes losslessly onto R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} . Decompositions into more than two schemas can be defined in the same way. == Criteria == A decomposition R = R 1 ∪ R 2 {\displaystyle R=R_{1}\cup R_{2}} has a lossless join with respect to F {\displaystyle F} if and only if the closure of R 1 ∩ R 2 {\displaystyle R_{1}\cap R_{2}} includes R 1 ∖ R 2 {\displaystyle R_{1}\setminus R_{2}} or R 2 ∖ R 1 {\displaystyle R_{2}\setminus R_{1}} . In other words, one of the following must hold: ( R 1 ∩ R 2 ) → ( R 1 ∖ R 2 ) ∈ F + {\displaystyle (R_{1}\cap R_{2})\to (R_{1}\setminus R_{2})\in F^{+}} ( R 1 ∩ R 2 ) → ( R 2 ∖ R 1 ) ∈ F + {\displaystyle (R_{1}\cap R_{2})\to (R_{2}\setminus R_{1})\in F^{+}} === Criteria for multiple sub-schemas === Multiple sub-schemas R 1 , R 2 , . . . , R n {\displaystyle R_{1},R_{2},...,R_{n}} have a lossless join if there is some way in which we can repeatedly perform lossless joins until all the schemas have been joined into a single schema. Once we have a new sub-schema made from a lossless join, we are not allowed to use any of its isolated sub-schema to join with any of the other schemas. For example, if we can do a lossless join on a pair of schemas R i , R j {\displaystyle R_{i},R_{j}} to form a new schema R i , j {\displaystyle R_{i,j}} , we use this new schema (rather than R i {\displaystyle R_{i}} or R j {\displaystyle R_{j}} ) to form a lossless join with another schema R k {\displaystyle R_{k}} (which may already be joined (e.g., R k , l {\displaystyle R_{k,l}} )). == Example == Let R = { A , B , C , D } {\displaystyle R=\{A,B,C,D\}} be the relation schema, with attributes A, B, C and D. Let F = { A → B C } {\displaystyle F=\{A\rightarrow BC\}} be the set of functional dependencies. Decomposition into R 1 = { A , B , C } {\displaystyle R_{1}=\{A,B,C\}} and R 2 = { A , D } {\displaystyle R_{2}=\{A,D\}} is lossless under F because R 1 ∩ R 2 = A {\displaystyle R_{1}\cap R_{2}=A} and we have a functional dependency A → B C {\displaystyle A\rightarrow BC} . In other words, we have proven that ( R 1 ∩ R 2 → R 1 ∖ R 2 ) ∈ F + {\displaystyle (R_{1}\cap R_{2}\rightarrow R_{1}\setminus R_{2})\in F^{+}} .
Teknomo–Fernandez algorithm
The Teknomo–Fernandez algorithm (TF algorithm), is an efficient algorithm for generating the background image of a given video sequence. By assuming that the background image is shown in the majority of the video, the algorithm is able to generate a good background image of a video in O ( R ) {\displaystyle O(R)} -time using only a small number of binary operations and Boolean bit operations, which require a small amount of memory and has built-in operators found in many programming languages such as C, C++, and Java. == History == People tracking from videos usually involves some form of background subtraction to segment foreground from background. Once foreground images are extracted, then desired algorithms (such as those for motion tracking, object tracking, and facial recognition) may be executed using these images. However, background subtraction requires that the background image is already available and unfortunately, this is not always the case. Traditionally, the background image is searched for manually or automatically from the video images when there are no objects. More recently, automatic background generation through object detection, medial filtering, medoid filtering, approximated median filtering, linear predictive filter, non-parametric model, Kalman filter, and adaptive smoothening have been suggested; however, most of these methods have high computational complexity and are resource-intensive. The Teknomo–Fernandez algorithm is also an automatic background generation algorithm. Its advantage, however, is its computational speed of only O ( R ) {\displaystyle O(R)} -time, depending on the resolution R {\displaystyle R} of an image and its accuracy gained within a manageable number of frames. Only at least three frames from a video is needed to produce the background image assuming that for every pixel position, the background occurs in the majority of the videos. Furthermore, it can be performed for both grayscale and colored videos. == Assumptions == The camera is stationary. The light of the environment changes only slowly relative to the motions of the people in the scene. The number of people does not occupy the scene for most of the time at the same place. Generally, however, the algorithm will certainly work whenever the following single important assumption holds: For each pixel position, the majority of the pixel values in the entire video contain the pixel value of the actual background image (at that position).As long as each part of the background is shown in the majority of the video, the entire background image needs not to appear in any of its frames. The algorithm is expected to work accurately. == Background image generation == === Equations === For three frames of image sequence x 1 {\displaystyle x_{1}} , x 2 {\displaystyle x_{2}} , and x 3 {\displaystyle x_{3}} , the background image B {\displaystyle B} is obtained using B = x 3 ( x 1 ⊕ x 2 ) + x 1 x 2 {\displaystyle B=x_{3}(x_{1}\oplus x_{2})+x_{1}x_{2}} where ⊕ {\displaystyle \oplus } denotes the exclusive disjunctive bit operator. The Boolean mode function S {\displaystyle S} of the table occurs when the number of 1 entries is larger than half of the number of images such that S = { 1 , if ∑ i = 1 n x i ≥ ⌈ n 2 + 1 ⌉ , and n ≥ 3 0 , otherwise {\displaystyle S={\begin{cases}1,&{\text{if }}\sum _{i=1}^{n}x_{i}\geq \left\lceil {\frac {n}{2}}+1\right\rceil ,{\text{ and }}n\geq 3\\0,&{\text{otherwise}}\end{cases}}} For three images, the background image B {\displaystyle B} can be taken as the value x ¯ 1 x 2 x 3 + x 1 x ¯ 2 x 3 + x 1 x 2 x ¯ 3 + x 1 x 2 x 3 {\displaystyle {\bar {x}}_{1}x_{2}x_{3}+x_{1}{\bar {x}}_{2}x_{3}+x_{1}x_{2}{\bar {x}}_{3}+x_{1}x_{2}x_{3}} === Background generation algorithm === At the first level, three frames are selected at random from the image sequence to produce a background image by combining them using the first equation. This yields a better background image at the second level. The procedure is repeated until desired level L {\displaystyle L} . == Theoretical accuracy == At level ℓ {\displaystyle \ell } , the probability p ℓ {\displaystyle p_{\ell }} that the modal bit predicted is the actual modal bit is represented by the equation p ℓ = ( p ℓ − 1 ) 3 + 3 ( p ℓ − 1 ) 2 ( 1 − p ℓ − 1 ) {\displaystyle p_{\ell }=(p_{\ell -1})^{3}+3(p_{\ell -1})^{2}(1-p_{\ell -1})} . The table below gives the computed probability values across several levels using some specific initial probabilities. It can be observed that even if the modal bit at the considered position is at a low 60% of the frames, the probability of accurate modal bit determination is already more than 99% at 6 levels. == Space complexity == The space requirement of the Teknomo–Fernandez algorithm is given by the function O ( R F + R 3 L ) {\displaystyle O(RF+R3^{L})} , depending on the resolution R {\displaystyle R} of the image, the number F {\displaystyle F} of frames in the video, and the desired number L {\displaystyle L} of levels. However, the fact that L {\displaystyle L} will probably not exceed 6 reduces the space complexity to O ( R F ) {\displaystyle O(RF)} . == Time complexity == The entire algorithm runs in O ( R ) {\displaystyle O(R)} -time, only depending on the resolution of the image. Computing the modal bit for each bit can be done in O ( 1 ) {\displaystyle O(1)} -time while the computation of the resulting image from the three given images can be done in O ( R ) {\displaystyle O(R)} -time. The number of the images to be processed in L {\displaystyle L} levels is O ( 3 L ) {\displaystyle O(3^{L})} . However, since L ≤ 6 {\displaystyle L\leq 6} , then this is actually O ( 1 ) {\displaystyle O(1)} , thus the algorithm runs in O ( R ) {\displaystyle O(R)} . == Variants == A variant of the Teknomo–Fernandez algorithm that incorporates the Monte-Carlo method named CRF has been developed. Two different configurations of CRF were implemented: CRF9,2 and CRF81,1. Experiments on some colored video sequences showed that the CRF configurations outperform the TF algorithm in terms of accuracy. However, the TF algorithm remains more efficient in terms of processing time. == Applications == Object detection Face detection Face recognition Pedestrian detection Video surveillance Motion capture Human-computer interaction Content-based video coding Traffic monitoring Real-time gesture recognition
Wavelet noise
Wavelet noise is an alternative to Perlin noise which reduces the problems of aliasing and detail loss that are encountered when Perlin noise is summed into a fractal. == Algorithm detail == The basic algorithm for 2-dimensional wavelet noise is as follows: Create an image, R {\displaystyle R} , filled with uniform white noise. Downsample R {\displaystyle R} to half-size to create R ↓ {\displaystyle R^{\downarrow }} , then upsample it back up to full size to create R ↓↑ {\displaystyle R^{\downarrow \uparrow }} . Subtract R ↓↑ {\displaystyle R^{\downarrow \uparrow }} from R {\displaystyle R} to create the end result, N {\displaystyle N} . This results in an image that contains all the information that cannot be represented at half-scale. From here, N {\displaystyle N} can be used similarly to Perlin noise to create fractal patterns.