Layers are used in digital image editing to separate different elements of an image. A layer can be compared to a transparency on which imaging effects or images are applied and placed over or under an image. Today they are an integral feature of image editors. In the early days of computing, memory was at a premium and the idea of using multi-layered images was considered infeasible in personal computer applications as the tradeoffs were image size and color depth. As the price of memory fell it became feasible to apply the concept of layering to raster images. The first software known to apply the concept of layers was LALF, which was released in 1989 for the NEC PC-9801. LALF's terminology for layers is "cells", after the concept of drawing animation frames over-top of a stencil. Layers were introduced in Western markets by Fauve Matisse (later Macromedia xRes), and then available in Adobe Photoshop 3.0, in 1994, which lead to widespread adoption. In vector image editors that support animation, layers are used to further enable manipulation along a common timeline for the animation; in SVG images, the equivalent to layers are "groups". == Layer types == There are different kinds of layers, and not all of them exist in all programs. They represent a part of a picture, either as pixels or as modification instructions. They are stacked on top of each other, and depending on the order, determine the appearance of the final picture. In graphics software, layers are the different levels at which one can place an object or image file. In the program, layers can be stacked, merged, or defined when creating a digital image. Layers can be partially obscured allowing portions of images within a layer to be hidden or shown in a translucent manner within another image. Layers can also be used to combine two or more images into a single digital image. For the purpose of editing, working with layers allows for applying changes to just one specific layer. == Layer (basic) == The standard layer available to most programs consists of a rectangular, semitransparent picture which may be superimposed over other layers. Some programs require that layers cover the same area as the final canvas, but others offer layers of multiple sizes. Each layer may bear individual settings, such as opacity, blending modes, dynamic filters, and potentially hundreds of other properties. == Layer mask == A layer mask is linked to a layer and hides part of the layer from the picture. What is painted black on the layer mask will not be visible in the final picture. What is grey will be more or less transparent depending on the shade of grey. As the layer mask can be both edited and moved around independently of both the background layer and the layer it applies to, it gives the user the ability to test a lot of different combinations of overlay. == Adjustment layer == An adjustment layer typically applies a common effect like brightness or saturation to other layers. However, as the effect is stored in a separate layer, it is easy to try it out and switch between different alternatives, without changing the original layer. In addition, an adjustment layer can easily be edited, just like a layer mask, so an effect can be applied to just part of the image.
EyeOS
eyeOS was a web desktop for cloud computing, whose main purpose is to enable collaboration and communication among users. It is mainly written in PHP, XML, and JavaScript. It is a private-cloud application platform with a web-based desktop interface. eyeOS delivers a whole desktop from the cloud with file management, personal management information tools, and collaborative tools, with the integration of the client's applications. == History == The first publicly available eyeOS version was released on August 1, 2005, as eyeOS 0.6.0 in Olesa de Montserrat, Barcelona (Spain). A worldwide community of developers soon took part in the project and helped improve it by translating, testing, and developing it. After two years of development, the eyeOS Team published eyeOS 1.0 on June 4, 2007. Compared with previous versions, eyeOS 1.0 introduced a complete reorganization of the code and some new web technologies, like eyeSoft, a portage-based web software installation system. Moreover, eyeOS also included the eyeOS Toolkit, a set of libraries allowing easy and fast development of new web applications. With the release of eyeOS 1.1 on July 2, 2007, eyeOS changed its license and migrated from GNU GPL Version 2 to Version 3. Version 1.2 was released just a month after the 1.1 version and integrated full compatibility with Microsoft Word files. eyeOS 1.5 Gala was released on January 15, 2008. This version was the first to support both Microsoft Office and OpenOffice.org file formats for documents, presentations, and spreadsheets. With this version, eyeOS also gained the ability to import and export documents in both formats using server-side scripting. eyeOS 1.6 was released on April 25, 2008, and included many improvements such as synchronization with local computers, drag and drop, a mobile version, and more. eyeOS 1.8 Lars was released on January 7, 2009, and featured a completely rewritten file manager and a new sound API to develop media-rich applications. Later, on April 1, 2009, 1.8.5 was released with a new default theme and some rewritten apps, such as the Word Processor and the Address Book. On July 13, 2009, 1.8.6 was released with an interface for the iPhone and a new version of eyeMail with support for POP3 and IMAP. eyeOS 1.9 was released on December 29, 2009. It was followed up with the 1.9.0.1 release with minor fixes on February 18, 2010. These releases were the last of the "classic desktop" interfaces. A major re-work was completed in March 2010, now called eyeOS 2.x. However, a small group of eyeOS developers still maintain the code within the eyeOS forum, where support is provided, but the eyeOS group itself has stopped active 1.x development. It is now available as the On-eye project on GitHub. Active development was halted on 1.x as of February 3, 2010. eyeOS 2.0 release took place on March 3, 2010. This was a total restructure of the operating system. The 2.x stable is the new series of eyeOS, which is in active development and will replace 1.x as stable in a few months. It includes live collaboration and more social capabilities than eyeOS 1.x. eyeOS then released 2.2.0.0 on July 28, 2010. On December 14, 2010, a working group inside the eyeOS open-source development community began the structure development and further upgrade of eyeOS 1.9.x. The group's main goal is to continue the work eyeOS has stopped on 1.9.x. eyeOS released 2.5 on May 17, 2011. This was the last release under an open source license. It is available on SourceForge for download under another project called eyeOS 2.5 Open Source Version. On April 1, 2014, Telefónica announced their acquisition of eyeOS. eyeOS would maintain its headquarters in the Catalonia, Spain, where their staff would continue to work but now as part of Telefónica. After its integration into Telefónica, eyeOS would continue to function as an independent subsidiary under CEO Michel Kisfaludi. == Structure and API == For developers, EyeOS provides the eyeOS Toolkit, a set of libraries and functions to develop applications for eyeOS. Using the integrated Portage-based eyeSoft system, one can create their own repository for eyeOS and distribute applications through it. Each core part of the desktop is its own application, using JavaScript to send server commands as the user interacts. As actions are performed using AJAX (such as launching an application), it sends event information to the server. The server then sends back tasks for the client to do in XML format, such as drawing a widget. On the server, eyeOS uses XML files to store information. This makes it simple for a user to set up on the server, as it requires zero configuration other than the account information for the first user, making it simple to deploy. To avoid bottlenecks that flat files present, each user's information and settings are stored in different files, preventing resource starvation from occurring, though this in turn may create issues in high volume user environments due to host operating system open file descriptor limits. == Professional edition == A Professional Edition of eyeOS was launched on September 15, 2011, as an operating system for businesses. It uses a new version number and was released under version 1.0 instead of continuing with the next version number in the open source project. The Professional Edition retains the web desktop interface used by the open source version while targeting enterprise users. A host of new features designed for enterprises, like file sharing and synchronization (called eyeSync), Active Directory/LDAP connectivity, system-wide administration controls, and a local file execution tool called eyeRun were introduced. A new suite of Web Apps (a mail client, calendar, instant messaging, and collaboration tools) was also introduced, specific to the enterprise edition for the web desktop. With eyeOS Professional Edition 1.1, a to-do task manager tool, Citrix XenApp integration, and a Facebook like 'wall' for collaboration were introduced. == Awards == 2007 – Received the Softpedia's Pick award. 2007 – Finalist at SourceForge's 2007 Community Choice Awards at the "Best Project" category. The winner for that category was 7-Zip. 2007 – Won the Yahoo! Spain Web Revelation award in the Technology category. 2008 – Finalist for the Webware 100 awards by CNET, under the "Browsing" category. 2008 – Finalist at the SourceForge's 2008 Community Choice Awards at the "Most Likely to Change the World" category. The winner for that category was Linux. 2009 – Selected Project of the Month (August 2009) by SourceForge. 2009 – BMW Innovation Award. 2010 – Winner of Accelera (Ernst & Young). 2010 – Asturias & Girona Spanish Prince award “IMPULSA”. 2011 – Winner of MIT's TR35 award as Innovator of the Year in Spain. == Community == eyeOS community is formed with the eyeOS forums, which reached 10,000 members on April 4, 2008; the eyeOS wiki; and the eyeOS Application Communities, available at the eyeOS-Apps website, hosted and provided by openDesktop.org as well as Softpedia.
Ishikawa diagram
Ishikawa diagrams (also called fishbone diagrams, herringbone diagrams, cause-and-effect diagrams) are causal diagrams created by Kaoru Ishikawa that show the potential causes of a specific event. Common uses of the Ishikawa diagram are product design and quality defect prevention to identify potential factors causing an overall effect. Each cause or reason for imperfection is a source of variation. Causes are usually grouped into major categories to identify and classify these sources of variation. == Overview == The defect, or the problem to be solved, is shown as the fish's head, facing to the right, with the causes extending to the left as fishbones; the ribs branch off the backbone for major causes, with sub-branches for root-causes, to as many levels as required. Ishikawa diagrams were popularized in the 1960s by Kaoru Ishikawa, who pioneered quality management processes in the Kawasaki shipyards, and in the process became one of the founding fathers of modern management. The basic concept was first used in the 1920s, and is considered one of the seven basic tools of quality control. It is known as a fishbone diagram because of its shape, similar to the side view of a fish skeleton. Mazda Motors famously used an Ishikawa diagram in the development of the Miata (MX5) sports car. == Root causes == Root-cause analysis is intended to reveal key relationships among various variables, and the possible causes provide additional insight into process behavior. It shows high-level causes that lead to the problem encountered by providing a snapshot of the current situation. There can be confusion about the relationships between problems, causes, symptoms and effects. Smith highlights this and the common question “Is that a problem or a symptom?” which mistakenly presumes that problems and symptoms are mutually exclusive categories. A problem is a situation that bears improvement; a symptom is the effect of a cause: a situation can be both a problem and a symptom. At a practical level, a cause is whatever is responsible for, or explains, an effect - a factor "whose presence makes a critical difference to the occurrence of an outcome". The causes emerge by analysis, often through brainstorming sessions, and are grouped into categories on the main branches off the fishbone. To help structure the approach, the categories are often selected from one of the common models shown below, but may emerge as something unique to the application in a specific case. Each potential cause is traced back to find the root cause, often using the 5 Whys technique. Typical categories include: === The 5 Ms (used in manufacturing) === Originating with lean manufacturing and the Toyota Production System, the 5 Ms is one of the most common frameworks for root-cause analysis: Manpower / Mindpower (physical or knowledge work, includes: kaizens, suggestions) Machine (equipment, technology) Material (includes raw material, consumables, and information) Method (process) Measurement / medium (inspection, environment) These have been expanded by some to include an additional three, and are referred to as the 8 Ms: Mission / mother nature (purpose, environment) Management / money power (leadership) Maintenance === The 8 Ps (used in product marketing) === This common model for identifying crucial attributes for planning in product marketing is often also used in root-cause analysis as categories for the Ishikawa diagram: Product (or service) Price Place Promotion People (personnel) Process Physical evidence (proof) Performance === The 4 or 5 Ss (used in service industries) === An alternative used for service industries, uses four categories of possible cause: Surroundings: Refers to the environment in which the process occurs. Suppliers: Refers to external parties that provide inputs—raw materials, components, or services. Systems: Refers to the procedures, processes, and technologies used to perform the work. Skill: Refers to the human factor, particularly the knowledge and abilities of employees. Safety: Refers to physical and psychological well-being in the workplace. == Use in specific industries == The Ishikawa diagram has been widely adopted across various industries as an effective tool for root cause analysis in quality, efficiency, and safety-related issues. Its versatility allows it to be applied in both manufacturing and service contexts. In the manufacturing industry, particularly in the automotive and electronics sectors, the diagram is frequently used in continuous improvement initiatives such as Six Sigma and Lean Manufacturing. Quality teams use it to identify causes related to materials, methods, machinery, manpower, environment, and measurement, facilitating informed decision-making to reduce defects and optimize processes. In the food industry, the Ishikawa diagram is applied to analyze issues related to food safety, temperature control, cross-contamination, and regulatory compliance. Its use enables companies to identify improvement opportunities in production, packaging, and distribution stages. In the pharmaceutical sector, it is a key tool in process validation, quality control, and compliance with Good Manufacturing Practices (GMP). It helps visualize factors affecting product quality from formulation to storage. It has also been successfully implemented in sectors such as aerospace, pulp and paper, construction, education, and healthcare, where it supports structured problem-solving and promotes continuous improvement and a culture of quality.
Zvi Mowshowitz
Zvi Mowshowitz is an American writer and member of the rationalist community who primarily discusses new developments in artificial intelligence. He is a former competitive Magic: The Gathering player and was CEO of MetaMed. == Career == Mowshowitz is an alumnus of Columbia University and holds a bachelor's degree in mathematics. He co-founded and was the CEO of MetaMed, a medical research analysis firm. He has worked at Jane Street Capital, and has worked for the gambling industry in Las Vegas. He attempted to launch a blockchain game, Emergents, in 2020. === Magic: The Gathering === Mowshowitz held a developer intern position at Wizards of the Coast R&D in 2005. He created the deck TurboZvi. His first-place finishes at major competitions were the 1999 World Championships as part of the four-person United States national team, the 2001 Pro Tour Tokyo, and two 2003 Grand Prix. He has placed in the top eight of four Pro Tours, and earned over $140,000 playing Magic competitively. In 2007, Mowshowitz was elected into the Magic Hall of Fame. Last updated: 12 May 2013Source: Wizards.com Mowshowitz has written about Magic for several outlets, including the official Magic website. === Later career === Mowshowitz is on the board of directors for the Center for Applied Rationality, and is a member of the rationalist community. He also founded Balsa Research, a nonprofit think tank which advocated for the repeal of the Jones Act, increasing the housing supply, and reform of the National Environmental Policy Act. In 2023, Mowshowitz wrote an article for Vox on the topic of artificial intelligence safety. Mowshowitz has a blog on Substack under the name "Don't Worry about the Vase". He has written on topics such as artificial intelligence, economics, and the COVID-19 pandemic. == Personal life == Mowshowitz is the son of American biochemist Deborah Mowshowitz. His parents have both worked as Columbia University professors.
Hubert Dreyfus
Hubert Lederer Dreyfus ( DRY-fəs; October 15, 1929 – April 22, 2017) was an American philosopher and a professor of philosophy at the University of California, Berkeley. His main interests included phenomenology, existentialism and the philosophy of both psychology and literature, as well as the philosophical implications of artificial intelligence. He was widely known for his exegesis of Martin Heidegger, which critics labeled "Dreydegger". Dreyfus was featured in Tao Ruspoli's film Being in the World (2010), and was among the philosophers interviewed by Bryan Magee for the BBC Television series The Great Philosophers (1987). The Futurama character Professor Hubert Farnsworth is partly named after him, writer Eric Kaplan having been a former student. == Life and career == Dreyfus was born on 15 October 1929, in Terre Haute, Indiana, to Stanley S. and Irene (Lederer) Dreyfus. He attended Harvard University from 1947. With a senior honors thesis on Causality and Quantum Theory (for which W. V. O. Quine was the main examiner) he was awarded a B.A. summa cum laude in 1951 and joined Phi Beta Kappa. He was awarded a M.A. in 1952. He was a Teaching Fellow at Harvard from 1952 to 1953 (as he was again in 1954 and 1956). Then, on a Harvard Sheldon traveling fellowship, Dreyfus studied at the University of Freiburg from 1953 to 1954. During this time he had an interview with Martin Heidegger. Sean D. Kelly records that Dreyfus found the meeting 'disappointing.' A brief mention of it was made by Dreyfus during his 1987 BBC interview with Bryan Magee in remarks that are revealing of both his and Heidegger's opinion of the work of Jean-Paul Sartre. Between 1956 and 1957, Dreyfus undertook research at the Husserl Archives at the University of Louvain on a Fulbright Fellowship. Towards the end of his stay, his first (jointly authored) paper "Curds and Lions in Don Quijote" would appear in print. After acting as an instructor in philosophy at Brandeis University (1957–1959), he attended the Ecole Normale Supérieure, Paris, on a French government grant (1959–1960). From 1960, first as an instructor, then as an assistant and then associate professor, Dreyfus taught philosophy at the Massachusetts Institute of Technology (MIT). In 1964, with his dissertation Husserl's Phenomenology of Perception, he obtained his Ph.D. from Harvard. (Due to his knowledge of Husserl, Dagfinn Føllesdal sat on the thesis committee but he has asserted that Dreyfus "was not really my student.") That same year, his co-translation (with his first wife) of Sense and Non-Sense by Maurice Merleau-Ponty was published. Also in 1964, and whilst still at MIT, he was employed as a consultant by the RAND Corporation to review the work of Allen Newell and Herbert A. Simon in the field of artificial intelligence (AI). This resulted in the publication, in 1965, of the "famously combative" Alchemy and Artificial Intelligence, which proved to be the first of a series of papers and books attacking the AI field's claims and assumptions. The first edition of What Computers Can't Do would follow in 1972, and this critique of AI (which has been translated into at least ten languages) would establish Dreyfus's public reputation. However, as the editors of his Festschrift noted: "the study and interpretation of 'continental' philosophers... came first in the order of his philosophical interests and influences." === Berkeley === In 1968, although he had been granted tenure, Dreyfus left MIT and became an associate professor of philosophy at the University of California, Berkeley, (winning, that same year, the Harbison Prize for Outstanding Teaching). In 1972 he was promoted to full professor. Though Dreyfus retired from his chair in 1994, he continued as professor of philosophy in the Graduate School (and held, from 1999, a joint appointment in the rhetoric department). He continued to teach philosophy at UC Berkeley until his last class in December 2016. Dreyfus was elected a fellow of the American Academy of Arts and Sciences in 2001. He was also awarded an honorary doctorate for "his brilliant and highly influential work in the field of artificial intelligence" and his interpretation of twentieth century continental philosophy by Erasmus University. Dreyfus died on April 22, 2017. His younger brother and sometimes collaborator, Stuart Dreyfus, is a professor emeritus of industrial engineering and operations research at the University of California, Berkeley. == Dreyfus' criticism of AI == Dreyfus' critique of artificial intelligence (AI) concerns what he considers to be the four primary assumptions of AI research. The first two assumptions are what he calls the "biological" and "psychological" assumptions. The biological assumption is that the brain is analogous to computer hardware and the mind is analogous to computer software. The psychological assumption is that the mind works by performing discrete computations (in the form of algorithmic rules) on discrete representations or symbols. Dreyfus claims that the plausibility of the psychological assumption rests on two others: the epistemological and ontological assumptions. The epistemological assumption is that all activity (either by animate or inanimate objects) can be formalized (mathematically) in the form of predictive rules or laws. The ontological assumption is that reality consists entirely of a set of mutually independent, atomic (indivisible) facts. It's because of the epistemological assumption that workers in the field argue that intelligence is the same as formal rule-following, and it's because of the ontological one that they argue that human knowledge consists entirely of internal representations of reality. On the basis of these two assumptions, workers in the field claim that cognition is the manipulation of internal symbols by internal rules, and that, therefore, human behaviour is, to a large extent, context free (see contextualism). Therefore, a truly scientific psychology is possible, which will detail the 'internal' rules of the human mind, in the same way the laws of physics detail the 'external' laws of the physical world. However, it is this key assumption that Dreyfus denies. In other words, he argues that we cannot now (and never will be able to) understand our own behavior in the same way as we understand objects in, for example, physics or chemistry: that is, by considering ourselves as things whose behaviour can be predicted via 'objective', context free scientific laws. According to Dreyfus, a context-free psychology is a contradiction in terms. Dreyfus's arguments against this position are taken from the phenomenological and hermeneutical tradition (especially the work of Martin Heidegger). Heidegger argued that, contrary to the cognitivist views (on which AI has been based), our being is in fact highly context-bound, which is why the two context-free assumptions are false. Dreyfus doesn't deny that we can choose to see human (or any) activity as being 'law-governed', in the same way that we can choose to see reality as consisting of indivisible atomic facts... if we wish. But it is a huge leap from that to state that because we want to or can see things in this way that it is therefore an objective fact that they are the case. In fact, Dreyfus argues that they are not (necessarily) the case, and that, therefore, any research program that assumes they are will quickly run into profound theoretical and practical problems. Therefore, the current efforts of workers in the field are doomed to failure. Dreyfus argues that to get a device or devices with human-like intelligence would require them to have a human-like being-in-the-world and to have bodies more or less like ours, and social acculturation (i.e. a society) more or less like ours. (This view is shared by psychologists in the embodied psychology (Lakoff and Johnson 1999) and distributed cognition traditions. His opinions are similar to those of robotics researchers such as Rodney Brooks as well as researchers in the field of artificial life.) Contrary to a popular misconception, Dreyfus never predicted that computers would never beat humans at chess. In Alchemy and Artificial Intelligence, he only reported (correctly) the state of the art of the time: "Still no chess program can play even amateur chess." Daniel Crevier writes: "time has proven the accuracy and perceptiveness of some of Dreyfus's comments. Had he formulated them less aggressively, constructive actions they suggested might have been taken much earlier." == Webcasting philosophy == When UC Berkeley and Apple began making a selected number of lecture classes freely available to the public as podcasts beginning around 2006, a recording of Dreyfus teaching a course called "Man, God, and Society in Western Literature – From Gods to God and Back" rose to the 58th most popular webcast on iTunes. These webcasts have attracted the attention of many, including non-academics, to Dreyfus and his
Groover
Groover is an online platform, record label and distributor, connecting artists and musicians with music professionals and media outlets. The service was founded in 2018 in France and operates from offices in Paris and New York. The platform has over 3,000 active contacts, including SPIN Magazine and Sofar Sounds. Groover uses a micro-payment model. Among the platform's over 500,000 regular users are record labels such as Ninja Tune, Ba Da Bing Records, Dance To The Radio, Roche Musique, Wagram Music, Secret City Records, and artists including Bonobo, Michael Bolton, Aloe Blacc, Haddaway, Passenger, La Femme and Chinese Man. == History == Groover was launched at the MaMA Music Convention in October 2018. It was co-founded by Dorian Perron, Romain Palmieri, and Rafaël Cohen while they were students at UC Berkeley. Initially growing in France, the company has expanded to the United States, Canada, the United Kingdom, Brazil, Italy, and elsewhere in Europe. In March 2019, Groover was part of the Business France delegation at the South by Southwest (SXSW) festival. In June 2019, Groover raised €1.3 million from various angel investors. In April 2021, Groover acquired the platform Soonvibes, which had 70,000 users at the time, in order to strengthen its community in the electronic music space. In November 2021, Groover announced a €6 million funding round from Bpifrance Creative Industries and Partech. Between 2023 and 2025, Groover entered strategic partnerships with major artist service providers, including CD Baby, TuneCore, SoundCloud, UnitedMasters, Symphonic Distribution, Audiomack and SACEM. In February 2024, Groover announced a Series A funding round of $8 million from OneRagTime, Trind, Techmind, and Mozza Angels. == Function == Using a micro-payment system, professionals listen to tracks and provide written feedback. These professionals retain full editorial independence and are under no obligation to share the track or contact the artist. == Awards == 2nd Prize for Music Innovation 2023 from the Centre national de la musique (France) "Future Creator" Award at the Petit Poucet Competition 2019 Jury's Special Mention at the MaMA Invent 2019 competition 1st Prize for Digital Initiative in Culture, Communication & Media 2019 awarded by Audiens "Start-up of the Year" at the Social Music Awards 2020 French American Entrepreneurship Award 2022 at the French Consulate in New York
Simultaneous localization and mapping
Simultaneous localization and mapping (SLAM) is a process where a computer constructs or updates a map of an unknown environment while simultaneously keeping track of an entity's location within it. While this initially appears to be a chicken or the egg problem, there are several algorithms known to solve it in, at least approximately, tractable time for certain environments. Popular approximate solution methods include the particle filter, extended Kalman filter, covariance intersection, and GraphSLAM. SLAM algorithms are based on concepts in computational geometry and computer vision, and are used in robot navigation, robotic mapping and odometry for virtual reality or augmented reality. SLAM algorithms are tailored to the available resources and are not aimed at perfection but at operational compliance. Published approaches are employed in self-driving cars, unmanned aerial vehicles, autonomous underwater vehicles, planetary rovers, newer domestic robots and even inside the human body. == Mathematical description of the problem == Given a series of controls u t {\displaystyle u_{t}} and sensor observations o t {\displaystyle o_{t}} over discrete time steps t {\displaystyle t} , the SLAM problem is to compute an estimate of the agent's state x t {\displaystyle x_{t}} and a map of the environment m t {\displaystyle m_{t}} . All quantities are usually probabilistic, so the objective is to compute P ( m t + 1 , x t + 1 | o 1 : t + 1 , u 1 : t ) {\displaystyle P(m_{t+1},x_{t+1}|o_{1:t+1},u_{1:t})} Applying Bayes' rule gives a framework for sequentially updating the location posteriors, given a map and a transition function P ( x t | x t − 1 ) {\displaystyle P(x_{t}|x_{t-1})} , P ( x t | o 1 : t , u 1 : t , m t ) = ∑ m t − 1 P ( o t | x t , m t , u 1 : t ) ∑ x t − 1 P ( x t | x t − 1 ) P ( x t − 1 | m t , o 1 : t − 1 , u 1 : t ) / Z {\displaystyle P(x_{t}|o_{1:t},u_{1:t},m_{t})=\sum _{m_{t-1}}P(o_{t}|x_{t},m_{t},u_{1:t})\sum _{x_{t-1}}P(x_{t}|x_{t-1})P(x_{t-1}|m_{t},o_{1:t-1},u_{1:t})/Z} where Z {\displaystyle Z} is the normalization constant, which ensures all the probabilities sum up to 1. Similarly the map can be updated sequentially by P ( m t | x t , o 1 : t , u 1 : t ) = ∑ x t ∑ m t P ( m t | x t , m t − 1 , o t , u 1 : t ) P ( m t − 1 , x t | o 1 : t − 1 , m t − 1 , u 1 : t ) {\displaystyle P(m_{t}|x_{t},o_{1:t},u_{1:t})=\sum _{x_{t}}\sum _{m_{t}}P(m_{t}|x_{t},m_{t-1},o_{t},u_{1:t})P(m_{t-1},x_{t}|o_{1:t-1},m_{t-1},u_{1:t})} Like many inference problems, the solutions to inferring the two variables together can be found, to a local optimum solution, by alternating updates of the two beliefs in a form of an expectation–maximization algorithm. == Algorithms == Statistical techniques used to approximate the above equations include Kalman filters and particle filters (the algorithm behind Monte Carlo Localization). They provide an estimation of the posterior probability distribution for the pose of the robot and for the parameters of the map. Methods which conservatively approximate the above model using covariance intersection are able to avoid reliance on statistical independence assumptions to reduce algorithmic complexity for large-scale applications. Other approximation methods achieve improved computational efficiency by using simple bounded-region representations of uncertainty. Set-membership techniques are mainly based on interval constraint propagation. They provide a set which encloses the pose of the robot and a set approximation of the map. Bundle adjustment, and more generally maximum a posteriori estimation (MAP), is another popular technique for SLAM using image data, which jointly estimates poses and landmark positions, increasing map fidelity, and is used in commercialized SLAM systems such as Google's ARCore which replaces their prior augmented reality computing platform named Tango, formerly Project Tango. MAP estimators compute the most likely explanation of the robot poses and the map given the sensor data, rather than trying to estimate the entire posterior probability. New SLAM algorithms remain an active research area, and are often driven by differing requirements and assumptions about the types of maps, sensors and models as detailed below. Many SLAM systems can be viewed as combinations of choices from each of these aspects. === Mapping === Topological maps are a method of environment representation which capture the connectivity (i.e., topology) of the environment rather than creating a geometrically accurate map. Topological SLAM approaches have been used to enforce global consistency in metric SLAM algorithms. In contrast, grid maps use arrays (typically square or hexagonal) of discretized cells to represent a topological world, and make inferences about which cells are occupied. Typically the cells are assumed to be statistically independent to simplify computation. Under such assumption, P ( m t | x t , m t − 1 , o t ) {\displaystyle P(m_{t}|x_{t},m_{t-1},o_{t})} are set to 1 if the new map's cells are consistent with the observation o t {\displaystyle o_{t}} at location x t {\displaystyle x_{t}} and 0 if inconsistent. Modern self driving cars mostly simplify the mapping problem to almost nothing, by making extensive use of highly detailed map data collected in advance. This can include map annotations to the level of marking locations of individual white line segments and curbs on the road. Location-tagged visual data such as Google's StreetView may also be used as part of maps. Essentially such systems simplify the SLAM problem to a simpler localization only task, perhaps allowing for moving objects such as cars and people only to be updated in the map at runtime. === Sensing === SLAM will always use several different types of sensors, and the powers and limits of various sensor types have been a major driver of new algorithms. Statistical independence is the mandatory requirement to cope with metric bias and with noise in measurements. Different types of sensors give rise to different SLAM algorithms which assumptions are most appropriate to the sensors. At one extreme, laser scans or visual features provide details of many points within an area, sometimes rendering SLAM inference unnecessary because shapes in these point clouds can be easily and unambiguously aligned at each step via image registration. At the opposite extreme, tactile sensors are extremely sparse as they contain only information about points very close to the agent, so they require strong prior models to compensate in purely tactile SLAM. Most practical SLAM tasks fall somewhere between these visual and tactile extremes. Sensor models divide broadly into landmark-based and raw-data approaches. Landmarks are uniquely identifiable objects in the world which location can be estimated by a sensor, such as Wi-Fi access points or radio beacons. Raw-data approaches make no assumption that landmarks can be identified, and instead model P ( o t | x t ) {\displaystyle P(o_{t}|x_{t})} directly as a function of the location. Optical sensors may be one-dimensional (single beam) or 2D- (sweeping) laser rangefinders, 3D high definition light detection and ranging (lidar), 3D flash lidar, 2D or 3D sonar sensors, and one or more 2D cameras. Since the invention of local features, such as SIFT, there has been intense research into visual SLAM (VSLAM) using primarily visual (camera) sensors, because of the increasing ubiquity of cameras such as those in mobile devices. Follow up research includes. Both visual and lidar sensors are informative enough to allow for landmark extraction in many cases. Other recent forms of SLAM include tactile SLAM (sensing by local touch only), radar SLAM, acoustic SLAM, and Wi-Fi-SLAM (sensing by strengths of nearby Wi-Fi access points). Recent approaches apply quasi-optical wireless ranging for multi-lateration (real-time locating system (RTLS)) or multi-angulation in conjunction with SLAM as a tribute to erratic wireless measures. A kind of SLAM for human pedestrians uses a shoe mounted inertial measurement unit as the main sensor and relies on the fact that pedestrians are able to avoid walls to automatically build floor plans of buildings by an indoor positioning system. For some outdoor applications, the need for SLAM has been almost entirely removed due to high precision differential GPS sensors. From a SLAM perspective, these may be viewed as location sensors which likelihoods are so sharp that they completely dominate the inference. However, GPS sensors may occasionally decline or go down entirely, e.g. during times of military conflict, which are of particular interest to some robotics applications. === Kinematics modeling === The P ( x t | x t − 1 ) {\displaystyle P(x_{t}|x_{t-1})} term represents the kinematics of the model, which usually include information about action commands given to a robot. As a part of the model, the kinematics of the robot is included, to improve estimates of sensing under con