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  Software development process

  A software development process prescribes a process for developing software. It typically divides an overall effort into smaller steps or sub-processes that are intended to ensure high-quality results. The process may describe specific deliverables – artifacts to be created and completed. Although not strictly limited to it, software development process often refers to the high-level process that governs the development of a software system from its beginning to its end of life – known as a methodology, model or framework. The system development life cycle (SDLC) describes the typical phases that a development effort goes through from the beginning to the end of life for a system – including a software system. A methodology prescribes how engineers go about their work in order to move the system through its life cycle. A methodology is a classification of processes or a blueprint for a process that is devised for the SDLC. For example, many processes can be classified as a spiral model. Software process and software quality are closely interrelated; some unexpected facets and effects have been observed in practice. == Methodology == The SDLC drives the definition of a methodology in that a methodology must address the phases of the SDLC. Generally, a methodology is designed to result in a high-quality system that meets or exceeds expectations (requirements) and is delivered on time and within budget even though computer systems can be complex and integrate disparate components. Various methodologies have been devised, including waterfall, spiral, agile, rapid prototyping, incremental, and synchronize and stabilize. A major difference between methodologies is the degree to which the phases are sequential vs. iterative. Agile methodologies, such as XP and scrum, focus on lightweight processes that allow for rapid changes. Iterative methodologies, such as Rational Unified Process and dynamic systems development method, focus on stabilizing project scope and iteratively expanding or improving products. Sequential or big-design-up-front (BDUF) models, such as waterfall, focus on complete and correct planning to guide larger projects and limit risks to successful and predictable results. Anamorphic development is guided by project scope and adaptive iterations. In scrum, for example, one could say a single user story goes through all the phases of the SDLC within a two-week sprint. By contrast the waterfall methodology, where every business requirement is translated into feature/functional descriptions which are then all implemented typically over a period of months or longer. A project can include both a project life cycle (PLC) and an SDLC, which describe different activities. According to Taylor (2004), "the project life cycle encompasses all the activities of the project, while the systems development life cycle focuses on realizing the product requirements". === History === The term SDLC is often used as an abbreviated version of SDLC methodology. Further, some use SDLC and traditional SDLC to mean the waterfall methodology. According to Elliott (2004), SDLC "originated in the 1960s, to develop large scale functional business systems in an age of large scale business conglomerates. Information systems activities revolved around heavy data processing and number crunching routines". The structured systems analysis and design method (SSADM) was produced for the UK government Office of Government Commerce in the 1980s. Ever since, according to Elliott (2004), "the traditional life cycle approaches to systems development have been increasingly replaced with alternative approaches and frameworks, which attempted to overcome some of the inherent deficiencies of the traditional SDLC". The main idea of the SDLC has been "to pursue the development of information systems in a very deliberate, structured and methodical way, requiring each stage of the life cycle––from the inception of the idea to delivery of the final system––to be carried out rigidly and sequentially" within the context of the framework being applied. Other methodologies were devised later: 1970s Structured programming since 1969 Cap Gemini SDM, originally from PANDATA, the first English translation was published in 1974. SDM stands for System Development Methodology 1980s Structured systems analysis and design method (SSADM) from 1980 onwards Information Requirement Analysis/Soft systems methodology 1990s Object-oriented programming (OOP) developed in the early 1960s and became a dominant programming approach during the mid-1990s Rapid application development (RAD), since 1991 Dynamic systems development method (DSDM), since 1994 Scrum, since 1995 Team software process, since 1998 Rational Unified Process (RUP), maintained by IBM since 1998 Extreme programming, since 1999 2000s Agile Unified Process (AUP) maintained since 2005 by Scott Ambler Disciplined agile delivery (DAD) Supersedes AUP 2010s Scaled Agile Framework (SAFe) Large-Scale Scrum (LeSS) DevOps Since DSDM in 1994, all of the methodologies on the above list except RUP have been agile methodologies - yet many organizations, especially governments, still use pre-agile processes (often waterfall or similar). === Examples === The following are notable methodologies somewhat ordered by popularity. Agile Agile software development refers to a group of frameworks based on iterative development, where requirements and solutions evolve via collaboration between self-organizing cross-functional teams. The term was coined in the year 2001 when the Agile Manifesto was formulated. Waterfall The waterfall model is a sequential development approach, in which development flows one-way (like a waterfall) through the SDLC phases. Spiral In 1988, Barry Boehm published a software system development spiral model, which combines key aspects of the waterfall model and rapid prototyping, in an effort to combine advantages of top-down and bottom-up concepts. It emphases a key area many felt had been neglected by other methodologies: deliberate iterative risk analysis, particularly suited to large-scale complex systems. Incremental Various methods combine linear and iterative methodologies, with the primary objective of reducing inherent project risk by breaking a project into smaller segments and providing more ease-of-change during the development process. Prototyping Software prototyping is about creating prototypes, i.e. incomplete versions of the software program being developed. Rapid Rapid application development (RAD) is a methodology which favors iterative development and the rapid construction of prototypes instead of large amounts of up-front planning. The "planning" of software developed using RAD is interleaved with writing the software itself. The lack of extensive pre-planning generally allows software to be written much faster and makes it easier to change requirements. Shape Up Shape Up is a software development approach introduced by Basecamp in 2018. It is a set of principles and techniques that Basecamp developed internally to overcome the problem of projects dragging on with no clear end. Its primary target audience is remote teams. Shape Up has no estimation and velocity tracking, backlogs, or sprints, unlike waterfall, agile, or scrum. Instead, those concepts are replaced with appetite, betting, and cycles. As of 2022, besides Basecamp, notable organizations that have adopted Shape Up include UserVoice and Block. Chaos Chaos model has one main rule: always resolve the most important issue first. Incremental funding Incremental funding methodology - an iterative approach. Lightweight Lightweight methodology - a general term for methods that only have a few rules and practices. Structured systems analysis and design Structured systems analysis and design method - a specific version of waterfall. Slow programming As part of the larger slow movement, emphasizes careful and gradual work without (or minimal) time pressures. Slow programming aims to avoid bugs and overly quick release schedules. V-Model V-Model (software development) - an extension of the waterfall model. Unified Process Unified Process (UP) is an iterative software development methodology framework, based on Unified Modeling Language (UML). UP organizes the development of software into four phases, each consisting of one or more executable iterations of the software at that stage of development: inception, elaboration, construction, and guidelines. === Comparison === The waterfall model describes the SDLC phases such that each builds on the result of the previous one. Not every project requires that the phases be sequential. For relatively simple projects, phases may be combined or overlapping. Alternative methodologies to waterfall are described and compared below. == Process meta-models == Some process models are abstract descriptions for evaluating, comparing, and improving the specific process adopted by an organization. ISO/IEC 12207 ISO/IEC 12207 i

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  Avid Symphony

  Avid Symphony is non-linear editing software aimed at professionals in the film and television industry. It is available for Microsoft Windows PCs and Apple Macintosh platforms. Symphony is Avid's high end SD/HD finishing platform for long form work, such as documentary and episodic TV. Its interface is based on the same look and feature set as the Media Composer and Xpress systems, but contains the highest level of features and resolution including secondary color correction, uncompressed HD, and higher real-time performance. == Release history == Symphony is the software component of a tightly integrated package that includes specific hardware audio/video interfaces, storage, and the computer, also sold by Avid. Its release history is therefore tightly related to the release of new Avid interface hardware: Symphony was introduced to the market in 1998. It was based on Avid's Meridien hardware, supporting SD only, and was available first only for the PC and later for the Macintosh platforms. Its last release was 5.0.5 which supported Windows 2000 and Mac OS X v10.2. The next major upgrade was Symphony Nitris in 2005, with a redesigned software and integration with the Nitris DNA hardware (PCI-X). It supported 8 bit and 10 bit SD and HD resolutions in both compressed and uncompressed forms, the MXF format and DNxHD codec, and ran only on Windows PC platforms. Symphony Nitris DX, released in 2008, added support for a range of HD codecs, including HDV, XDCAM-HD, DVCPRO HD, and AVC-I, and brought back Mac OS support for OS X 10.5, as well as Windows Vista. Since the introduction of Symphony 6, it can be used in software-only mode (where a Nitris or Nitris DX BOB used to be required), and at the same time, like Media Composer, Symphony was opened up with "Open I/O", allowing users to have Symphony use their third party hardware from companies like AJA, Matrox, BlueFish, Blackmagic Design and MOTU. The last remaining features that differentiate it from Media Composer are Advanced Color Correction (channels, secondary color correction,), Relational Color Correction (corrections based on common clip name, tape name, program track) and Universal HD Mastering (only with Nitris DX hardware). The latter allows cross-conversions of 23.976p or 24p projects sequences to most any other format during Digital Cut. In 2013, Avid announced it would no longer offer Symphony a standalone product. Starting version 7, Symphony will be sold as an option to Media Composer. This optional package (sold at a premium) will contain all the traditional Symphony-only features to any Media Composer install. == Use in movies == The Celibacy, Director: Horacio Bocaranda Avid Media Composer 6 and Avid Symphony 6 Nitris DX American Hardcore, Director: Paul Rachman Avid Xpress Pro and Symphony Summercamp!, Director: Spike Lee Avid Xpress Pro and Symphony When the Levees Broke Avid Media Composer and Symphony Nitris Superman Returns Edited with Mac-based Film Composer XL, but HD screenings prepped with Symphony

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  Spectral shape analysis

  Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under isometries, it is well suited for the analysis or retrieval of non-rigid shapes, i.e. bendable objects such as humans, animals, plants, etc. == Laplace == The Laplace–Beltrami operator is involved in many important differential equations, such as the heat equation and the wave equation. It can be defined on a Riemannian manifold as the divergence of the gradient of a real-valued function f: Δ f := div ⁡ grad ⁡ f . {\displaystyle \Delta f:=\operatorname {div} \operatorname {grad} f.} Its spectral components can be computed by solving the Helmholtz equation (or Laplacian eigenvalue problem): Δ φ i + λ i φ i = 0. {\displaystyle \Delta \varphi _{i}+\lambda _{i}\varphi _{i}=0.} The solutions are the eigenfunctions φ i {\displaystyle \varphi _{i}} (modes) and corresponding eigenvalues λ i {\displaystyle \lambda _{i}} , representing a diverging sequence of positive real numbers. The first eigenvalue is zero for closed domains or when using the Neumann boundary condition. For some shapes, the spectrum can be computed analytically (e.g. rectangle, flat torus, cylinder, disk or sphere). For the sphere, for example, the eigenfunctions are the spherical harmonics. The most important properties of the eigenvalues and eigenfunctions are that they are isometry invariants. In other words, if the shape is not stretched (e.g. a sheet of paper bent into the third dimension), the spectral values will not change. Bendable objects, like animals, plants and humans, can move into different body postures with only minimal stretching at the joints. The resulting shapes are called near-isometric and can be compared using spectral shape analysis. == Discretizations == Geometric shapes are often represented as 2D curved surfaces, 2D surface meshes (usually triangle meshes) or 3D solid objects (e.g. using voxels or tetrahedra meshes). The Helmholtz equation can be solved for all these cases. If a boundary exists, e.g. a square, or the volume of any 3D geometric shape, boundary conditions need to be specified. Several discretizations of the Laplace operator exist (see Discrete Laplace operator) for the different types of geometry representations. Many of these operators do not approximate well the underlying continuous operator. == Spectral shape descriptors == === ShapeDNA and its variants === The ShapeDNA is one of the first spectral shape descriptors. It is the normalized beginning sequence of the eigenvalues of the Laplace–Beltrami operator. Its main advantages are the simple representation (a vector of numbers) and comparison, scale invariance, and in spite of its simplicity a very good performance for shape retrieval of non-rigid shapes. Competitors of shapeDNA include singular values of Geodesic Distance Matrix (SD-GDM) and Reduced BiHarmonic Distance Matrix (R-BiHDM). However, the eigenvalues are global descriptors, therefore the shapeDNA and other global spectral descriptors cannot be used for local or partial shape analysis. === Global point signature (GPS) === The global point signature at a point x {\displaystyle x} is a vector of scaled eigenfunctions of the Laplace–Beltrami operator computed at x {\displaystyle x} (i.e. the spectral embedding of the shape). The GPS is a global feature in the sense that it cannot be used for partial shape matching. === Heat kernel signature (HKS) === The heat kernel signature makes use of the eigen-decomposition of the heat kernel: h t ( x , y ) = ∑ i = 0 ∞ exp ⁡ ( − λ i t ) φ i ( x ) φ i ( y ) . {\displaystyle h_{t}(x,y)=\sum _{i=0}^{\infty }\exp(-\lambda _{i}t)\varphi _{i}(x)\varphi _{i}(y).} For each point on the surface the diagonal of the heat kernel h t ( x , x ) {\displaystyle h_{t}(x,x)} is sampled at specific time values t j {\displaystyle t_{j}} and yields a local signature that can also be used for partial matching or symmetry detection. === Wave kernel signature (WKS) === The WKS follows a similar idea to the HKS, replacing the heat equation with the Schrödinger wave equation. === Improved wave kernel signature (IWKS) === The IWKS improves the WKS for non-rigid shape retrieval by introducing a new scaling function to the eigenvalues and aggregating a new curvature term. === Spectral graph wavelet signature (SGWS) === SGWS is a local descriptor that is not only isometric invariant, but also compact, easy to compute and combines the advantages of both band-pass and low-pass filters. An important facet of SGWS is the ability to combine the advantages of WKS and HKS into a single signature, while allowing a multiresolution representation of shapes. == Spectral Matching == The spectral decomposition of the graph Laplacian associated with complex shapes (see Discrete Laplace operator) provides eigenfunctions (modes) which are invariant to isometries. Each vertex on the shape could be uniquely represented with a combinations of the eigenmodal values at each point, sometimes called spectral coordinates: s ( x ) = ( φ 1 ( x ) , φ 2 ( x ) , … , φ N ( x ) ) for vertex x . {\displaystyle s(x)=(\varphi _{1}(x),\varphi _{2}(x),\ldots ,\varphi _{N}(x)){\text{ for vertex }}x.} Spectral matching consists of establishing the point correspondences by pairing vertices on different shapes that have the most similar spectral coordinates. Early work focused on sparse correspondences for stereoscopy. Computational efficiency now enables dense correspondences on full meshes, for instance between cortical surfaces. Spectral matching could also be used for complex non-rigid image registration, which is notably difficult when images have very large deformations. Such image registration methods based on spectral eigenmodal values indeed capture global shape characteristics, and contrast with conventional non-rigid image registration methods which are often based on local shape characteristics (e.g., image gradients).

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  Rapid prototyping

  Rapid prototyping is a group of techniques used to quickly fabricate a scale model of a physical part or assembly using three-dimensional computer aided design (CAD) data. Construction of the part or assembly is usually done using 3D printing or "additive layer manufacturing" technology. The first methods for rapid prototyping became available in mid 1987 and were used to produce models and prototype parts. Today, they are used for a wide range of applications and are used to manufacture production-quality parts in relatively small numbers if desired without the typical unfavorable short-run economics. This economy has encouraged online service bureaus. Historical surveys of RP technology start with discussions of simulacra production techniques used by 19th-century sculptors. Some modern sculptors use the progeny technology to produce exhibitions and various objects. The ability to reproduce designs from a dataset has given rise to issues of rights, as it is now possible to interpolate volumetric data from 2D images. As with CNC subtractive methods, the computer-aided-design – computer-aided manufacturing CAD -CAM workflow in the traditional rapid prototyping process starts with the creation of geometric data, either as a 3D solid using a CAD workstation, or 2D slices using a scanning device. For rapid prototyping this data must represent a valid geometric model; namely, one whose boundary surfaces enclose a finite volume, contain no holes exposing the interior, and do not fold back on themselves. In other words, the object must have an "inside". The model is valid if for each point in 3D space the computer can determine uniquely whether that point lies inside, on, or outside the boundary surface of the model. CAD post-processors will approximate the application vendors' internal CAD geometric forms (e.g., B-splines) with a simplified mathematical form, which in turn is expressed in a specified data format which is a common feature in additive manufacturing: STL file format, a de facto standard for transferring solid geometric models to SFF machines. To obtain the necessary motion control trajectories to drive the actual SFF, rapid prototyping, 3D printing or additive manufacturing mechanism, the prepared geometric model is typically sliced into layers, and the slices are scanned into lines (producing a "2D drawing" used to generate trajectory as in CNC's toolpath), mimicking in reverse the layer-to-layer physical building process. == Application areas == Rapid prototyping is also commonly applied in software engineering to try out new business models and application architectures such as Aerospace, Automotive, Financial Services, Product development, and Healthcare. Aerospace design and industrial teams rely on prototyping in order to create new AM methodologies in the industry. Using SLA they can quickly make multiple versions of their projects in a few days and begin testing quicker. Rapid Prototyping allows designers/developers to provide an accurate idea of how the finished product will turn out before putting too much time and money into the prototype. 3D printing being used for Rapid Prototyping allows for Industrial 3D printing to take place. With this, you could have large-scale moulds to spare parts being pumped out quickly within a short period of time. == Types of Rapid Prototyping == Stereolithography (SLA) → a laser-cured photopolymer for materials such as thermoplastic-like photopolymers. Selective Laser Sintering (SLS) → a laser-sintered powder for materials such as Nylon or TPU. Direct Metal Laser Sintering (DMLS) → laser-sintered metal powder for materials like stainless steel, titanium, chrome, and aluminum. Fused Deposition Modeling (FDM) → fused extrusions of filaments like ABS, PC, and PPCU. Multi Jet Fusion (MJF) → it is an inkjet array selective fusing across bed of nylon powder for Black Nylon 12. PolyJet (PJET) → it is a uv-cured jetted photopolymer to work with acrylic-based and elastomeric photopolymers. Computer Numerical Controlled Machine (CNC) → it is used for manipulating engineering-grade thermoplastics and metals. Injection Molding (IM) → the injection is done using aluminum molds and it is used for thermoplastics, metals and liquid silicone rubber. Vacuum Casting→ is a manufacturing process used to create high-quality prototypes and small batches of parts. == History == In the 1970s, Joseph Henry Condon and others at Bell Labs developed the Unix Circuit Design System (UCDS), automating the laborious and error-prone task of manually converting drawings to fabricate circuit boards for the purposes of research and development. By the 1980s, U.S. policy makers and industrial managers were forced to take note that America's dominance in the field of machine tool manufacturing evaporated, in what was named the machine tool crisis. Numerous projects sought to counter these trends in the traditional CNC CAM area, which had begun in the US. Later when Rapid Prototyping Systems moved out of labs to be commercialized, it was recognized that developments were already international and U.S. rapid prototyping companies would not have the luxury of letting a lead slip away. The National Science Foundation was an umbrella for the National Aeronautics and Space Administration (NASA), the US Department of Energy, the US Department of Commerce NIST, the US Department of Defense, Defense Advanced Research Projects Agency (DARPA), and the Office of Naval Research coordinated studies to inform strategic planners in their deliberations. One such report was the 1997 Rapid Prototyping in Europe and Japan Panel Report in which Joseph J. Beaman founder of DTM Corporation [DTM RapidTool pictured] provides a historical perspective: The roots of rapid prototyping technology can be traced to practices in topography and photosculpture. Within TOPOGRAPHY Blanther (1892) suggested a layered method for making a mold for raised relief paper topographical maps .The process involved cutting the contour lines on a series of plates which were then stacked. Matsubara (1974) of Mitsubishi proposed a topographical process with a photo-hardening photopolymer resin to form thin layers stacked to make a casting mold. PHOTOSCULPTURE was a 19th-century technique to create exact three-dimensional replicas of objects. Most famously Francois Willeme (1860) placed 24 cameras in a circular array and simultaneously photographed an object. The silhouette of each photograph was then used to carve a replica. Morioka (1935, 1944) developed a hybrid photo sculpture and topographic process using structured light to photographically create contour lines of an object. The lines could then be developed into sheets and cut and stacked, or projected onto stock material for carving. The Munz (1956) Process reproduced a three-dimensional image of an object by selectively exposing, layer by layer, a photo emulsion on a lowering piston. After fixing, a solid transparent cylinder contains an image of the object. "The Origins of Rapid Prototyping - RP stems from the ever-growing CAD industry, more specifically, the solid modeling side of CAD. Before solid modeling was introduced in the late 1980's, three-dimensional models were created with wire frames and surfaces. But not until the development of true solid modeling could innovative processes such as RP be developed. Charles Hull, who helped found 3D Systems in 1986, developed the first RP process. This process, called stereolithography, builds objects by curing thin consecutive layers of certain ultraviolet light-sensitive liquid resins with a low-power laser. With the introduction of RP, CAD solid models could suddenly come to life". The technologies referred to as Solid Freeform Fabrication are what we recognize today as rapid prototyping, 3D printing or additive manufacturing: Swainson (1977), Schwerzel (1984) worked on polymerization of a photosensitive polymer at the intersection of two computer controlled laser beams. Ciraud (1972) considered magnetostatic or electrostatic deposition with electron beam, laser or plasma for sintered surface cladding. These were all proposed but it is unknown if working machines were built. Hideo Kodama of Nagoya Municipal Industrial Research Institute was the first to publish an account of a solid model fabricated using a photopolymer rapid prototyping system (1981). The first 3D rapid prototyping system relying on Fused Deposition Modeling (FDM) was made in April 1992 by Stratasys but the patent did not issue until June 9, 1992. Sanders Prototype, Inc introduced the first desktop inkjet 3D Printer (3DP) using an invention from August 4, 1992 (Helinski), Modelmaker 6Pro in late 1993 and then the larger industrial 3D printer, Modelmaker 2, in 1997. Z-Corp using the MIT 3DP powder binding for Direct Shell Casting (DSP) invented 1993 was introduced to the market in 1995. Even at that early date the technology was seen as having a place in manufacturing practice. A low resol

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  GasBuddy

  GasBuddy is a technology company headquartered in Dallas, United States, that offers mobile applications and websites for tracking crowd-sourced locations and prices of gas stations and convenience stores in the United States and Canada. Their platforms offer information sourced from users, gas station operators, and partner companies. They also provide business-to-business services to gas stations and convenience store owners. == History == GasBuddy was founded in Minneapolis in 2000 by Dustin Coupal, Jason Toews as a community website for sharing gas prices. In 2004, they filed as a for-profit corporation in Minnesota under the name GasBuddy Organization Inc. In 2009, GasBuddy launched OpenStore, a platform that allows convenience stores to build and manage their own mobile apps. In 2010, the company launched its own mobile apps that allowed users to input gas prices from their smartphones. In 2013, Oil Price Information Service (OPIS), a subsidiary of UCG, acquired GasBuddy. OPIS is a provider of petroleum pricing and news for businesses. In 2016, IHS acquired OPIS, separating from GasBuddy, which remained with UCG as a subsidiary company. Initially only available in the United States and Canada, GasBuddy launched in Australia in March 2016. Also in that year, GasBuddy released a completely redesigned app, its first major redesign since its release in 2010. GasBuddy also unveiled a new logo and launched GasBuddy Business Pages. GasBuddy shut down the Australian version of their app in 2022. In 2017, GasBuddy launched a gas savings program titled "Pay with GasBuddy" intended to let consumers save at gas stations in the United States. In the same year, GasBuddy was involved in a lawsuit with Reveal Mobile, a location-based marketing company, over the sale of user location data. It was revealed that GasBuddy sold information on more than 4.5 million users to Reveal each month for $9.50 per 1000 users. According to CNET, that information included "users' latitude, longitude, IP address, and time stamps on the data collected," which sparked concern in the media and between its users. In 2021, the GasBuddy app rose to the most popular app on both Android and iPhone platforms in the wake of the Colonial Pipeline ransomware attack PDI acquired GasBuddy in 2021.

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  Quantum robotics

  Quantum robotics is an interdisciplinary field that investigates the intersection of robotics and quantum mechanics. This field, in particular, explores the applications of quantum phenomena such as quantum entanglement within the realm of robotics. Examples of its applications include quantum communication in multi-agent cooperative robotic scenarios, the use of quantum algorithms in performing robotics tasks, and the integration of quantum devices (e.g., quantum detectors) in robotic systems. == Introduction == The free-space quantum communication between mobile platforms was proposed for reconfigurable quantum key distribution (QKD) applications using unmanned aerial vehicle (UAVs, a.k.a. drones) in 2017. This technology was later advanced in various aspects in mobile drone and vehicle platforms in several configurations such as drone-to-drone, drone-to-moving vehicle, and vehicle-to-vehicle systems. Some research has contributed to low-size, low-weight, and low-power quantum key distribution systems for small-form UAVs, the characterization of a polarization-based receiver for mobile free-space optical QKD, and optical-relayed entanglement distribution using drones as mobile nodes. The topic of free-space quantum communication between mobile platforms, initially developed to meet the need for free-space QKD and entanglement distribution using mobile nodes, was brought into the robotics domain as an emerging interdisciplinary mechatronics topic to investigate the interface between quantum technologies and the robotic systems domain. The main advantage of such integrated technology is the guaranteed security in communication between multi-agent and cooperative autonomous systems. Other advances are anticipated. == Quantum entanglement == According to quantum mechanics, entanglement occurs when more than one particle become connected. If the state of one particle changes then it will instantly change the state of other particles regardless of their distance. Entangled sensors do the same kind of work and achieve strong sensitivity. A group of quantum robots can measure magnetic fields, gravitational fields and other physical properties using entangled sensors with high rate of accuracy. Again the connection of one robot to other is increased (become strong) by quantum entanglement. == Quantum teleportation == Quantum teleportation is the transfer of quantum information (not physical objects). This is used in case of multi robot process. One robot is programmed with a complex quantum update. Then that robot can teleport that complex quantum information (the update) to other robots. This teleportation or communication is very secure because all the work is done in quantum state. == Kinematics == Quantum computing has been proposed as being optimal for calculating inverse kinematics values. == Alice and Bob robots == In the realm of quantum mechanics, the names Alice and Bob are frequently employed to illustrate various phenomena, protocols, and applications. These include their roles in QKD, quantum cryptography, entanglement, and teleportation. The terms "Alice Robot" and "Bob Robot" serve as analogous expressions that merge the concepts of Alice and Bob from quantum mechanics with mechatronic mobile platforms (such as robots, drones, and autonomous vehicles). For example, the Alice Robot functions as a transmitter platform that communicates with the Bob Robot, housing the receiving detectors.

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  Affinity (software)

  Affinity is a graphics editor developed by Serif, a subsidiary of Canva. It is simultaneously a vector graphics editor, a raster graphics editor and a desktop publishing application. It was first released in 2025 as a successor to Serif's Affinity Designer, Affinity Photo and Affinity Publisher, uniting the three editors into one application. While the previous versions competed individually against Adobe's Illustrator, Photoshop, and InDesign, Affinity 3.0 integrates their functionality into a single application. It uses a freemium model monetized by AI features exclusive to Canva Pro subscribers. == Functionality == Affinity is divided into a number of workspaces ("studios"), which are equivalent to the previous suite of Affinity applications: "vector" for vector graphics (Designer), "pixel" for raster editing (Photo), and "layout" for desktop publishing (Publisher). Additionally, it introduces the ability to create custom workspaces. The application supports real-time previews and non-destructive editing, which are based on GPU acceleration. Supported file formats include Adobe Photoshop, InDesign and Illustrator files, PDF, SVG, and TIFF, as well as a custom .af file format. === Vector editing === === Raster editing === Affinity includes photo editing tools including adjustments, masks, blend modes, batch processing, and retouching facilities. Additionally, the application can develop RAW files, similar to Adobe Lightroom. === Desktop publishing === Publishing features include master pages, text styles, and advanced typography. === AI features === The application supports Canva's existing AI features, such as background removal and generative fill. This requires a Canva subscription. == Development == === Background and acquisition (2014–2024) === Serif launched the original Affinity suite starting with Affinity Designer in 2014, followed by Photo (2015) and Publisher (2019). The software gained popularity for its one-time purchase model, contrasting with Adobe's subscription-based Creative Cloud. In November 2022, Serif released Version 2 of the suite, introducing a "Universal License" that covered all three apps across all platforms. In March 2024, Canva acquired Serif for approximately A$580 million (£300 million). Following user backlash regarding a potential shift to subscriptions, Canva and Serif issued a joint "Pledge" committing to four key principles: fair pricing, no mandatory subscriptions, perpetual licenses for existing products, and continued development of Affinity as a standalone suite. === Unified release (2025) === In September 2025, Serif pulled all existing versions of Affinity Designer, Affinity Photo and Affinity Publisher from sale ahead an upcoming announcement on 30 October; also ahead of the announcement, the iPadOS versions of the Affinity suite became free on App Store. During a "Creative Freedom" keynote on 30 October 2025, Canva released a new version now simply branded as "Affinity" (also known as "Affinity by Canva"), and referred to internally as version 3.0. Version 3 drops the separate applications and integrates their functionality into a singular application, and adds the ability to export directly to the Canva platform. It also adds a Canva AI studio, including background removal, "Expand & Edit", and generative fill. As of version 3, Affinity has switched to a freemium model; it is now available at no charge to users, although access to Canva AI features are locked behind the existing Canva Pro subscription service. Serif stated that the perpetually-licensed version 2 will remain available to existing owners, although it will no longer be actively maintained. The new version is currently available for macOS and Windows only, with an iPadOS version to be released soon. == Reception == The change in business model by Canva in 2025 was met with mixed reception, including concerns about its incorporation of AI features. Some users were concerned that their projects would be used for machine learning purposes, or that future versions would suffer from a lack of maintenance or become adware. Additionally, some felt it turned Affinity into fundamentally subscription-based software, given the prevalence of these features in professional contexts. Affinity publicly stated on social media that it would remain "free forever", users' projects would not be used to train AI models, and that "Canva has built a sustainable business model that allows this kind of generosity. And when more professionals use Affinity, Canva can sell more seats into businesses."

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  Group of Governmental Experts on Lethal Autonomous Weapons Systems

  The Group of Governmental Experts on Lethal Autonomous Weapons Systems, commonly known as the GGE on LAWS, refers to a group of governmental experts established under the framework of the Convention on Certain Conventional Weapons (CCW), a United Nations arms control framework. The group examines legal, ethical, societal and moral questions that arise from the increased use of autonomous robots to carry weapons and to be programmed to engage in combat in various situations that might arise, including battles between countries, or in patrolling border areas or sensitive areas, or other similar roles. As of 18 March 2025, the Convention on Certain Conventional Weapons had 128 High Contracting Parties. In the Geneva Conventions, the term "High Contracting Parties" refers to the states that have joined the conventions and are therefore bound to uphold them. Among the countries that have joined are states with tense relations or ongoing armed conflict with one another, including Russia and Ukraine, Israel and the State of Palestine, and Pakistan and Afghanistan. == Background == In 2013, the Meeting of State Parties to the Convention on Certain Conventional Weapons agreed on a mandate on lethal autonomous weapon systems and tasked its chairperson with convening an informal Meeting of Experts to discuss issues related to emerging technologies in the area of LAWS. Those informal Meetings of Experts were then held in 2014, 2015 and 2016, and their reports fed into subsequent meetings of the High Contracting Parties. At the Fifth CCW Review Conference in 2016, the High Contracting Parties decided to establish an open-ended Group of Governmental Experts on emerging technologies in the area of LAWS, building on the earlier expert meetings. Since then, the group has been reconvened annually. In 2023, the Meeting of the High Contracting Parties to the CCW decided that the GGE on LAWS would continue its work in 2024 and 2025. The group was tasked with developing, by consensus, elements of a possible instrument, without predetermining its form, as well as other measures addressing lethal autonomous weapon systems, drawing on existing CCW protocols, earlier recommendations, state proposals, and legal, military, and technological expertise. == 2024 == In 2024, the GGE met twice, and the group was chaired by Robert in den Bosch, the Netherlands' disarmament ambassador. The 2024 Meeting of the High Contracting Parties decided that the group would meet for 10 days in 2025, in two five-day sessions, and reaffirmed its mandate to continue work by consensus on possible elements of an instrument and other measures addressing lethal autonomous weapon systems. == 2025 == At its first 2025 session, held in Geneva from 3 to 7 March 2025, the Group of Governmental Experts on Lethal Autonomous Weapon Systems discussed revisions to the chair's rolling text. The text was structured into five sections, or "boxes", though delegates held differing views on whether headings were useful or appropriate. Broadly, the discussions covered the characterization of lethal autonomous weapon systems, the application of international humanitarian law, possible prohibitions and regulations, legal review, and questions of accountability and responsibility. At its second session, held from 1 to 5 September 2025, delegations continued work on the chair's rolling text, which set out elements of a possible instrument and was organized into five thematic "boxes". == 2026 == === Developments before the 2026 session === A few weeks before the meeting, autonomous weapons drew renewed attention when the United States pressured Anthropic to revise the terms of use for its AI model Claude. Anthropic prohibited the model's use for mass domestic surveillance and for fully autonomous weapons operating without human oversight, while reports also emerged that OpenAI had reached an agreement with the U.S. Department of War for the use of its AI models, reportedly stipulating that they would not independently direct autonomous weapons where human control was required. The U.S. military nevertheless continued to use Claude during its war on Iran, and there was increasing alarm about the use of AI-assisted semi-autonomous weapons in conflicts including those in Ukraine, Sudan, Gaza, and Iran. Before the start of the sessions, Robert in den Bosch, as chair, warned that progress was urgent because technological developments were moving quickly. At the same time, although states agreed that international humanitarian law applied to LAWS, specific internationally binding standards governing such systems remained largely absent. A key divide before the session was that Russia and the United States opposed new legally binding instruments, while other states argued that new rules were necessary. According to Robert in den Bosch, the talks could lead to new rules, amendments to an existing convention, or a new treaty. === First session === From 2 to 6 March 2026, the group held its penultimate session under the group's three-year mandate. Delegations discussed the chair's rolling draft text, circulated in December 2025, on elements of a possible instrument or other measures concerning lethal autonomous weapon systems. In revised text circulated by the chair on 5 March 2026, a lethal autonomous weapon system was characterized as "a functionally integrated combination of one or more weapons and technological components, that can identify, select, and engage a target, without intervention by a human operator in the execution of these tasks". The text was divided into five boxes to structure discussion. During the session, delegates conducted a first reading of the draft text, and the chair later circulated revised language for several sections. Informal consultations were also held. According to campaign groups and participating observers, support grew during the week for moving to negotiations on the basis of the rolling text, with more than 70 states said to support that step by the end of the session, though some participants warned that attempts to bridge differences risked blurring the group's core purpose. The International Committee of the Red Cross argued that the text should not only restate existing international humanitarian law, but also clarify how those rules apply to autonomous weapons and set out additional measures tailored to the specific challenges such systems raise. Stop Killer Robots likewise emphasized the need to preserve meaningful human judgment and control over increasingly autonomous systems. During the discussions, the U.S. delegation opposed the term "human control" and reportedly proposed the alternative phrase "good faith human judgment and care". Other delegations rejected that wording as too weak, while many states continued to insist that meaningful human control over weapon systems remained essential.

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  Virtual Woman

  Virtual Woman is a software program that has elements of a chatbot, virtual reality, artificial intelligence, a video game, and a virtual human. It claims to be the oldest form of virtual life in existence, as it has been distributed since the late 1980s. Recent releases of the program can update their intelligence by connecting online and downloading newer personalities and histories. == Program play == When Virtual Woman starts, the user is presented with a list of options and then may choose their Virtual Woman's ethnic type, personality, location, clothing, etc. or load a pre-built Virtual Woman from a Digital DNA file. Once the options are determined, the user is presented with a 3-D animated Virtual Woman of their selection and then can engage them in conversation, progressing in a manner similar to that of its predecessor, ELIZA and its successors, the chatbots. In most versions of Virtual Woman, this is done through the keyboard, but some versions also support voice input. == In popular culture == Software sales and usage statistics from private companies are difficult to verify. WinSite, an independent Internet shareware distribution site that does publish public download counts, has for some time now listed some version of Virtual Woman in their top three shareware downloads of all time with well over seven hundred thousand downloads. == Compadre == The group of beta testers and advisers for Virtual Woman are referred to as Compadre and have their own beta testing site and forum. == Criticisms == As Virtual Woman has developed the ability to conduct longer and more realistic interactions, particularly in recent beta releases, criticism has arisen that this may lead some users to social isolation, or to use the program as a substitute for real human interaction. However, these are criticisms that have been leveled at all video games and at the use of the Internet itself. == Release history == Versions of Virtual Woman with rough release dates and PC platforms for which they were designed: Virtual Woman (????) (DOS) Virtual Woman for Windows (1991) (Windows 3.0) Virtual Woman 95 (1995) (Windows 3X, Windows 95) Virtual Woman 98 (1998) (Windows 3X, Windows 95) Virtual Woman 2000 (2000) (Windows 95+) Virtual Woman Millennium (Windows 95, XP) Virtual Woman Net ( Windows XP/Vista specific)

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  Figure AI

  Figure AI, Inc. is an American robotics company developing humanoid robots that operate via artificial intelligence. The company was founded in 2022 by Brett Adcock. As of late 2025, the company has a $39 billion valuation. Three generations of humanoid robots (Figure 01–03) have been developed, as well as two iterations of a vision-language-action model (Helix 01–02), which can control up to two robots at once. By 2026, the robots demonstrated the potential ability to perform household work and the company gained publicity when a Figure 03 appeared at a White House event. == History == Figure AI was founded in 2022 by Brett Adcock, also known for founding Archer Aviation and Vettery. That year, the company introduced its prototype, Figure 01, a bipedal robot designed for manual labor, initially targeting the logistics and warehousing sectors. The initial model utilized external cabling for easier maintenance. In May 2023, Figure AI raised $70 million from investors including Adcock, who invested $20 million, and Parkway Venture Capital. In January 2024, Figure AI announced a partnership with BMW to deploy humanoid robots in automotive manufacturing facilities. In February 2024, Figure AI secured $675 million in venture capital funding from a consortium that includes Jeff Bezos, Microsoft, Nvidia, Intel, and the startup-funding divisions of Amazon and OpenAI; the company was then valued at $2.6 billion. Figure AI also announced a partnership with OpenAI, which would build specialized artificial intelligence (AI) models for Figure AI's humanoid robots, enabling its robots to process language; the collaboration ended after a year, with Adcock stating that large language models had become a smaller problem compared to those allowing for "high rate robot control". In August 2024, the company introduced Figure 02, describing it as the next step toward deploying humanoids for industrial use. The machine has 35 degrees of freedom (DOF), while the five-fingered hands have 16 DOF and the ability to carry up to 25 kilograms (55 lb). The model is equipped with cabling integrated into the limbs, a torso-placed battery, six RGB cameras, and an onboard vision-language-action (VLA) model. It has three times the computing power (including inference AI) of the previous model, including two graphics processing units, supported by Nvidia. Microphones, speakers, and custom AI models (developed with OpenAI) enable communication with humans. In early 2025, Figure AI announced BotQ, a manufacturing facility aiming to produce 12,000 humanoids per year with the help of its own humanoid robots, and Helix, a VLA model that can control up to two robots at once. Helix enables a robot to interact with the world without extensive manual training, according to the company allowing it to pick up nearly any small household object. By April, the company issued cease-and-desist letters to at least two secondary brokers promoting its private stock without authorization. In September, a third round of financing exceeded $1 billion, raising the company's total valuation to $39 billion. Investors included Brookfield Asset Management, Intel, Macquarie Capital, Nvidia, Parkway Venture Capital, Qualcomm, Salesforce, and T-Mobile. In October 2025, Figure 03 was introduced. According to the company, its hardware and software redesign aims to create a general-purpose robot able to learn directly from humans. An upgraded camera system delivers twice the frame rate, a quarter the latency, and a 60% wider field of view, in addition to a camera in each hand. Tactile sensors in the fingertips can detect forces as little as 3 grams (0.1 oz). It incorporates soft materials and a protected battery for safety, and removable, washable textiles. It supports wireless inductive charging. In November 2025, the former head of product safety sued the company on the basis of being fired for raising the concern that the company's robots were strong enough to fracture a human skull. By early 2026, Figure 02 had been used in demonstrations showing that it could load a washing machine, sort packages, and fold laundry. That January, Helix 02 was released, expanding the AI model to the entire body to allow for functional autonomy. A Helix 02–powered Figure 02 was shown to be capable of loading and unloading a dishwasher, based on hours of motion-capture data and simulation-based machine learning. In March, U.S. First Lady Melania Trump appeared at the White House with a Figure 03, promoting the presumptive eventual ability of AI to teach children. In May 2026, Figure AI livestreamed a group of their robots processing packages nonstop for almost a week, inspiring a 10-hour competition between their robot and a human, in which the robot performed 98.5% as well as the human.

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  Escapex

  Escapex, stylized as escapex, was a mobile app developer specializing in white-label fan engagement apps for celebrities. It was founded by Sephi Shapira in 2014 and has raised $18 million in funding. It allows celebrities to reach fans directly, as well as receiving revenue from fans through its freemium model. == Overview == Shapira is Israeli and previously founded Interchan and MassiveImpact. He graduated from Ben-Gurion University of the Negev. The company has raised $18 million in funding. Its 2018 revenue was $5.5 million. In 2016, the company had 57 employees split between Tel Aviv and New York City. The company's General Manager is Joe Cuello, formerly an executive at MTV, then Chief Creative Officer at TuneCore. Their director of social engagement is Rafe Lopresti-Oakes. A press release from the company described the service as having a "proprietary loyalty program" which allows "monetization of social engagement through e-commerce and in-app advertising". App launches typically offered a contest for one fan to meet the celebrity. The app also allows Escapex to collect and monetize user profiles for advertising. The New York Times described the concept of Escapex, musing, "If people love you, why not make money from them?". == Notable apps == The company has created over 350 applications, including: Enrique Iglesias, June 2016 or earlier Akon, June 2016 or earlier Ricky Martin, June 2016 or earlier Rohan Marley and the Bob Marley estate, February 2017 Marc Anthony, March 2017 Prince Royce, March 2017 Jeremy Renner, March 2017, making over $35,000 per month in April 2019 Galen Gering, June 2017 Yandel, June 2017 Greg Vaughan, June 2017 Jason Thompson, June 2017 Niecy Nash, September 2017 Tyler Posey, September 2017 Osric Chau, January 2018 Chris D'Elia Alessandra Ambrosio, making over $35,000 per month in April 2019 Abigail Ratchford, making over $35,000 per month in April 2019 Amber Rose, making over $35,000 per month in April 2019 Dita Von Teese Tommy Chong === Bollywood stars === Escapex has a large roster of Bollywood celebrities, including: Sunny Leone, December 2016 Remo D'Souza, January 2017 Amy Jackson, March 2017 Kajal Aggarwal, March 2017 Nargis Fakhri, April 2017 Disha Patani Sonam Kapoor Salman Khan == Jeremy Renner app == Renner released a mobile app called "Jeremy Renner" (Android) and "Jeremy Renner Official" (iOS) in March 2017. FastCompany wrote extensively about Renner's app in April 2019, calling it "a surprising new kind of social media". The Ringer's Kate Knibbs, explaining how self-referential the app is, summarized it stating "Jeremy Renner’s Jeremy Renner app is the Jeremy Renner of apps." The community developed to include memes, selfies, and a "Happy Rennsday" event on Wednesdays. As early as October 2017 there were claims of censorship, bullying, and "contest-rigging". In September 2019, comedian Stefan Heck wrote about discovering that any replies through the app would appear as if they were sent by Renner himself in push notifications. Heck wrote about notifications making it appear Renner was a big enthusiast of "porno"; other users made it appear Renner was a big fan of Casey Anthony. Renner had to ask Escapex to shut down the app the following day, stating "The app has jumped the shark. Literally." In September 2020, comedian/writer Caroline Goldfarb and actress Sarah Ramos launched The Renner Files podcast, a six-part series investigating the Jeremy Renner app.

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  Robomart

  Robomart is an American technology company headquartered in Santa Monica, California that builds autonomous smart shops for cafes, ice cream parlors, and quick-service restaurants. The company’s white label platform gives retailers the option to expand their footprint at a significantly lower cost than traditional brick-and-mortar real-estate. Robomarts are equipped with a proprietary checkout-free system, temperature controlled compartments, sensors for autonomous operation, and external cameras for added security. The company licenses its technology and white label applications to retailers who manage their fleet of stores and deploy them to their consumers’ locations. After consumers have taken goods from the robomart, their order is automatically calculated, their card on file is charged and they are sent a receipt. The company has announced partnerships with Unilever, Mars, and Fatty Mart. == History == Robomart was founded by Ali Ahmed, Tigran Shahverdyan, and Emad Suhail Rahim. The company debuted at CES 2018 where it unveiled its concept of a self-driving store. At GITEX 2018 the company presented its first functional prototype of a fully driverless Robomart. At the 2019 Consumer Electronics Show the company demonstrated the technology behind its autonomous stores and checkout-free shopping experience. In January 2019, Robomart announced its first partnership with U.S. grocery chain Stop & Shop to test its driverless stores. In December 2020, Robomart deployed the Pharmacy Robomart in a trial in West Hollywood. In June 2021, the company launched its commercial service with a fleet of Pharmacy and Snacks Robomarts operating within West Hollywood and Central Hollywood. In August 2023, Robomart announced a $2 million seed round, putting its to-date funding at $3.4 million. == Partnerships == In September 2019, Robomart partnered with Avery Dennison to source the RFID tags used to enable its checkout-free shopping experience. In December 2020, Robomart partnered with Zeeba Vans to provide vehicles for its growing fleet. In June 2021, Robomart partnered with REEF Technology to provide inventory management and restocking services. In addition, REEF's Light Speed grocery division serves as the first merchant selling products through Robomart. == Products == The company currently offers three Robomart types. The frozen Robomart that stocks ice cream, the refrigerated Robomart that stocks perishable foods, and the ambient Robomart that stocks shelf-stable goods.

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  Grammar systems theory

  Grammar systems theory is a field of theoretical computer science that studies systems of finite collections of formal grammars generating a formal language. Each grammar works on a string, a so-called sequential form that represents an environment. Grammar systems can thus be used as a formalization of decentralized or distributed systems of agents in artificial intelligence. Let A {\displaystyle \mathbb {A} } be a simple reactive agent moving on the table and trying not to fall down from the table with two reactions, t for turning and ƒ for moving forward. The set of possible behaviors of A {\displaystyle \mathbb {A} } can then be described as formal language L A = { ( f m t n f r ) + : 1 ≤ m ≤ k ; 1 ≤ n ≤ ℓ ; 1 ≤ r ≤ k } , {\displaystyle \mathbb {L_{A}} =\{(f^{m}t^{n}f^{r})^{+}:1\leq m\leq k;1\leq n\leq \ell ;1\leq r\leq k\},} where ƒ can be done maximally k times and t can be done maximally ℓ times considering the dimensions of the table. Let G A {\displaystyle \mathbb {G_{A}} } be a formal grammar which generates language L A {\displaystyle \mathbb {L_{A}} } . The behavior of A {\displaystyle \mathbb {A} } is then described by this grammar. Suppose the A {\displaystyle \mathbb {A} } has a subsumption architecture; each component of this architecture can be then represented as a formal grammar, too, and the final behavior of the agent is then described by this system of grammars. The schema on the right describes such a system of grammars which shares a common string representing an environment. The shared sequential form is sequentially rewritten by each grammar, which can represent either a component or generally an agent. If grammars communicate together and work on a shared sequential form, it is called a Cooperating Distributed (DC) grammar system. Shared sequential form is a similar concept to the blackboard approach in AI, which is inspired by an idea of experts solving some problem together while they share their proposals and ideas on a shared blackboard. Each grammar in a grammar system can also work on its own string and communicate with other grammars in a system by sending their sequential forms on request. Such a grammar system is then called a Parallel Communicating (PC) grammar system. PC and DC are inspired by distributed AI. If there is no communication between grammars, the system is close to the decentralized approaches in AI. These kinds of grammar systems are sometimes called colonies or Eco-Grammar systems, depending (besides others) on whether the environment is changing on its own (Eco-Grammar system) or not (colonies).

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  3D-Coat

  3DCoat is a commercial digital sculpting program from Pilgway designed to create free-form organic and hard surfaced 3D models, with tools which enable users to sculpt, add polygonal topology (automatically or manually), create UV maps (automatically or manually), texture the resulting models with natural painting tools, and render static images or animated "turntable" movies. The program can also be used to modify imported 3D models from a number of commercial 3D software products by means of plugins called Applinks. Imported models can be converted into voxel objects for further refinement and for adding high resolution detail, complete UV unwrapping and mapping, as well as adding PBR textures for displacement, bump maps, specular and diffuse color maps. A live connection to a chosen external 3D application can be established through the Applink pipeline, allowing for the transfer of model and texture information. 3DCoat specializes in voxel sculpting and polygonal sculpting using dynamic patch tessellation technology and polygonal sculpting tools. It includes "auto-retopology", a proprietary skinning algorithm which generates a polygonal mesh skin over any voxel sculpture, composed primarily of quadrangles.

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  Kernel (image processing)

  In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This is accomplished by doing a convolution between the kernel and an image. Or more simply, when each pixel in the output image is a function of the nearby pixels (including itself) in the input image, the kernel is that function. == Details == The general expression of a convolution is g x , y = ω ∗ f x , y = ∑ i = − a a ∑ j = − b b ω i , j f x − i , y − j , {\displaystyle g_{x,y}=\omega f_{x,y}=\sum _{i=-a}^{a}{\sum _{j=-b}^{b}{\omega _{i,j}f_{x-i,y-j}}},} where g ( x , y ) {\displaystyle g(x,y)} is the filtered image, f ( x , y ) {\displaystyle f(x,y)} is the original image, ω {\displaystyle \omega } is the filter kernel. Every element of the filter kernel is considered by − a ≤ i ≤ a {\displaystyle -a\leq i\leq a} and − b ≤ j ≤ b {\displaystyle -b\leq j\leq b} . Depending on the element values, a kernel can cause a wide range of effects: The above are just a few examples of effects achievable by convolving kernels and images. === Origin === The origin is the position of the kernel which is above (conceptually) the current output pixel. This could be outside of the actual kernel, though usually it corresponds to one of the kernel elements. For a symmetric kernel, the origin is usually the center element. == Convolution == Convolution is the process of adding each element of the image to its local neighbors, weighted by the kernel. This is related to a form of mathematical convolution. The matrix operation being performed—convolution—is not traditional matrix multiplication, despite being similarly denoted by . For example, if we have two three-by-three matrices, the first a kernel, and the second an image piece, convolution is the process of flipping both the rows and columns of the kernel and multiplying locally similar entries and summing. The element at coordinates [2, 2] (that is, the central element) of the resulting image would be a weighted combination of all the entries of the image matrix, with weights given by the kernel: ( [ a b c d e f g h i ] ∗ [ 1 2 3 4 5 6 7 8 9 ] ) [ 2 , 2 ] = {\displaystyle \left({\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}}{\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}}\right)[2,2]=} ( i ⋅ 1 ) + ( h ⋅ 2 ) + ( g ⋅ 3 ) + ( f ⋅ 4 ) + ( e ⋅ 5 ) + ( d ⋅ 6 ) + ( c ⋅ 7 ) + ( b ⋅ 8 ) + ( a ⋅ 9 ) . {\displaystyle (i\cdot 1)+(h\cdot 2)+(g\cdot 3)+(f\cdot 4)+(e\cdot 5)+(d\cdot 6)+(c\cdot 7)+(b\cdot 8)+(a\cdot 9).} The other entries would be similarly weighted, where we position the center of the kernel on each of the boundary points of the image, and compute a weighted sum. The values of a given pixel in the output image are calculated by multiplying each kernel value by the corresponding input image pixel values. This can be described algorithmically with the following pseudo-code: for each image row in input image: for each pixel in image row: set accumulator to zero for each kernel row in kernel: for each element in kernel row: if element position corresponding to pixel position then multiply element value corresponding to pixel value add result to accumulator endif set output image pixel to accumulator corresponding input image pixels are found relative to the kernel's origin. If the kernel is symmetric then place the center (origin) of the kernel on the current pixel. The kernel will overlap the neighboring pixels around the origin. Each kernel element should be multiplied with the pixel value it overlaps with and all of the obtained values should be summed. This resultant sum will be the new value for the current pixel currently overlapped with the center of the kernel. If the kernel is not symmetric, it has to be flipped both around its horizontal and vertical axis before calculating the convolution as above. The general form for matrix convolution is [ x 11 x 12 ⋯ x 1 n x 21 x 22 ⋯ x 2 n ⋮ ⋮ ⋱ ⋮ x m 1 x m 2 ⋯ x m n ] ∗ [ y 11 y 12 ⋯ y 1 n y 21 y 22 ⋯ y 2 n ⋮ ⋮ ⋱ ⋮ y m 1 y m 2 ⋯ y m n ] = ∑ i = 0 m − 1 ∑ j = 0 n − 1 x ( m − i ) ( n − j ) y ( 1 + i ) ( 1 + j ) {\displaystyle {\begin{bmatrix}x_{11}&x_{12}&\cdots &x_{1n}\\x_{21}&x_{22}&\cdots &x_{2n}\\\vdots &\vdots &\ddots &\vdots \\x_{m1}&x_{m2}&\cdots &x_{mn}\\\end{bmatrix}}{\begin{bmatrix}y_{11}&y_{12}&\cdots &y_{1n}\\y_{21}&y_{22}&\cdots &y_{2n}\\\vdots &\vdots &\ddots &\vdots \\y_{m1}&y_{m2}&\cdots &y_{mn}\\\end{bmatrix}}=\sum _{i=0}^{m-1}\sum _{j=0}^{n-1}x_{(m-i)(n-j)}y_{(1+i)(1+j)}} === Edge handling === Kernel convolution usually requires values from pixels outside of the image boundaries. There are a variety of methods for handling image edges. Extend The nearest border pixels are conceptually extended as far as necessary to provide values for the convolution. Corner pixels are extended in 90° wedges. Other edge pixels are extended in lines. Wrap The image is conceptually wrapped (or tiled) and values are taken from the opposite edge or corner. Mirror The image is conceptually mirrored at the edges. For example, attempting to read a pixel 3 units outside an edge reads one 3 units inside the edge instead. Crop / Avoid overlap Any pixel in the output image which would require values from beyond the edge is skipped. This method can result in the output image being slightly smaller, with the edges having been cropped. Move kernel so that values from outside of image is never required. Machine learning mainly uses this approach. Example: Kernel size 10x10, image size 32x32, result image is 23x23. Kernel Crop Any pixel in the kernel that extends past the input image isn't used and the normalizing is adjusted to compensate. Constant Use constant value for pixels outside of image. Usually black or sometimes gray is used. Generally this depends on application. === Normalization === Normalization is defined as the division of each element in the kernel by the sum of all kernel elements, so that the sum of the elements of a normalized kernel is unity. This will ensure the average pixel in the modified image is as bright as the average pixel in the original image. === Optimization === Fast convolution algorithms include: separable convolution ==== Separable convolution ==== 2D convolution with an M × N kernel requires M × N multiplications for each sample (pixel). If the kernel is separable, then the computation can be reduced to M + N multiplications. Using separable convolutions can significantly decrease the computation by doing 1D convolution twice instead of one 2D convolution. === Implementation === Here a concrete convolution implementation done with the GLSL shading language :

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