AI Art Tattoo

AI Art Tattoo — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  List of COBOL software and tools

  This is a list of software and programming tools for the COBOL programming language, which includes compilers, IDEs, build tools, testing, frameworks, and related projects. == Compilers and runtimes == Fujitsu NetCOBOL — COBOL compiler for Windows, Linux, and mainframes GnuCOBOL — open-source COBOL compiler translating COBOL to C and then compiling with GCC IBM COBOL — mainframe COBOL compiler for IBM z/OS and IBM i platforms Micro Focus COBOL — commercial COBOL compiler and runtime for enterprise systems FairCom RTG – A commercial real-time database and runtime solution developed by FairCom Corporation. It provides integration with COBOL applications for transaction processing and modernization projects, and is used in enterprise environments requiring high-performance data management. == Integrated development environments == Eclipse IDE — with COBOL plugin support, Micro Focus or Bitlang extensions. IBM Developer for z/OS — IDE for COBOL and PL/I mainframe development Micro Focus Visual COBOL — IDE integration for Visual Studio, Visual Studio Code, and Eclipse OpenCOBOLIDE — open-source lightweight IDE for GnuCOBOL Visual Studio Code — with COBOL extensions via Bitlang COBOL and GnuCOBOL Language Server == Frameworks, libraries, and APIs == ACUCOBOL-GT — runtime and API library suite from Micro Focus CICS — IBM middleware for transaction processing in COBOL applications DB2 and IMS APIs — database access libraries commonly used with COBOL applications == Build tools and package managers == Apache Ant — scripting and build automation for COBOL/Java hybrid systems GNU Make — common build tool for compiling COBOL via GnuCOBOL Jenkins — used for CI/CD automation with COBOL builds == Testing and quality assurance == COBOL Check — open-source unit testing framework for COBOL IBM Rational Performance Tester — automated performance testing of web and server-based applications from the Rational Software division of IBM Micro Focus Unit Testing Framework — integrated COBOL unit testing tool == Debugging and profiling tools == GnuCOBOL debug mode — command-line debugging integrated in GnuCOBOL compiler IBM Debug Tool for z/OS — mainframe debugging for COBOL and PL/I Micro Focus Animator — step-through debugger for COBOL code

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  Shape factor (image analysis and microscopy)

  Shape factors are dimensionless quantities used in image analysis and microscopy that numerically describe the shape of a particle, independent of its size. Shape factors are calculated from measured dimensions, such as diameter, chord lengths, area, perimeter, centroid, moments, etc. The dimensions of the particles are usually measured from two-dimensional cross-sections or projections, as in a microscope field, but shape factors also apply to three-dimensional objects. The particles could be the grains in a metallurgical or ceramic microstructure, or the microorganisms in a culture, for example. The dimensionless quantities often represent the degree of deviation from an ideal shape, such as a circle, sphere or equilateral polyhedron. Shape factors are often normalized, that is, the value ranges from zero to one. A shape factor equal to one usually represents an ideal case or maximum symmetry, such as a circle, sphere, square or cube. == Aspect ratio == The most common shape factor is the aspect ratio, a function of the largest diameter and the smallest diameter orthogonal to it: A R = d min d max {\displaystyle A_{R}={\frac {d_{\min }}{d_{\max }}}} The normalized aspect ratio varies from approaching zero for a very elongated particle, such as a grain in a cold-worked metal, to near unity for an equiaxed grain. The reciprocal of the right side of the above equation is also used, such that the AR varies from one to approaching infinity. == Circularity == Another very common shape factor is the circularity (or isoperimetric quotient), a function of the perimeter P and the area A: f circ = 4 π A P 2 {\displaystyle f_{\text{circ}}={\frac {4\pi A}{P^{2}}}} The circularity of a circle is 1, and much less than one for a starfish footprint. The reciprocal of the circularity equation is also used, such that fcirc varies from one for a circle to infinity. == Elongation shape factor == The less-common elongation shape factor is defined as the square root of the ratio of the two second moments in of the particle around its principal axes. f elong = i 2 i 1 {\displaystyle f_{\text{elong}}={\sqrt {\frac {i_{2}}{i_{1}}}}} == Compactness shape factor == The compactness shape factor is a function of the polar second moment in of a particle and a circle of equal area A. f comp = A 2 2 π i 1 2 + i 2 2 {\displaystyle f_{\text{comp}}={\frac {A^{2}}{2\pi {\sqrt {{i_{1}}^{2}+{i_{2}}^{2}}}}}} The fcomp of a circle is one, and much less than one for the cross-section of an I-beam. == Waviness shape factor == The waviness shape factor of the perimeter is a function of the convex portion Pcvx of the perimeter to the total. f wav = P cvx P {\displaystyle f_{\text{wav}}={\frac {P_{\text{cvx}}}{P}}} Some properties of metals and ceramics, such as fracture toughness, have been linked to grain shapes. == An application of shape factors == Greenland, the largest island in the world, has an area of 2,166,086 km2; a coastline (perimeter) of 39,330 km; a north–south length of 2670 km; and an east–west length of 1290 km. The aspect ratio of Greenland is A R = 1290 2670 = 0.483 {\displaystyle A_{R}={\frac {1290}{2670}}=0.483} The circularity of Greenland is f circ = 4 π ( 2166086 ) 39330 2 = 0.0176. {\displaystyle f_{\text{circ}}={\frac {4\pi (2166086)}{39330^{2}}}=0.0176.} The aspect ratio is agreeable with an eyeball-estimate on a globe. Such an estimate on a typical flat map, using the Mercator projection, would be less accurate due to the distorted scale at high latitudes. The circularity is deceptively low, due to the fjords that give Greenland a very jagged coastline (see the coastline paradox). A low value of circularity does not necessarily indicate a lack of symmetry, and shape factors are not limited to microscopic objects.

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  Scientific Working Group – Imaging Technology

  The Scientific Working Group on Imaging Technology was convened by the Federal Bureau of Investigation in 1997 to provide guidance to law enforcement agencies and others in the criminal justice system regarding the best practices for photography, videography, and video and image analysis. This group was terminated in 2015. == History == As technology has advanced through the years, law enforcement has needed to stay abreast of emerging technological advances and use these in the investigation of crime. A factor that is considered when new technology is used in these investigations is the determination of whether the use of that new technology will be admissible in court. The judicial system in the United States currently has two standards used in the determination of admissibility of testimony regarding scientific evidence; the Daubert Standard and the Frye Standard. These standards guide the courts in the admissibility of testimony derived from the use of new technologies and scientific techniques. The Federal Bureau of Investigation (FBI), seeking to address possible admissibility issues with such testimony, established Scientific Working Groups starting with the Scientific Working Group on DNA Analysis and Methods (SWGDAM) in 1988. The goal of these groups is to open lines of communication between law enforcement agencies and forensic laboratories around the world while providing guidance on the use of new and innovative technologies and techniques. This guidance can lead to admissibility of evidence and/or testimony, provided proper methods in the collection of evidence and its analysis are employed. In 2009, the National Academy of Sciences released a report entitled, "Strengthening Forensic Science in the United States: A Path Forward." This report addresses many topics including challenges and disparities facing the forensic science community, standardization, certification of practitioners and accreditation of their respective entities, problems related to the interpretation of forensic evidence, the need for research, and the admission of forensic science evidence in litigation. This report mentions the Scientific Working Groups and their role in forensic science. The history of imaging technology (photography) can be said to extend back to the times of Chinese philosopher Mo-Ti (470-390 B.C.) who described the principles behind the precursor to the camera obscura. Since that time, advances in imaging technology include the discovery of chemical photographic processes in the 19th century and the use of electronic imaging technology that includes analog video cameras and digital video and still cameras. By the mid 1990s, it was apparent that technologically advanced camera systems such as these were being adopted for use in the criminal justice system. This led the FBI to convene a meeting of individuals working in the field of forensic imaging from federal, state, local, and foreign law enforcement, and the U.S. military, during the summer of 1997. As a result of this meeting, the Technical Working Group on Imaging Technology was formed from a core group of the meeting’s participants. This group later became the Scientific Working Group on Imaging Technology (SWGIT). Prior to the inception of SWGIT, some law enforcement agencies began adopting digital imaging technology. Due to the lack of guidelines or standards, some of these agencies attempted to replace all their film cameras with substandard digital cameras, only to find that the equipment they had purchased was not capable of accomplishing the mission for which they were intended. At that time only low resolution digital cameras were deemed affordable by some law enforcement agencies. Some of these agencies were forced to rethink their photography procedures and reverted to the use of film cameras or replaced their low-resolution digital cameras with higher quality, more expensive equipment. Also lacking at this early stage was guidance on how to store and archive digital image files. When SWGIT was formed, it was tasked with providing guidance to law enforcement and others in the criminal justice system by releasing documents that describe the best practices and guidelines for the use of imaging technology, to include these concerns and many others. This group was terminated in 2015. == SWGIT Function == During its existence, SWGIT provided information on the appropriate use of various imaging technologies including both established and new. This was accomplished through the release of documents such as the SWGIT Best Practices documents. As changes in technology occurred, these documents were updated. Over the course of its existence, SWGIT collaborated with other Scientific Working Groups to address imaging concerns within their respective disciplines. SWGIT published over 20 documents that dealt specifically with imaging technology. SWGIT also co-published documents with the Scientific Working Group on Digital Evidence (SWGDE) that had a component or components dealing with imaging technology. SWGIT also provided imaging technology guidance and input for documents from the Scientific Working Group on Friction Ridge Analysis, Study and Technology (SWGFAST), the Scientific Working Group for Forensic Document Examination (SWGDOC), and the Scientific Working Group on Shoeprint and Tire Tread Evidence (SWGTREAD). SWGIT assisted the American Society of Crime Lab Directors/Laboratory Accreditation Board (ASCLD/LAB) in the writing of definitions and standards for the accreditation of Digital and Multimedia Evidence sections of crime laboratories. In addition to releasing documents, SWGIT members disseminated best practices for law enforcement professionals where imaging technology was concerned. This was carried out by attending and lecturing at meetings and conferences of various forensic organizations that included: The American Academy of Forensic Sciences (AAFS) The International Association for Identification (IAI) The Law Enforcement and Emergency Services Video Association (LEVA) The American Society of Crime Lab Directors (ASCLD) The SWGIT membership consisted of approximately fifty scientists, photographers, instructors, and managers from more than two dozen federal, state, and local law enforcement agencies, as well as from the academic and research communities. The membership elected its officers from within. SWGIT was composed of the Executive Committee, four standing subcommittees, and ad hoc subcommittees appointed on an as-needed basis. The standing subcommittees were: Image Analysis, Forensic Photography, Video, and Outreach. This group was terminated in 2015. == Legal Proceedings == The following court cases have conducted Daubert v. Merrell Dow Pharm., Inc., 509 U.S. 579 (1993) hearings in which SWGIT best practice documents have been cited as accepted protocol, methodology, and as generally accepted techniques in the forensic community: U. S. v. Rudy Frabizio, U.S. District Court, Boston, MA, 2008 (Image Authentication) U.S. v. Nobumochi Furukawa, U.S. District Court, Minnesota, 2007 (Video Authentication) U.S. v. John Stroman, U.S. District Court, South Carolina, 2007 (Facial Comparison Analysis) State of Texas v. Daniel Day, Tarrant County Texas, 2005 (Camera Identification to Images) U.S. v. Marc Watzman, U.S. District Court, Northern Illinois, 2004 (Video Authentication) U.S. v. McKreith, U.S. District Court, Fort Lauderdale, FL, 2002 (Photo comparison of shirt) == Termination == This group was unfunded by the FBI in 2015.

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  EffectsLab Pro

  EffectsLab Pro is a discontinued visual effects software product developed by FXhome. It has since been superseded by the FXhome HitFilm range. The company also produced a limited functionality version, EffectsLab Lite, containing just the Particle engine. A more extensive product, VisionLab Studio, combined the functionality of EffectsLab Pro and the company's CompositeLab Pro product with enhancements to both. == Effects Engines == The effects are generated by the program's effect engines: The Neon Light engine allows light beams to be drawn onto the video, allowing the generation of lightsaber-like weapons, neon lighting, fantasy glow effects and laser blasts. The Particle engine is used for particle effects, such as smoke, fire, explosions, and weather effects. The Muzzle Flash engine is designed for creating and animating muzzle flashes such as machine gun firing, tank blasts, etc. It's possible to rotate the created muzzle flash in 3D, making it the only engine with 3D use. The Optics engine is designed for creating artificial lens flares and light sources. It is useful for enhancing other light-based effects, and mimicking the distinctive flashes of light that accompany Star Wars' lightsaber battles. The Laser engine (introduced in EffectsLab Pro in late 2007) is designed as a simplified method of creating laser weapon effects, including the ability to add simulated perspective to the effect. == Presets == EffectsLab Pro allows the user to save the effects using presets. Since all effects are generated from settings in the different engines, it is fairly easy to generate an XML style description of the effect. It is also possible to share presets on FXhome's website.

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  Embodied agent

  In artificial intelligence, an embodied agent, also sometimes referred to as an interface agent, is an intelligent agent that interacts with the environment through a physical body within that environment. Agents that are represented graphically with a body, for example a human or a cartoon animal, are also called embodied agents, although they have only virtual, not physical, embodiment. A branch of artificial intelligence focuses on empowering such agents to interact autonomously with human beings and the environment. Mobile robots are one example of physically embodied agents; Ananova and Microsoft Agent are examples of graphically embodied agents. Embodied conversational agents are embodied agents (usually with a graphical front-end as opposed to a robotic body) that are capable of engaging in conversation with one another and with humans employing the same verbal and nonverbal means that humans do (such as gesture, facial expression, and so forth). == Embodied conversational agents == Embodied conversational agents are a form of intelligent user interface. Graphically embodied agents aim to unite gesture, facial expression and speech to enable face-to-face communication with users, providing a powerful means of human-computer interaction. == Advantages == Face-to-face communication allows communication protocols that give a much richer communication channel than other means of communicating. It enables pragmatic communication acts such as conversational turn-taking, facial expression of emotions, information structure and emphasis, visualization and iconic gestures, and orientation in a three-dimensional environment. This communication takes place through both verbal and non-verbal channels such as gaze, gesture, spoken intonation and body posture. Research has found that users prefer a non-verbal visual indication of an embodied system's internal state to a verbal indication, demonstrating the value of additional non-verbal communication channels. As well as this, the face-to-face communication involved in interacting with an embodied agent can be conducted alongside another task without distracting the human participants, instead improving the enjoyment of such an interaction. Furthermore, the use of an embodied presentation agent results in improved recall of the presented information. Embodied agents also provide a social dimension to the interaction. Humans willingly ascribe social awareness to computers, and thus interaction with embodied agents follows social conventions, similar to human to human interactions. This social interaction both raises the believably and perceived trustworthiness of agents, and increases the user's engagement with the system. Rickenberg and Reeves found that the presence of an embodied agent on a website increased the level of user trust in that website, but also increased users' anxiety and affected their performance, as if they were being watched by a real human. Another effect of the social aspect of agents is that presentations given by an embodied agent are perceived as being more entertaining and less difficult than similar presentations given without an agent. Research shows that perceived enjoyment, followed by perceived usefulness and ease of use, is the major factor influencing user adoption of embodied agents. A study in January 2004 by Byron Reeves at Stanford demonstrated how digital characters could "enhance online experiences" through explaining how virtual characters essentially add a sense of familiarity to the user experience and make it more approachable. This increase in likability in turn helps make the products better, which benefits both the end users and those creating the product. === Applications === The rich style of communication that characterizes human conversation makes conversational interaction with embodied conversational agents ideal for many non-traditional interaction tasks. A familiar application of graphically embodied agents is computer games; embodied agents are ideal for this setting because the richer communication style makes interacting with the agent enjoyable. Embodied conversational agents have also been used in virtual training environments, portable personal navigation guides, interactive fiction and storytelling systems, interactive online characters and automated presenters and commentators. Major virtual assistants like Siri, Amazon Alexa and Google Assistant do not come with any visual embodied representation, which is believed to limit the sense of human presence by users. The U.S. Department of Defense utilizes a software agent called SGT STAR on U.S. Army-run Web sites and Web applications for site navigation, recruitment and propaganda purposes. Sgt. Star is run by the Army Marketing and Research Group, a division operated directly from The Pentagon. Sgt. Star is based upon the ActiveSentry technology developed by Next IT, a Washington-based information technology services company. Other such bots in the Sgt. Star "family" are utilized by the Federal Bureau of Investigation and the Central Intelligence Agency for intelligence gathering purposes.

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  Light scanning photomacrography

  Light Scanning Photomacrography (LSP), also known as Scanning Light Photomacrography (SLP) or Deep-Field Photomacrography, is a photographic film technique that allows for high magnification light imaging with exceptional depth of field (DOF). This method overcomes the limitations of conventional macro photography, which typically only keeps a portion of the subject in acceptable focus at high magnifications. == Historical background == The principles of LSP were first documented in the early 1960s by Dan McLachlan Jr., who highlighted its capability for extreme focal depth in microscopy and in 1968 patented the process. The technique was revived and further developed in the 1980s by photographers such as Darwin Dale and Nile Root, a faculty member at the Rochester Institute of Technology. In the early 1990s, William Sharp and Charles Kazilek, both researchers at Arizona State University, also published articles describing their technique and system setup for capturing SLP images. == Predecessor to stack image photography == Light Scanning Photomacrography offered a powerful analog tool for high-detail imaging in the age of film photography. It provided a comprehensive depth of field, making it invaluable in scientific and biomedical photography. As technology and techniques continue to evolve, LSP has been replaced by digital image focus stacking. This technique uses a collection of images captured in series at different focal depths, which are then processed using computer software to create a single image with a greater focus depth than any single image. == LSP technique and results == LSP involves the use of a thin plane of light that scans across the subject, which is mounted on a stage moving perpendicular to the film plane. The technique utilizes traditional optics and is governed by the physical laws of depth of field. By moving the subject through a narrow band of illumination, the entire subject can be recorded in sharp focus from the nearest details to the farthest ones. This analog process produces sharp and detailed images by slowly recording the image on film as the specimen passes through the sheet of light that is thinner than the effective DOF. Because the image is captured at the same relative distance from the camera lens, the resulting images are axonometric rather than perspective projection, which is what the human eye sees and is typically captured by a film camera. Because all parts of an LSP image are captured at the same distance from the lens, relative measurements can be taken from an LSP photograph and can be used for comparison. == Equipment and setup == A typical LSP setup includes: A stage that can move the subject perpendicular to the film plane. Light sources, in some cases modified projectors, are used to project a thin plane of light. A camera mounted on a stable stand such as a tabletop copy stand. In 1991, Sharp and Kazilek described their SLP system that used three Kodak Ektagraphic slide projectors with zoom lenses to create a thin plane of light. The projectors each had a slide mount with two razor blades placed edge-to-edge to create a thin slit for the light to pass through. The image was captured using a Nikon FE-2 SLR camera mounted above the specimen. Kodachrome 25 slide film was used to record the image and to minimize film grain size and maximize image sharpness == Commercial systems == A commercial SLP instrument was produced by the Irvine Optical Corp. Their DYNAPHOT system was based on a photomacroscope and could capture images on 4x5 film. The instrument came with two or three illumination sources and a motorized specimen stage. The system advertised a 2X – 40X magnification range and the ability to capture images in black and white and color. Other systems have been developed by Nile Root and Theodore Clarke and reported higher magnification (up to 100X). == LSP process == Alignment and Focusing: The light sources are aligned and focused to project a thin, consistent plane of light across the subject. Stage Movement: The subject stage moves at a controlled speed, scanning through the plane of light. Image Capture: The camera shutter is set to a long exposure or can be opened and closed manually. As the subject moves through the illuminated plane, it is recorded on the film. This process is very much like painting an image onto the film using photons instead of paint. == Applications == LSP was particularly useful in biomedical photography, where it was used to document magnified subjects with increased depth of field over traditional macro and micro photography. It has been employed to capture detailed images of biological specimens, such as imaging small insects and their parts. SLP has been used to document shell collections for scientific documentation and research. Other applications include forensic science, mineralogy, and the imaging of fractured surfaces and parts == Advantages and challenges of LSP imaging == === Advantages === Exceptional depth of field: Subjects are rendered in sharp focus throughout. High magnification: Detailed images at significant magnification without sacrificing DOF. Analog precision: Provides a non-digital solution with accurate image representation. Versatility: Can be used for a range of subject sizes, from macro to non-macro scales. === Challenges === Technical complexity: Requires precise setup and alignment. Exposure time: Typically requires long exposure times due to the scanning process. Contrast control: The highly directional lighting can create harsh shadows and high contrast, which may need to be managed. Digital competition: Focus stacking has largely replaced LSP in the digital era due to convenience and flexibility. == DIY contributions == Enthusiasts and researchers have contributed to the development and accessibility of LSP by creating and sharing DIY guides. These contributions have enabled others to build their own LSP systems using readily available materials and components. Nile Root's publications provide detailed instructions and recommendations for constructing an LSP setup. These DIY systems have allowed a wider audience to explore and utilize the benefits of LSP imaging in various fields.

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  Pixelmator Pro

  Pixelmator Pro is a photo, video, and vector graphic editor developed by Apple for macOS and iPadOS as part of its Pixelmator and pro apps platforms and as a part of their Apple Creator Studio suite of applications. Pixelmator Pro relies heavily on technologies from Apple platforms such as Metal, CoreML, Core Image, AVFoundation, GCD, and SwiftUI. == Features == GPU accelerated with Metal 50+ standard image editing tools Layer-based image editor Video editing support Vector graphic support (including SVG support) AI-powered editing features such as background removal ML Super Resolution and Smart Replace Supports a variety of media formats (JPEG, RAW, Apple ProRAW, PSD, PNG, GIF, MP4, HEIF, etc) == Reception == Pixelmator Pro was generally well-received by reviewers who praised its deep use of machine learning, fully macOS-native design, and relatively affordable one-time purchase compared to subscription software such as Adobe Photoshop. Some reviewers criticized that some features are hard to find or hard to use. It was awarded Apple's Mac App of the Year in 2018. Pixelmator Pro does not have support for panorama stitching. == Acquisition by Apple == On November 1, 2024, the Pixelmator Team announced that they were to be acquired by Apple, subject to regulatory approval. Their site promises "There will be no material changes to the Pixelmator Pro, Pixelmator for iOS, and Photomator apps at this time." The acquisition was completed in February 2025. On January 13, 2026, Apple announced that a new version of Pixelmator Pro with AI features would be included in its new Apple Creator Studio subscription, the app would be brought to the iPad and the Mac app would be redesigned with Liquid Glass. == Version history == == Applescript == In 2020 Pixelmator Pro added the ability to leverage Apple's automation language 'AppleScript' to automate many tasks in version 1.8 (Lynx). This enabled simple and advanced automation activities such as image resize, crop, color adjustments, format change, moving layers around, and more advanced actions like removing background, Gaussian blur, text replacement, shadows, color replacement, etc.

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  Anti-Grain Geometry

  Anti-Grain Geometry (AGG) is a 2D rendering graphics library written in C++. It features anti-aliasing and sub-pixel resolution. It is not a graphics library, per se, but rather a framework to build a graphics library upon. The library is operating system independent and renders to an abstract memory object. It comes with examples interfaced to the X Window System, Microsoft Windows, Mac OS X, AmigaOS, BeOS, SDL. The examples also include an SVG viewer. The design of AGG uses C++ templates only at a very high level, rather than extensively, to achieve the flexibility to plug custom classes into the rendering pipeline, without requiring a rigid class hierarchy, and allows the compiler to inline many of the method calls for high performance. For a library of its complexity, it is remarkably lightweight: it has no dependencies above the standard C++ libraries and it avoids the C++ STL in the implementation of the basic algorithms. The implicit interfaces are not well documented, however, and this can make the learning process quite cumbersome. While AGG version 2.5 is licensed under the GNU General Public License, version 2 or greater, AGG version 2.4 is still available under the 3-clause BSD license and is virtually the same as version 2.5. == History == Active development of the AGG codebase stalled in 2006, around the time of the v2.5 release, due to shifting priorities of its main developer and maintainer Maxim Shemanarev. M. Shemanarev remained active in the community until his sudden death in 2013. Development has continued on a fork of the more liberally licensed v2.4 on SourceForge.net. == Usage == The Haiku operating system uses AGG in its windowing system. It is one of the renderers available for use in GNU's Gnash Flash player. Graphical version of Rebol language interpreter is using AGG for scalable vector graphics DRAW dialect. Hilti uses it in some of their rebar detection tools, like the PS 1000. Matplotlib uses AGG as its canonical renderer for interactive user interfaces. fpGUI Toolkit has an optional AggPas back-end rendering engine. Work is being done to make AggPas the default or sole rendering engine for fpGUI. Mapnik, the toolkit that renders the maps on the OpenStreetMap website, uses AGG for all its bitmap map rendering by default. HTTPhotos uses AGG to scale photos. Pdfium, the PDF rendering engine used by Google Chrome makes use of AGG, although work is progressing to replace this with Skia Graphics Engine. Graphics Mill, the .NET imaging SDK uses AGG as its drawing engine. Image-Line FL Studio, a digital audio workstation, since version 10.8 released on September 30, 2012, uses AGG for drawing. Native Instruments's Supercharger and Supercharger GT compressors use AGG for its user interface. == Author == The main author of the library was Maxim Shemanarev (Russian: Максим Шеманарёв). On November 26, 2013 Shemanarev (born June 15, 1966, Nizhny Novgorod, Russia) was reported dead at the age of 47 at his home in Columbia, Maryland (US). He died suddenly, allegedly from an epileptic seizure that he had suffered for a while. He was a graduate from Nizhny Novgorod State Technical University. Little is known about his personal life. It's known though that he was divorced and his mother was alive at the time of his death. He used to love skiing, snowboarding (in Colorado), and inline skating. He was praised by his friends for his intelligent programming skills.

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  17LIVE

  17LIVE is an international entertainment platform. As of 2024, 17LIVE is the #3 live broadcasting platform globally, formed by its flagship live stream app 17LIVE (LIVIT in English markets), MEME Live and live stream e-commerce platforms HandsUP and OrderPally. == History == 17LIVE was first founded in Taiwan in 2015 by Jeffery Huang. The company has maintained its leading position since its entry into the Japan market in 2017, becoming the biggest platform for live entertainment in Japan, Taiwan, Hong Kong, and other countries. In 2017, 17 closed out US$33M in series B round to merge with dating software Paktor, with Joseph Phua (Co-founder of Paktor) taking over the leadership of 17LIVE as CEO and Co-founder, as well as to enter the Japan and Hong Kong market. Within one year, 17 Media became the #1 market leader in Japan. In 2018, the company raised $25M in series C round as it got ready for US IPO, which failed to materialize. 17LIVE had an unsuccessful US IPO attempt in 2018. Since then, the company reformed and transformed the business. Some key initiatives include the hiring of current CEO Hirofumi Ono, spin-off of Paktor (dating software business unit), full buy-out of founder Jeffery Huang, acquisition of MEME and HandsUp, and more. Despite the failed IPO attempt, the company continued to push for international expansion, including creating ‘LIVIT’ for the English-speaking markets to enter US, India, and North Africa. In 2019, 17's flagship live streaming app reached 10M downloads in Japan, and the business continues to push for both organic and inorganic expansion. Some key M&A highlights in the year include the acquisition of MEME Live in Southeast Asia, as well as HandsUp, a live e-commerce platform. In 2020, M17 closed out $26.5M in Series D round to continue organic growth in Japan, US and Middle East. In the same year, the company also sold its dating app business, Parktor, to rationalise M17 into a live-stream pure play business, followed by the appointment of its current Chairman, Joseph Phua, and previous Global CEO, Hirofumi Ono. With the buy-out and departure of founder Jeff Huang, the parent holding company M17 Entertainment Limited was officially renamed as 17 LIVE Group. An estimated 60 million users registered in 154 countries and territories in April 2022. In 2022, September, 17LIVE announced Group CEO Hirofumi Ono steps down. Alex Lien takes over the leadership as new Group COO; Jing Shen Ng appointed Group CTO. In 2023, March, 17LIVE announced Alex Lien promoted to Global CEO. Kenta Masuda appointed as Global CFO. === Collaboration with Ayumi Hamasaki === To celebrate its 4th anniversary, 17LIVE collaborated with Japanese singer-songwriter Ayumi Hamasaki, who led the 17LIVE 4th Anniversary meets Ayumi Hamasaki series starting October 18, 2021. Along with composer and arranger Yuta Nakano, Hamasaki judged auditioning artists competing for the chance to work with her and her production team for a debut single. The series was streamed live on the 17LIVE website, the final airing on November 11. The eventual winner was named as Yoshitaka_song. When asked why she collaborated with 17LIVE as a producer, Hamasaki commented: "Although the world has become like this (during COVID-19), I believe that the art of entertainment can give people dreams, hope, courage, and strength. I hope that kind of light will continue to shine through the entertainment industry." == Features == On 17LIVE, artists (LIVERs) are able to broadcast live, and post photos and videos from their album. The app has been designed for LIVERs to simply open the App, and start sharing contents without the need to edit or professionally curate their videos. The platform cultivates LIVERs, supports them with a local content management team, and provides artists with various functions, such as real time chatting, gifting, fan clubs, interactive competition and events. Today, 17LIVE has 46 thousands contracted artists and more than 2.3 million MAU, who spend 44 minutes on the platform every day. 17LIVE continues to advocate content-driven philosophy and delivers diverse topics, from politics and music to entertainment, to broaden its audience groups. 17LIVE also hosts offline flash events and concerts to attract new users and support LIVERs better connect with their fans. == Operation == 17LIVE has over 700 employees globally. The app provides few monetization models for LIVERs on the platform, including: Gifting: user / fans buy virtual gifts on the app to send to their favored LIVERs. Subscription: monthly subscription fan club service for access to exclusive content Pay-per-view: ticket service for online streaming concerts E-commerce: live e-commerce platform In the past, 17LIVE has encountered some regulatory headwinds with reported incidents of inappropriate livestream content on the platform. The incidents were direct results of the lack of oversight and supervision capability in place in the business at the time. Over the years, 17LIVE claims to have put in tremendous manpower and effort into improving, monitoring and maintaining control over both the live stream content and the KYC procedures and systems.

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  D/Vision Pro

  D/Vision Pro was one of the earliest marketed non-linear editing systems. It was released by TouchVision Systems, Inc. in the mid-1990s. The program was DOS-based and worked on either Intel's 386 or 486 processor. The system used AVI compression and worked with the Action Media II board. The system allowed users to digitize video, audio, and timecode, create an edit decision list (EDL), instantly play back the edited program, and output the finished EDL in a wide variety of formats. These cost-effective editing systems were used by numerous independent filmmakers and in low-budget productions during the mid-late 1990s. D/Vision Pro's low-quality compression led TouchVision (later renamed D/Vision Systems) to abandon it in favor of D/Vision Online, which was purchased by Discreet Logic and renamed edit. In June 2002, Discreet discontinued edit, as they did not want it to interfere with smoke sales which were more profitable. Discreet was later purchased by Autodesk.

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  Flo (app)

  Flo is a period-tracking app that provides menstrual cycle, ovulation and pregnancy tracking as well as perimenopause symptom tracking that was developed by Flo Health, Inc. It has over 380 million downloads worldwide and over 70 million monthly active users as of November 2024. In mid-2024, it reached unicorn status, and became Europe’s first femtech unicorn. The company has been accused of sharing users' sensitive health data with third parties without consent and misleading its users about data practices. == History == Flo Health, Inc. was co-founded in 2015 by Dmitry and Yuri Gurski, in Belarus. Their backgrounds helped build the first version of the software having experience in other fitness and health apps. Dmitry serves as the company's CEO. The company's development hubs are in London, Amsterdam and Vilnius. In 2016, the company raised $1 million in seed round funding from Flint Capital and Haxus Venture Fund. In 2017, Flo received an investment of $5 million from Flint Capital and model Natalia Vodianova with Vodianova helping develop an awareness campaign for the company. In 2018, Flo received an investment of $6 million from Mangrove Capital Partners, with participation from Flint Capital and Haxus, giving the company a valuation of $200 million. In mid-2019, Flo received an additional investment of $7.5 million led by Founders Fund. In 2020, the Federal Trade Commission alleged that Flo had misled users about its handling of health information to third parties including Google, Facebook, AppsFlyer, and Flurry since 2016. These allegations followed a 2019 report by The Wall Street Journal in reference to Facebook. The company reached a settlement in 2021 and was required to notify users of how their personal information was shared and obtain permission before any further information was shared. The agreement also required that Flo to undertake an independent privacy audit which it completed in March 2022. In early September 2021, Flo announced it closed $50M in a Series B financing, bringing the total capital raised to $65 million and company valuation to $800M led by VNV Global and Target Global. In March 2024, the Supreme Court of British Columbia certified a class action suit against Flo for sharing intimate data with Facebook and other third parties without user knowledge. In July 2024, Flo announced it raised more than $200M in Series C financing from General Atlantic bringing its valuation beyond $1 billion. As of November 2024, the app had over 380 million downloads world wide, and over 70 million monthly active users. In 2025, Flo adopted a data intelligence platform from Databricks to power its analytics and AI features, allowing users personalized cycle predictions. In 2025, a class action lawsuit in California was settled for $56 million with Flo paying $8 million and Google paying $48 million. == Features and privacy == Flo was initially created as a period and ovulation tracking application. It now provides reminders of upcoming menstrual cycles and a place to record various other health symptoms such as contraceptive methods, vaginal discharge (leukorrhea), water intake, pains, mood swings, and sexual activity. The application is available on iOS and Android. Flo is free to download and the free basic version gives you access to period and ovulation tracking and predictions, symptom tracking, cycle history, and anonymous mode. In Pregnancy mode, the app provides tracking features and educational material for pregnancy. In October 2023, Flo launched Flo for Partners, a feature that allows users to share their Flo data with their partner. In September 2022, as a response to Roe v. Wade being overturned, Flo sped up the release of a feature called "Anonymous Mode". Flo said this mode allows users to access the app without any personal identifiers such as name, email address, or technical identifiers being associated with their health data. Flo said it uses a technology called Oblivious HTTP to help protect user privacy in Anonymous Mode. == Recognition == Flo was named to Bloomberg’s Top 25 UK Startups to Watch for 2024. Flo's Anonymous Mode feature was recognized on both Fast Company's World Changing Ideas 2023 and TIME's Best Inventions List 2023. Flo is a CES 2019 Innovation Awards Honoree in the Software and Mobile Applications category.

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  Colors!

  Colors! is a series of digital painting applications for handheld game consoles and mobile devices. Originally created as a homebrew application for Nintendo DS (as Colors!), which was since legitimately distributed on PlayStation Vita, iOS, and Android, the project eventually evolved into an officially licensed application for Nintendo 3DS (as Colors! 3D) and Nintendo Switch (as Colors Live). == History == === Colors! === Colors! was originally released in June 2007 as a simple homebrew painting application for the Nintendo DS. It was developed by Jens Andersson, a programmer and designer on sabbatical from the games industry who wanted to experiment with the potential of the new handheld platform. Shortly after, Rafał Piasek created an online gallery where users could upload paintings made with the program. Colors! quickly became one of the best-known homebrew applications on the Nintendo DS, and in September 2008, it was also released for the iPhone and iPod Touch. As of August 2010, it had been downloaded almost half a million times. It was voted the most popular homebrew application on the Nintendo DS by readers of the R4 for DS blog. Development of Colors! DS homebrew officially ended in December 2010 although the official gallery still accepted submissions from DS users until 2020 when Colors! Gallery was discontinued. === Colors! 3D === Colors! 3D is a successor to the application Colors! for the Nintendo 3DS. It was released as an officially licensed application for the Nintendo eShop in North America on April 5, 2012, and in the PAL region on April 19, 2012. It was later released in Japan on August 21, 2013, published by Arc System Works. Colors! 3D allows users to draw on five layers, each on their own stereoscopic 3D plane. Drawing is done on the bottom screen, while the top screen displays the painting in 3D. While drawing, players can use the various controls on the Nintendo 3DS to change layers, zoom and pan, and alter the pressure of their brush. Pressing the L button allows users to access a menu to change brush type, size, and opacity, modify the layers, use the camera to provide references, and more. When the user finishes their painting, they can export it to the SD card for viewing in the Nintendo 3DS Camera application. Users can also upload their finished creations to an online gallery, viewed on the 3DS or the official website. Gallery features include hashtags and the ability to follow artists and post comments. Each painting also features a replay feature that allows viewers to see how it was drawn. The application also features local multiplayer, allowing several people to work cooperatively on a painting. In April 2024, the developers of Colors! 3D collaborated with the Pretendo Network project to officially add support for the application, meaning Colors! 3D will continue to operate as normal when using Pretendo Network. ==== Reception ==== IGN gave the application a score of 9.0 and an Editor's Choice award, praising its simple interface and tutorials. Destructoid gave the app a 9.0, calling it "a simple and incredibly fun tool with an amazing community of artists proudly displaying their beautiful and funny 3D images." Nintendo Life gave the app a 9/10, stating, "Though lacking in any structured play, Colors! 3D’s robust free drawing system and unique ability to let anyone create their own three-dimensional artwork more than make up for this." === Colors Live === A Nintendo Switch successor called Colors Live (stylised as Colors L!ve) was released in 2020 after being funded via a Kickstarter campaign. This expanded upon the features of previous installments by adding new brushes, increasing the maximum number of layers to ten, and introducing blend modes. A new game mode called Colors Quest was also included. A pressure-sensitive pen called the Colors SonarPen was developed in collaboration with GreenBulb to facilitate drawing on the Nintendo Switch, and comes pre-bundled with physical copies of the game. ==== Colors Quest ==== This new mode acts as a story-driven adventure wherein players are given a daily drawing challenge with a specific theme and certain stipulations that must be fulfilled. Once the drawing is complete, players must anonymously score other players' submissions, these scores are then aggregated to produce a personal ranking that measures the improvement in the player's art skills over time.

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  Free Studio

  Free Studio is a freeware set of multimedia computer programs developed by DVDVideoSoft. The programs are available in one integrated package and also as separate downloads (Free Studio Manager is included in both). == Overview == The Free Studio software bundle consists of about 48 programs, grouped into several sections: YouTube, MP3 & Audio, CD-DVD-BD, DVD & Video, Photo & Images, Mobiles, Apple Devices, and 3D. The largest group is the DVD & Video section containing 14 different applications. Mobiles section is the second largest group with 13 programs. However, the YouTube section, particularly YouTube downloading programs, has gained more popularity among users. The programs have been tested and endorsed by a dozen of software portals and have won awards from these sites. Free Studio is most popular in Germany, Greece, Italy, and the United States. It is also popular in Japan, France, and the United Kingdom. Some of the programs in the package are free and open-source software. == History == DVDVideoSoft project was launched in 2006 by company Digital Wave Ltd., for software development to produce multimedia application software. The founders distributed paid software as an affiliate at the start, later their own products appeared on the site. Free YouTube Download was the first successful program, then DVDVideoSoft created and launched several other 'Free YouTube' applications. Later on upon users' requests DVDVideoSoft started developing other kinds of applications including media converters etc. Today DVDVideoSoft offers up to 49 different programs for video, audio and image processing individually or integrated into the Free Studio package. == Features == DVDVideoSoft YouTube programs can be used to download YouTube videos in their original format and convert them to AVI, DVD, MP4, WMV etc. or different audio formats. YouTube section contains Free Video Call Recorder for Skype button, but the program itself is not included into FS installation (it has to be downloaded and installed separately). The "MP3 & Audio" section consists of the programs which convert audio files between different formats, convert audio files to Flash for web, extract audio from video files, edit audio files (Free Audio Dub), rip and burn CDs. Enclosed in the CD-DVD-BD section are the applications that enable users to burn files and folders to discs, to convert videos to a DVD format and vice versa, to burn CDs, and to copy music from audio CDs into files. The "DVD and Video" section contains several desktop video and DVD converters. Some of the programs can flip, rotate and cut (Free Video Dub) videos. One of the most popular programs from the section is Free Video Dub. Converted videos are now, contrary to previous versions, watermarked if no paid membership is present. Free Studio includes several applications for Apple phones, iPods and other devices. The Mobiles section contains a dozen video converters for various mobile devices such as cell phones, Tablets and Game consoles. They convert videos to play them on (BlackBerry, HTC, LG phones, Sony/Sony Ericsson, Nintendo, Xbox, Motorola phones, etc.) The "Photo & Images" section incorporates the programs for image conversion and resizing, extracting JPEG frames from videos (Free Video To JPEG Converter), recording screen activities, making screenshots (Free Screen Recorder). The 3D section is composed of the programs to make 3D videos and 3D images. There are several algorithms which allow to create different types of 3D images. == Supported formats == === Video formats === Input: .avi; .ivf; .div; .divx; .mpg; .mpeg; .mpe; .mp4; .m4v; .wmv; .asf; .webm; .mkv; .mov; .qt; .ts; .mts; .m2t; .m2ts; .mod; .tod; .vro; .dat; .3gp2; .3gpp; .3gp; .3g2; .dvr-ms; .flv; .f4v; .amv; .rm; .rmm; .rv; .rmvb; .ogv; DVD video Output: .mp4; .wmv; .avi; .mkv; .webm; .flv; .swf; .mov; .3gp; .m2ts; DVD video === Audio formats === Input: .mp3 .wav; .aac; .m4a; .m4b; .wma; .ogg; .flac; .ra; .ram; .amr; .ape; .mka; .tta; .aiff; .au; .mpc; .spx; .ac3; audio cd Output: .mp3; .m4a; .aac; .wav; .wma; .ogg; .flac; .ape; audio CD === Image formats === Input: .jpg, .png, .bmp, .gif, .tga Output: .jpg, .png, .bmp, .gif, .tga, .pdf == Reception == The programs have been tested and endorsed by Chip Online, Tucows, SnapFiles, Brothersoft, and Softonic and have won awards from these sites. Free Studio is most popular in Germany, United States and Italy. It is also popular in Japan, France and the United Kingdom. The most popular applications, according to CNET statistics, include Free YouTube to MP3 Converter, Free Video to MP3 Converter, Free MP4 Video Converter and Free YouTube Download. Other programs with high rank: Free AVI Video Converter, Free Video Editor, Free Audio Converter and Free Studio in a whole. == Criticism == Free Studio (as can be common for freeware packages) is criticized for toolbar and Web search engine installation. Older versions have also included OpenCandy, which is loaded automatically, with no request for user approval. There can be difficulties installing only the programs needed without installing bundled extra programs. In March 2017, DVDVideoSoft announced that it had stopped showing other products' ads during installation and removed all toolbars, search engines, and OpenCandy.

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  Adobe Encore

  Adobe Encore (previously Adobe Encore DVD) was a DVD authoring software tool produced by Adobe Systems and targeted at professional video producers. Video and audio resources could be used in their current format for development, allowing the user to transcode them to MPEG-2 video and Dolby Digital audio upon project completion. DVD menus could be created and edited in Adobe Photoshop using special layering techniques. Adobe Encore did not support writing to a Blu-ray Disc using AVCHD 2.0. Encore is bundled with Adobe Premiere Pro CS6. Adobe Encore CS6 was the last release. While Premiere Pro CC has moved to the Creative Cloud, Encore has now been discontinued. == Licensing == All forms of Adobe Encore used a proprietary licensing system from its developer, Adobe Systems. Versions 1.0 and 1.5 required a separate license fee (rather than making 1.5 available as a free update). Version 3, also known as CS3, was sold only in bundle with Premiere CS3. Encore CS4, CS5, CS5.5 and CS6 were only sold in the Premiere Pro CS4, CS5, CS5.5 and CS6 bundles, respectively. Adobe CC subscribers no longer have access to Adobe Encore CS6. Adobe Encore is not included with Premiere Pro CC. == Functionality == Adobe Encore allowed for creating interactive DVD menus from Photoshop documents, which could be tweaked from within Encore. Video and audio streams could be embedded in the DVD and be made to play when certain elements of the menu are interacted with. It had similar functionality to Adobe Flash and Premiere Pro, due to its ability to both edit video on a timeline and embed interactive content.

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  Super-resolution optical fluctuation imaging

  Super-resolution optical fluctuation imaging (SOFI) is a post-processing method for the calculation of super-resolved images from recorded image time series that is based on the temporal correlations of independently fluctuating fluorescent emitters. SOFI has been developed for super-resolution of biological specimen that are labelled with independently fluctuating fluorescent emitters (organic dyes, fluorescent proteins). In comparison to other super-resolution microscopy techniques such as STORM or PALM that rely on single-molecule localization and hence only allow one active molecule per diffraction-limited area (DLA) and timepoint, SOFI does not necessitate a controlled photoswitching and/ or photoactivation as well as long imaging times. Nevertheless, it still requires fluorophores that are cycling through two distinguishable states, either real on-/off-states or states with different fluorescence intensities. In mathematical terms SOFI-imaging relies on the calculation of cumulants, for what two distinguishable ways exist. For one thing an image can be calculated via auto-cumulants that by definition only rely on the information of each pixel itself, and for another thing an improved method utilizes the information of different pixels via the calculation of cross-cumulants. Both methods can increase the final image resolution significantly although the cumulant calculation has its limitations. Actually SOFI is able to increase the resolution in all three dimensions. == Principle == Likewise to other super-resolution methods SOFI is based on recording an image time series on a CCD- or CMOS camera. In contrary to other methods the recorded time series can be substantially shorter, since a precise localization of emitters is not required and therefore a larger quantity of activated fluorophores per diffraction-limited area is allowed. The pixel values of a SOFI-image of the n-th order are calculated from the values of the pixel time series in the form of a n-th order cumulant, whereas the final value assigned to a pixel can be imagined as the integral over a correlation function. The finally assigned pixel value intensities are a measure of the brightness and correlation of the fluorescence signal. Mathematically, the n-th order cumulant is related to the n-th order correlation function, but exhibits some advantages concerning the resulting resolution of the image. Since in SOFI several emitters per DLA are allowed, the photon count at each pixel results from the superposition of the signals of all activated nearby emitters. The cumulant calculation now filters the signal and leaves only highly correlated fluctuations. This provides a contrast enhancement and therefore a background reduction for good measure. As it is implied in the figure on the left the fluorescence source distribution: ∑ k = 1 N δ ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) {\displaystyle \sum _{k=1}^{N}\delta ({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t)} is convolved with the system's point spread function (PSF) U(r). Hence the fluorescence signal at time t and position r → {\displaystyle {\vec {r}}} is given by F ( r → , t ) = ∑ k = 1 N U ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) . {\displaystyle F({\vec {r}},t)=\sum _{k=1}^{N}U({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t).} Within the above equations N is the amount of emitters, located at the positions r → k {\displaystyle {\vec {r}}_{k}} with a time-dependent molecular brightness ε k ⋅ s k {\displaystyle \varepsilon _{k}\cdot s_{k}} where ε k {\displaystyle \varepsilon _{k}} is a variable for the constant molecular brightness and s k ( t ) {\displaystyle s_{k}(t)} is a time-dependent fluctuation function. The molecular brightness is just the average fluorescence count-rate divided by the number of molecules within a specific region. For simplification it has to be assumed that the sample is in a stationary equilibrium and therefore the fluorescence signal can be expressed as a zero-mean fluctuation: δ F ( r → , t ) = F ( r → , t ) − ⟨ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=F({\vec {r}},t)-\langle F({\vec {r}},t)\rangle _{t}} where ⟨ ⋯ ⟩ t {\displaystyle \langle \cdots \rangle _{t}} denotes time-averaging. The auto-correlation here e.g. the second-order can then be described deductively as follows for a certain time-lag τ {\displaystyle \tau } : δ F ( r → , t ) = ⟨ δ F ( r → , t + τ ) ⋅ δ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=\langle \delta F({\vec {r}},t+\tau )\cdot \delta F({\vec {r}},t)\rangle _{t}} From these equations it follows that the PSF of the optical system has to be taken to the power of the order of the correlation. Thus in a second-order correlation the PSF would be reduced along all dimensions by a factor of 2 {\displaystyle {\sqrt {2}}} . As a result, the resolution of the SOFI-images increases according to this factor. === Cumulants versus correlations === Using only the simple correlation function for a reassignment of pixel values, would ascribe to the independency of fluctuations of the emitters in time in a way that no cross-correlation terms would contribute to the new pixel value. Calculations of higher-order correlation functions would suffer from lower-order correlations for what reason it is superior to calculate cumulants, since all lower-order correlation terms vanish. == Cumulant-calculation == === Auto-cumulants === For computational reasons it is convenient to set all time-lags in higher-order cumulants to zero so that a general expression for the n-th order auto-cumulant can be found: A C n ( r → , τ 1 … n − 1 = 0 ) = ∑ k = 1 N U n ( r → − r → k ) ε k n w k ( 0 ) {\displaystyle AC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\sum _{k=1}^{N}U^{n}({\vec {r}}-{\vec {r}}_{k})\varepsilon _{k}^{n}w_{k}(0)} w k {\displaystyle w_{k}} is a specific correlation based weighting function influenced by the order of the cumulant and mainly depending on the fluctuation properties of the emitters. Albeit there is no fundamental limitation in calculating very high orders of cumulants and thereby shrinking the FWHM of the PSF there are practical limitations according to the weighting of the values assigned to the final image. Emitters with a higher molecular brightness will show a strong increase in terms of the pixel cumulant value assigned at higher-orders as well as this performance can be expected from a diverse appearance of fluctuations of different emitters. A wide intensity range of the resulting image can therefore be expected and as a result dim emitters can get masked by bright emitters in higher-order images:. The calculation of auto-cumulants can be realized in a very attractive way in a mathematical sense. The n-th order cumulant can be calculated with a basic recursion from moments K n ( r → ) = μ n ( r → ) − ∑ i = 1 n − 1 ( n − 1 i ) K n − i ( r → ) μ i ( r → ) {\displaystyle K_{n}({\vec {r}})=\mu _{n}({\vec {r}})-\sum _{i=1}^{n-1}{\begin{pmatrix}n-1\\i\end{pmatrix}}K_{n-i}({\vec {r}})\mu _{i}({\vec {r}})} where K is a cumulant of the index's order, likewise μ {\displaystyle \mu } represents the moments. The term within the brackets indicates a binomial coefficient. This way of computation is straightforward in comparison with calculating cumulants with standard formulas. It allows for the calculation of cumulants with only little time of computing and is, as it is well implemented, even suitable for the calculation of high-order cumulants on large images. === Cross-cumulants === In a more advanced approach cross-cumulants are calculated by taking the information of several pixels into account. Cross-cumulants can be described as follows: C C n ( r → , τ 1 … n − 1 = 0 ) = ∏ j < l n U ( r → j − r → l n ) ⋅ ∑ i = 1 N U n ( r → i − ∑ k n r → k n ) ε i n w i ( 0 ) {\displaystyle CC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\prod _{j Read more →