Pixelmator is a series of graphics editors developed by Apple for macOS, iOS, and iPadOS. Pixelmator apps leverage Apple-specific technologies such as CoreML and Metal. Pixelmator uses a proprietary format across their apps (.PXD), but supports editing a variety of file types including Photoshop, RAW, and WebP. == History == Pixelmator Team was founded in 2007 by Lithuanian brothers Saulius and Aidas Dailidė, and released Pixelmator (now Pixelmator Classic) 1.0 in September of the same year. The company resided in Vilnius, Lithuania. In November 2024, Pixelmator Team agreed to be acquired by Apple for an unknown monetary amount, which was completed on 11 February 2025, the company was later folded into Apple with its products coming under them fully. == Pixelmator Classic == Pixelmator Classic was the original version of Pixelmator released for Mac on 25 September 2007. It uses a palette-style interface with floating toolbars compared to Pixelmator Pro's single-window interface. It is no longer being updated and has been delisted from the Mac App Store. == Pixelmator iOS == Pixelmator for iOS launched on 23 October 2014 as an iPad-exclusive app with touch-optimized versions of Pixelmator's desktop features. In May 2015, Pixelmator for iOS 2.0 was released with support for the iPhone. Apple no longer updates Pixelmator for iOS as of 13 January 2026, shortly before the release of Pixelmator Pro for iPad. == Pixelmator Pro == Pixelmator Pro is an image, video, and vector editing software for macOS that launched on 29 November 2017. It was a paid upgrade for Pixelmator Classic users, featuring a redesigned interface, a graphics pipeline rewritten using Metal, Apple silicon support and a greater focus on ML/AI editing features. On 28 January 2026, Apple announced Apple Creator Studio, a subscription bundle for their professional software that contains Pixelmator Pro. They also brought Pixelmator Pro to iPad, shortly after discontinuing Pixelmator iOS. == Photomator == Photomator (formerly Pixelmator Photo) is a photo-oriented editing app which launched on iPad in 2019, on iOS in 2021, and macOS in 2022. After launching the macOS version, the app moved from a one-time purchase to a subscription; however, a lifetime license can still be purchased for $99. Photomator differentiates itself from other Pixelmator apps with features such as batch editing of full photoshoots and AI-powered color correction. Edits in Photomator are made on a single layer and are non-destructive.
List of 3D rendering software
3D rendering software products are the dedicated engines used for rendering computer-generated imagery. This is not the same as 3D modeling software, which involves the creation of 3D models, for which the software listed below can produce realistically rendered visualisations.General-purpose packages which can have their own built-in rendering capabilities are not listed here; these can be found in the list of 3D computer graphics software and list of 3D animation software. See 3D computer graphics software for more discussion about the distinctions.
Demis Hassabis
Sir Demis Hassabis (/ˈdɛ.mɪs/ DE-mis /hɑːˈsɑː.bis/ hah-SAH-bees; born Dimitrios Hassapis, Greek: Δημήτριος Χασάπης, 27 July 1976) is a British artificial intelligence (AI) researcher and entrepreneur. He is the chief executive officer and co-founder of Google DeepMind and Isomorphic Labs, and a UK Government AI Adviser. In 2024, Hassabis and John M. Jumper were jointly awarded the Nobel Prize in Chemistry for their AI research contributions to protein structure prediction. Hassabis is a Fellow of the Royal Society and has won awards for his research efforts, including the Breakthrough Prize, the Canada Gairdner International Award and the Lasker Award. He was appointed a CBE in 2017, and knighted in 2024 for his work on AI. He was also listed among the Time 100 most influential people in the world in 2017 and 2025, and was one of the "Architects of AI" collectively chosen as Time's 2025 Person of the Year. == Early life and education == Hassabis was born to Costas and Angela Hassapis. His father is a Greek Cypriot and his mother is a Chinese Singaporean. Demis grew up in North London. His original surname was "Hassapis" (Greek: Χασάπης), meaning "butcher" in Greek, but he later, according to Ingo Althöfer, "executed a point mutation by changing ‘p’ to ‘b’". One of his younger brothers still carries the original surname. In his early career, he was a video game AI programmer and designer, and an expert board games player. A child prodigy in chess from the age of four, when he first learnt chess by watching his father playing against his uncle, Hassabis reached master standard at the age of 13 with an Elo rating of 2300 and captained many of the England junior chess teams. He represented the University of Cambridge in the Oxford–Cambridge varsity chess matches of 1995, 1996 and 1997, winning a half blue. He first got interested in technology after buying his first computer in 1984, a ZX Spectrum 48K, funded from chess winnings. He taught himself how to program from books. He subsequently wrote his first AI program on a Commodore Amiga to play the reversi board game. Between 1988 and 1990, Hassabis was educated at Queen Elizabeth's School, Barnet, a boys' grammar school in North London. He was subsequently home-schooled by his parents for a year, before studying at the comprehensive school of Christ's College in East Finchley. He completed his A-level exams two years early at 16. === Bullfrog Productions === Asked by Cambridge University to take a gap year owing to his young age, Hassabis began his computer games career at Bullfrog Productions after entering an Amiga Power "Win-a-job-at-Bullfrog" competition. He began by playtesting on Syndicate and then at 17 co-designing and lead-programming on the 1994 game Theme Park, with the game's designer Peter Molyneux. Theme Park, a simulation video game, sold several million copies and inspired a whole genre of simulation sandbox games. Despite being offered a seven-figure sum to remain in the games industry, he turned it down. He earned enough from his gap year to pay his own way through university. === University of Cambridge === Hassabis left Bullfrog to study at Queens' College of the University of Cambridge, where he completed the Computer Science Tripos and graduated in 1997 with a double first. == Career and research == === Lionhead === After graduating from Cambridge, Hassabis worked at Lionhead Studios. Games designer Peter Molyneux, with whom Hassabis had worked at Bullfrog Productions, had recently founded the company. At Lionhead, Hassabis worked as lead AI programmer on the 2001 god game Black & White. === Elixir Studios === Hassabis left Lionhead in 1998 to found Elixir Studios, a London-based independent games developer, signing publishing deals with Eidos Interactive, Vivendi Universal and Microsoft. In addition to managing the company, Hassabis served as executive designer of the games Republic: The Revolution and Evil Genius. Each received BAFTA nominations for their interactive music scores, created by James Hannigan. The release of Elixir's first game, Republic: The Revolution, a highly ambitious and unusual political simulation game, was delayed due to its huge scope, which involved an AI simulation of the workings of an entire fictional country. The final game was reduced from its original vision and greeted with lukewarm reviews, receiving a Metacritic score of 62/100. Evil Genius, a tongue-in-cheek Austin Powers parody, fared much better with a score of 75/100. In April 2005 the intellectual property and technology rights were sold to various publishers and the studio was closed. === Neuroscience research === Following Elixir Studios, Hassabis returned to academia to obtain his PhD in cognitive neuroscience from UCL Queen Square Institute of Neurology in 2009 supervised by Eleanor Maguire. He sought to find inspiration in the human brain for new AI algorithms. He continued his neuroscience and artificial intelligence research as a visiting scientist jointly at Massachusetts Institute of Technology (MIT), in the lab of Tomaso Poggio, and Harvard University, before earning a Henry Wellcome postdoctoral research fellowship to the Gatsby Computational Neuroscience Unit at UCL in 2009 working with Peter Dayan. Working in the field of imagination, memory, and amnesia, he co-authored several influential papers published in Nature, Science, Neuron, and PNAS. His very first academic work, published in PNAS, was a landmark paper that showed systematically for the first time that patients with damage to their hippocampus, known to cause amnesia, were also unable to imagine themselves in new experiences. The finding established a link between the constructive process of imagination and the reconstructive process of episodic memory recall. Based on this work and a follow-up functional magnetic resonance imaging (fMRI) study, Hassabis developed a new theoretical account of the episodic memory system identifying scene construction, the generation and online maintenance of a complex and coherent scene, as a key process underlying both memory recall and imagination. This work received widespread coverage in the mainstream media and was listed in the top 10 scientific breakthroughs of the year by the journal Science. He later generalised these ideas to advance the notion of a 'simulation engine of the mind' whose role it was to imagine events and scenarios to aid with better planning. === DeepMind === Hassabis is the CEO and co-founder of DeepMind, a machine learning AI startup, founded in London in 2010 with Shane Legg and Mustafa Suleyman. Hassabis met Legg when both were postdocs at the Gatsby Computational Neuroscience Unit, and he and Suleyman had been friends through family. Hassabis also recruited his university friend and Elixir partner David Silver. DeepMind's mission is to "solve intelligence" and then use intelligence "to solve everything else". More concretely, DeepMind aims to combine insights from systems neuroscience with new developments in machine learning and computing hardware to unlock increasingly powerful general-purpose learning algorithms that will work towards the creation of an artificial general intelligence (AGI). The company has focused on training learning algorithms to master games, and in December 2013 it announced that it had made a pioneering breakthrough by training an algorithm called a Deep Q-Network (DQN) to play Atari games at a superhuman level by using only the raw pixels on the screen as inputs. DeepMind's early investors included several high-profile tech entrepreneurs. In 2014, Google purchased DeepMind for £400 million. Although most of the company has remained an independent entity based in London, DeepMind Health has since been directly incorporated into Google Health. Since the Google acquisition, the company has notched up a number of significant achievements, perhaps the most notable being the creation of AlphaGo, a program that defeated world champion Lee Sedol at the complex game of Go. Go had been considered a holy grail of AI, for its high number of possible board positions and resistance to existing programming techniques. However, AlphaGo beat European champion Fan Hui 5–0 in October 2015 before winning 4–1 against former world champion Lee Sedol in March 2016 and winning 3–0 against the world's top-ranked player Ke Jie in 2017. Additional DeepMind accomplishments include creating a neural Turing machine, reducing the energy used by the cooling systems in Google's data centres by 40%, and advancing research on AI safety. DeepMind has also been responsible for technical advances in machine learning, having produced a number of award-winning papers. In particular, the company has made significant advances in deep learning and reinforcement learning, and pioneered the field of deep reinforcement learning which combines these two methods. Hassabis has predicted that artificial intelligence will be "one of the most beneficial techn
Demis Hassabis
Sir Demis Hassabis (/ˈdɛ.mɪs/ DE-mis /hɑːˈsɑː.bis/ hah-SAH-bees; born Dimitrios Hassapis, Greek: Δημήτριος Χασάπης, 27 July 1976) is a British artificial intelligence (AI) researcher and entrepreneur. He is the chief executive officer and co-founder of Google DeepMind and Isomorphic Labs, and a UK Government AI Adviser. In 2024, Hassabis and John M. Jumper were jointly awarded the Nobel Prize in Chemistry for their AI research contributions to protein structure prediction. Hassabis is a Fellow of the Royal Society and has won awards for his research efforts, including the Breakthrough Prize, the Canada Gairdner International Award and the Lasker Award. He was appointed a CBE in 2017, and knighted in 2024 for his work on AI. He was also listed among the Time 100 most influential people in the world in 2017 and 2025, and was one of the "Architects of AI" collectively chosen as Time's 2025 Person of the Year. == Early life and education == Hassabis was born to Costas and Angela Hassapis. His father is a Greek Cypriot and his mother is a Chinese Singaporean. Demis grew up in North London. His original surname was "Hassapis" (Greek: Χασάπης), meaning "butcher" in Greek, but he later, according to Ingo Althöfer, "executed a point mutation by changing ‘p’ to ‘b’". One of his younger brothers still carries the original surname. In his early career, he was a video game AI programmer and designer, and an expert board games player. A child prodigy in chess from the age of four, when he first learnt chess by watching his father playing against his uncle, Hassabis reached master standard at the age of 13 with an Elo rating of 2300 and captained many of the England junior chess teams. He represented the University of Cambridge in the Oxford–Cambridge varsity chess matches of 1995, 1996 and 1997, winning a half blue. He first got interested in technology after buying his first computer in 1984, a ZX Spectrum 48K, funded from chess winnings. He taught himself how to program from books. He subsequently wrote his first AI program on a Commodore Amiga to play the reversi board game. Between 1988 and 1990, Hassabis was educated at Queen Elizabeth's School, Barnet, a boys' grammar school in North London. He was subsequently home-schooled by his parents for a year, before studying at the comprehensive school of Christ's College in East Finchley. He completed his A-level exams two years early at 16. === Bullfrog Productions === Asked by Cambridge University to take a gap year owing to his young age, Hassabis began his computer games career at Bullfrog Productions after entering an Amiga Power "Win-a-job-at-Bullfrog" competition. He began by playtesting on Syndicate and then at 17 co-designing and lead-programming on the 1994 game Theme Park, with the game's designer Peter Molyneux. Theme Park, a simulation video game, sold several million copies and inspired a whole genre of simulation sandbox games. Despite being offered a seven-figure sum to remain in the games industry, he turned it down. He earned enough from his gap year to pay his own way through university. === University of Cambridge === Hassabis left Bullfrog to study at Queens' College of the University of Cambridge, where he completed the Computer Science Tripos and graduated in 1997 with a double first. == Career and research == === Lionhead === After graduating from Cambridge, Hassabis worked at Lionhead Studios. Games designer Peter Molyneux, with whom Hassabis had worked at Bullfrog Productions, had recently founded the company. At Lionhead, Hassabis worked as lead AI programmer on the 2001 god game Black & White. === Elixir Studios === Hassabis left Lionhead in 1998 to found Elixir Studios, a London-based independent games developer, signing publishing deals with Eidos Interactive, Vivendi Universal and Microsoft. In addition to managing the company, Hassabis served as executive designer of the games Republic: The Revolution and Evil Genius. Each received BAFTA nominations for their interactive music scores, created by James Hannigan. The release of Elixir's first game, Republic: The Revolution, a highly ambitious and unusual political simulation game, was delayed due to its huge scope, which involved an AI simulation of the workings of an entire fictional country. The final game was reduced from its original vision and greeted with lukewarm reviews, receiving a Metacritic score of 62/100. Evil Genius, a tongue-in-cheek Austin Powers parody, fared much better with a score of 75/100. In April 2005 the intellectual property and technology rights were sold to various publishers and the studio was closed. === Neuroscience research === Following Elixir Studios, Hassabis returned to academia to obtain his PhD in cognitive neuroscience from UCL Queen Square Institute of Neurology in 2009 supervised by Eleanor Maguire. He sought to find inspiration in the human brain for new AI algorithms. He continued his neuroscience and artificial intelligence research as a visiting scientist jointly at Massachusetts Institute of Technology (MIT), in the lab of Tomaso Poggio, and Harvard University, before earning a Henry Wellcome postdoctoral research fellowship to the Gatsby Computational Neuroscience Unit at UCL in 2009 working with Peter Dayan. Working in the field of imagination, memory, and amnesia, he co-authored several influential papers published in Nature, Science, Neuron, and PNAS. His very first academic work, published in PNAS, was a landmark paper that showed systematically for the first time that patients with damage to their hippocampus, known to cause amnesia, were also unable to imagine themselves in new experiences. The finding established a link between the constructive process of imagination and the reconstructive process of episodic memory recall. Based on this work and a follow-up functional magnetic resonance imaging (fMRI) study, Hassabis developed a new theoretical account of the episodic memory system identifying scene construction, the generation and online maintenance of a complex and coherent scene, as a key process underlying both memory recall and imagination. This work received widespread coverage in the mainstream media and was listed in the top 10 scientific breakthroughs of the year by the journal Science. He later generalised these ideas to advance the notion of a 'simulation engine of the mind' whose role it was to imagine events and scenarios to aid with better planning. === DeepMind === Hassabis is the CEO and co-founder of DeepMind, a machine learning AI startup, founded in London in 2010 with Shane Legg and Mustafa Suleyman. Hassabis met Legg when both were postdocs at the Gatsby Computational Neuroscience Unit, and he and Suleyman had been friends through family. Hassabis also recruited his university friend and Elixir partner David Silver. DeepMind's mission is to "solve intelligence" and then use intelligence "to solve everything else". More concretely, DeepMind aims to combine insights from systems neuroscience with new developments in machine learning and computing hardware to unlock increasingly powerful general-purpose learning algorithms that will work towards the creation of an artificial general intelligence (AGI). The company has focused on training learning algorithms to master games, and in December 2013 it announced that it had made a pioneering breakthrough by training an algorithm called a Deep Q-Network (DQN) to play Atari games at a superhuman level by using only the raw pixels on the screen as inputs. DeepMind's early investors included several high-profile tech entrepreneurs. In 2014, Google purchased DeepMind for £400 million. Although most of the company has remained an independent entity based in London, DeepMind Health has since been directly incorporated into Google Health. Since the Google acquisition, the company has notched up a number of significant achievements, perhaps the most notable being the creation of AlphaGo, a program that defeated world champion Lee Sedol at the complex game of Go. Go had been considered a holy grail of AI, for its high number of possible board positions and resistance to existing programming techniques. However, AlphaGo beat European champion Fan Hui 5–0 in October 2015 before winning 4–1 against former world champion Lee Sedol in March 2016 and winning 3–0 against the world's top-ranked player Ke Jie in 2017. Additional DeepMind accomplishments include creating a neural Turing machine, reducing the energy used by the cooling systems in Google's data centres by 40%, and advancing research on AI safety. DeepMind has also been responsible for technical advances in machine learning, having produced a number of award-winning papers. In particular, the company has made significant advances in deep learning and reinforcement learning, and pioneered the field of deep reinforcement learning which combines these two methods. Hassabis has predicted that artificial intelligence will be "one of the most beneficial techn
Jakub Pachocki
Jakub Pachocki (born 1991) is a Polish computer scientist and former competitive programmer. He is best known as OpenAI's chief scientist and for his role in overseeing development of GPT-4. == Background == Pachocki was born in 1991 in Gdańsk, Poland. In high school, he was a six-time finalist of the Polish Olympiad in Informatics. In 2009, he qualified for the International Olympiad in Informatics, winning a silver medal. Pachocki obtained his undergraduate degree in Computer Science from the University of Warsaw. He represented his university at the International Collegiate Programming Contest with his team winning a gold medal and coming second place overall in 2012. In the same year he was also the champion of the Google Code Jam. From 2011 to 2012, Pachocki worked at Facebook as a software engineering intern. Pachocki attended graduate school at Carnegie Mellon University, where he obtained his PhD under the supervision of Gary Miller. == Career == After graduation, Pachocki did postdoc work at Harvard University and Simons Institute for the Theory of Computing. === OpenAI === In 2017, Pachocki joined OpenAI. In 2021, he became OpenAI's research director where he led the development of GPT-4 and OpenAI Five. In May 2024, he became chief scientist after his mentor Ilya Sutskever left the company. OpenAI CEO Sam Altman has called Pachocki "easily one of the greatest minds of our generation". == Competitive programming achievements == International Olympiad in Informatics: Silver medal (2009) International Collegiate Programming Contest World Finals: Gold medal (second place overall in 2012) Google Code Jam: Champion (2012), Third place (2011) Facebook Hacker Cup: Second place (2013) TopCoder Open Algorithm: Second place (2012) A more comprehensive list of achievements can be found at the Competitive Programming Hall Of Fame website.
Structural similarity index measure
The structural similarity index measure (SSIM) is a method for predicting the perceived quality of digital television and cinematic pictures, as well as other kinds of digital images and videos. It is also used for measuring the similarity between two images. The SSIM index is a full reference metric; in other words, the measurement or prediction of image quality is based on an initial uncompressed or distortion-free image as reference. SSIM is a perception-based model that considers image degradation as perceived change in structural information, while also incorporating important perceptual phenomena, including both luminance masking and contrast masking terms. This distinguishes from other techniques such as mean squared error (MSE) or peak signal-to-noise ratio (PSNR) that instead estimate absolute errors. Structural information is the idea that the pixels have strong inter-dependencies especially when they are spatially close. These dependencies carry important information about the structure of the objects in the visual scene. Luminance masking is a phenomenon whereby image distortions (in this context) tend to be less visible in bright regions, while contrast masking is a phenomenon whereby distortions become less visible where there is significant activity or "texture" in the image. == History == The predecessor of SSIM was called Universal Quality Index (UQI), or Wang–Bovik index, which was developed by Zhou Wang and Alan Bovik in 2001. This evolved, through their collaboration with Hamid Sheikh and Eero Simoncelli, into the current version of SSIM, which was published in April 2004 in the IEEE Transactions on Image Processing. In addition to defining the SSIM quality index, the paper provides a general context for developing and evaluating perceptual quality measures, including connections to human visual neurobiology and perception, and direct validation of the index against human subject ratings. The basic model was developed in the Laboratory for Image and Video Engineering (LIVE) at The University of Texas at Austin and further developed jointly with the Laboratory for Computational Vision (LCV) at New York University. Further variants of the model have been developed in the Image and Visual Computing Laboratory at University of Waterloo and have been commercially marketed. SSIM subsequently found strong adoption in the image processing community and in the television and social media industries. The 2004 SSIM paper has been cited over 50,000 times according to Google Scholar, making it one of the highest cited papers in the image processing and video engineering fields. It was recognized with the IEEE Signal Processing Society Best Paper Award for 2009. It also received the IEEE Signal Processing Society Sustained Impact Award for 2016, indicative of a paper having an unusually high impact for at least 10 years following its publication. Because of its high adoption by the television industry, the authors of the original SSIM paper were each accorded a Primetime Engineering Emmy Award in 2015 by the Television Academy. == Algorithm == The SSIM index is calculated between two windows of pixel values x {\displaystyle x} and y {\displaystyle y} of common size, from corresponding locations in two images to be compared. These SSIM values can be aggregated across the full images by averaging or other variations. === Special-case formula === In one simple special case, further explained in the next section, the SSIM measure between x {\displaystyle x} and y {\displaystyle y} is: SSIM ( x , y ) = ( 2 μ x μ y + c 1 ) ( 2 σ x y + c 2 ) ( μ x 2 + μ y 2 + c 1 ) ( σ x 2 + σ y 2 + c 2 ) {\displaystyle {\hbox{SSIM}}(x,y)={\frac {(2\mu _{x}\mu _{y}+c_{1})(2\sigma _{xy}+c_{2})}{(\mu _{x}^{2}+\mu _{y}^{2}+c_{1})(\sigma _{x}^{2}+\sigma _{y}^{2}+c_{2})}}} with: μ x {\displaystyle \mu _{x}} the pixel sample mean of x {\displaystyle x} ; μ y {\displaystyle \mu _{y}} the pixel sample mean of y {\displaystyle y} ; σ x 2 {\displaystyle \sigma _{x}^{2}} the sample variance of x {\displaystyle x} ; σ y 2 {\displaystyle \sigma _{y}^{2}} the sample variance of y {\displaystyle y} ; σ x y {\displaystyle \sigma _{xy}} the sample covariance of x {\displaystyle x} and y {\displaystyle y} ; c 1 = ( k 1 L ) 2 {\displaystyle c_{1}=(k_{1}L)^{2}} , c 2 = ( k 2 L ) 2 {\displaystyle c_{2}=(k_{2}L)^{2}} two variables to stabilize the division with weak denominator; L {\displaystyle L} the dynamic range of the pixel-values (typically this is 2 # b i t s p e r p i x e l − 1 {\displaystyle 2^{\#bits\ per\ pixel}-1} ); k 1 = 0.01 {\displaystyle k_{1}=0.01} and k 2 = 0.03 {\displaystyle k_{2}=0.03} by default. === General formula and components === The SSIM formula is based on three comparison measurements between the samples of x {\displaystyle x} and y {\displaystyle y} : luminance ( l {\displaystyle l} ), contrast ( c {\displaystyle c} ), and structure ( s {\displaystyle s} ). The individual comparison functions are: l ( x , y ) = 2 μ x μ y + c 1 μ x 2 + μ y 2 + c 1 {\displaystyle l(x,y)={\frac {2\mu _{x}\mu _{y}+c_{1}}{\mu _{x}^{2}+\mu _{y}^{2}+c_{1}}}} c ( x , y ) = 2 σ x σ y + c 2 σ x 2 + σ y 2 + c 2 {\displaystyle c(x,y)={\frac {2\sigma _{x}\sigma _{y}+c_{2}}{\sigma _{x}^{2}+\sigma _{y}^{2}+c_{2}}}} s ( x , y ) = σ x y + c 3 σ x σ y + c 3 {\displaystyle s(x,y)={\frac {\sigma _{xy}+c_{3}}{\sigma _{x}\sigma _{y}+c_{3}}}} The SSIM for each block is then a weighted combination of those comparative measures: SSIM ( x , y ) = l ( x , y ) α ⋅ c ( x , y ) β ⋅ s ( x , y ) γ {\displaystyle {\text{SSIM}}(x,y)=l(x,y)^{\alpha }\cdot c(x,y)^{\beta }\cdot s(x,y)^{\gamma }} Choosing the third denominator stabilizing constant as: c 3 = c 2 / 2 {\displaystyle c_{3}=c_{2}/2} leads to a simplification when combining the c and s components with equal exponents ( β = γ {\displaystyle \beta =\gamma } ), as the numerator of c is then twice the denominator of s, leading to a cancellation leaving just a 2. Setting the weights (exponents) α , β , γ {\displaystyle \alpha ,\beta ,\gamma } to 1, the formula can then be reduced to the special case shown above. === Mathematical properties === SSIM satisfies the identity of indiscernibles, and symmetry properties, but not the triangle inequality or non-negativity, and thus is not a distance function. However, under certain conditions, SSIM may be converted to a normalized root MSE measure, which is a distance function. The square of such a function is not convex, but is locally convex and quasiconvex, making SSIM a feasible target for optimization. === Application of the formula === In order to evaluate the image quality, this formula is usually applied only on luma, although it may also be applied on color (e.g., RGB) values or chromatic (e.g. YCbCr) values. The resultant SSIM index is a decimal value between -1 and 1, where 1 indicates perfect similarity, 0 indicates no similarity, and -1 indicates perfect anti-correlation. For an image, it is typically calculated using a sliding Gaussian window of size 11×11 or a block window of size 8×8. The window can be displaced pixel-by-pixel on the image to create an SSIM quality map of the image. In the case of video quality assessment, the authors propose to use only a subgroup of the possible windows to reduce the complexity of the calculation. === Variants === ==== Multi-scale SSIM ==== A more advanced form of SSIM, called Multiscale SSIM (MS-SSIM) is conducted over multiple scales through a process of multiple stages of sub-sampling, reminiscent of multiscale processing in the early vision system. It has been shown to perform equally well or better than SSIM on different subjective image and video databases. ==== Multi-component SSIM ==== Three-component SSIM (3-SSIM) is a form of SSIM that takes into account the fact that the human eye can see differences more precisely on textured or edge regions than on smooth regions. The resulting metric is calculated as a weighted average of SSIM for three categories of regions: edges, textures, and smooth regions. The proposed weighting is 0.5 for edges, 0.25 for the textured and smooth regions. The authors mention that a 1/0/0 weighting (ignoring anything but edge distortions) leads to results that are closer to subjective ratings. This suggests that edge regions play a dominant role in image quality perception. The authors of 3-SSIM have also extended the model into four-component SSIM (4-SSIM). The edge types are further subdivided into preserved and changed edges by their distortion status. The proposed weighting is 0.25 for all four components. ==== Structural dissimilarity ==== Structural dissimilarity (DSSIM) may be derived from SSIM, though it does not constitute a distance function as the triangle inequality is not necessarily satisfied. DSSIM ( x , y ) = 1 − SSIM ( x , y ) 2 {\displaystyle {\hbox{DSSIM}}(x,y)={\frac {1-{\hbox{SSIM}}(x,y)}{2}}} ==== Video quality metrics and temporal variants ==== It is worth noting that the original vers
GENESIS (software)
GENESIS (The General Neural Simulation System) is a simulation environment for constructing realistic models of neurobiological systems at many levels of scale including: sub-cellular processes, individual neurons, networks of neurons, and neuronal systems. These simulations are “computer-based implementations of models whose primary objective is to capture what is known of the anatomical structure and physiological characteristics of the neural system of interest”. GENESIS is intended to quantify the physical framework of the nervous system in a way that allows for easy understanding of the physical structure of the nerves in question. “At present only GENESIS allows parallelized modeling of single neurons and networks on multiple-instruction-multiple-data parallel computers.” Development of GENESIS software spread from its home at Caltech to labs at the University of Texas at San Antonio, the University of Antwerp, the National Centre for Biological Sciences in Bangalore, the University of Colorado, the Pittsburgh Supercomputing Center, the San Diego Supercomputer Center, and Emory University. == Neurons and Neural Systems == GENESIS works by creating simulation environments for constructing models of neurons or neural systems. "Nerve cells are capable of communicating with each other in such a highly structured manner as to form neuronal networks. To understand neural networks, it is necessary to understand the ways in which one neuron communicates with another through synaptic connections and the process called synaptic transmission". Neurons have a specialized structure for their function, they "are different from most other cells in the body in that they are polarized and have distinct morphological regions, each with specific functions". The two important regions of a neuron are the dendrite and the axon. "Dendrites are the region where one neuron receives connections from other neurons. The cell body or soma contains the nucleus and the other organelles necessary for cellular function. The axon is a key component of nerve cells over which information is transmitted from one part of the neuron (e.g., the cell body) to the terminal regions of the neuron". The third important piece of a neuron is the synapse. "The synapse is the terminal region of the axon this is where one neuron forms a connection with another and conveys information through the process of synaptic transmission". Neural networks like the ones simulated with GENESIS software can quickly become highly complex and difficult to understand. "Just a few interconnected neurons (a microcircuit) can perform sophisticated tasks such as mediate reflexes, process sensory information, generate locomotion and mediate learning and memory. Even more complex networks, macrocircuits, consist of multiple embedded microcircuits. Macrocircuits mediate higher brain functions such as object recognition and cognition". GENESIS endeavors to simulate neural systems as they are found in nature. Often, "a neuron can receive contacts from up to 10,000 presynaptic neurons, and, in turn, any one neuron can contact up to 10,000 postsynaptic neurons. The combinatorial possibility could give rise to enormously complex neuronal circuits or network topologies, which might be very difficult to understand". == History == GENESIS was developed by Dr. James M. Bower, in the Caltech laboratory, and first released to the public in 1988 in association with the first Methods in Computational Neuroscience Course at the Marine Biological Laboratory in Woods Hole, MA. Full source code for the software was released in the same year under an open software model for development. It's now supported by the Computational Biology Initiative at the University of Texas at San Antonio and is available free along with tutorial guides on its use. P-GENESIS, a parallel version of GENESIS, was first run in 1990 on the Intel Delta, which was the prototype for the Intel Paragon family of massively parallel supercomputers. == How GENESIS Works == GENESIS is useful in creating a simulation environment for constructing models of neurobiological systems, such as: sub-cellular processes individual neurons networks of neurons neuronal systems The GENESIS system is complicated, but relatively easy to use. An individual can input commands through one of three ways: script files, graphical user interface, or the GENESIS command shell. These commands are then processed by the script language interpreter. "The Script Language Interpreter processes commands entered through the keyboard, script files, or the graphical user interface, and passes them to the GENESIS simulation engine. The simulation engine also loads compiled object libraries, reads and writes data files, and interacts with the graphical user interface". Below is a graphical representation of the user input process and a sample GENESIS output. == Applications == Most current applications for GENESIS involve realistic simulations of biological systems. It is usually used to simulate the behavior of larger brain structures, for example the cerebral cortex. These studies most often occur in lab courses in neural simulation at Caltech and the Marine Biological Laboratory at Woods Hole, Massachusetts. GENESIS can be used in combination with Yale University’s software called NEURON as a means for scientists to collaborate to construct a physical description of the nervous system. The GENESIS software can also be used with Kinetikit in the modeling of signal transduction pathways. GENESIS has been used in many studies. Some of these studies involve research that focuses on the development of software that would be useful across many disciplines. Others are studies of neurons, such as Purkinje cells. These studies used GENESIS to simulate Purkinje cells and could be useful for the planning and development of later experiments using the GENESIS software. There may also be biomedical applications of the software. For example, St. Jude Medical in Europe has developed an implanted GENESIS device.