In artificial intelligence and cognitive science, the structure mapping engine (SME) is an implementation in software of an algorithm for analogical matching based on the psychological theory of Dedre Gentner. The basis of Gentner's structure-mapping idea is that an analogy is a mapping of knowledge from one domain (the base) into another (the target). The structure-mapping engine is a computer simulation of the analogy and similarity comparisons. The theory is useful because it ignores surface features and finds matches between potentially very different things if they have the same representational structure. For example, SME could determine that a pen is like a sponge because both are involved in dispensing liquid, even though they do this very differently. == Structure mapping theory == Structure mapping theory is based on the systematicity principle, which states that connected knowledge is preferred over independent facts. Therefore, the structure mapping engine should ignore isolated source-target mappings unless they are part of a bigger structure. The SME, the theory goes, should map objects that are related to knowledge that has already been mapped. The theory also requires that mappings be done one-to-one, which means that no part of the source description can map to more than one item in the target and no part of the target description can be mapped to more than one part of the source. The theory also requires that if a match maps subject to target, the arguments of subject and target must also be mapped. If both these conditions are met, the mapping is said to be "structurally consistent." == Concepts in SME == SME maps knowledge from a source into a target. SME calls each description a dgroup. Dgroups contain a list of entities and predicates. Entities represent the objects or concepts in a description — such as an input gear or a switch. Predicates are one of three types and are a general way to express knowledge for SME. Relation predicates contain multiple arguments, which can be other predicates or entities. An example relation is: (transmit (what from to)). This relation has a functor transmit and takes three arguments: what, from, and to. Attribute predicates are the properties of an entity. An example of an attribute is (red gear) which means that gear has the attribute red. Function predicates map an entity into another entity or constant. An example of a function is (joules power source) which maps the entity power source onto the numerical quantity joules. Functions and attributes have different meanings, and consequently SME processes them differently. For example, in SME's true analogy rule set, attributes differ from functions because they cannot match unless there is a higher-order match between them. The difference between attributes and functions will be explained further in this section's examples. All predicates have four parameters. They have (1) a functor, which identifies it, and (2) a type, which is either relation, attribute, or function. The other two parameters (3 and 4) are for determining how to process the arguments in the SME algorithm. If the arguments have to be matched in order, commutative is false. If the predicate can take any number of arguments, N-ary is false. An example of a predicate definition is: (sme:defPredicate behavior-set (predicate) relation :n-ary? t :commutative? t) The predicate's functor is “behavior-set,” its type is “relation,” and its n-ary and commutative parameters are both set to true. The “(predicate)” part of the definition specifies that there will be one or more predicates inside an instantiation of behavior-set. == Algorithm details == The algorithm has several steps. The first step of the algorithm is to create a set of match hypotheses between source and target dgroups. A match hypothesis represents a possible mapping between any part of the source and the target. This mapping is controlled by a set of match rules. By changing the match rules, one can change the type of reasoning SME does. For example, one set of match rules may perform a kind of analogy called literal similarity, and another performs a kind of analogy called true-analogy. These rules are not the place where domain-dependent information is added, but rather where the analogy process is tweaked, depending on the type of cognitive function the user is trying to emulate. For a given match rule, there are two types of rules that further define how it will be applied: filter rules and intern rules. Intern rules use only the arguments of the expressions in the match hypotheses that the filter rules identify. This limitation makes the processing more efficient by constraining the number of match hypotheses that are generated. At the same time, it also helps to build the structural consistencies that are needed later on in the algorithm. An example of a filter rule from the true-analogy rule set creates match hypotheses between predicates that have the same functor. The true-analogy rule set has an intern rule that iterates over the arguments of any match hypothesis, creating more match hypotheses if the arguments are entities or functions, or if the arguments are attributes and have the same functor. In order to illustrate how the match rules produce match hypotheses consider these two predicates: transmit torque inputgear secondgear (p1) transmit signal switch div10 (p2) Here we use true analogy for the type of reasoning. The filter match rule generates a match between p1 and p2 because they share the same functor, transmit. The intern rules then produce three more match hypotheses: torque to signal, inputgear to switch, and secondgear to div10. The intern rules created these match hypotheses because all the arguments were entities. If the arguments were functions or attributes instead of entities, the predicates would be expressed as: transmit torque (inputgear gear) (secondgear gear) (p3) transmit signal (switch circuit) (div10 circuit) (p4) These additional predicates make inputgear, secondgear, switch, and div10 functions or attributes depending on the value defined in the language input file. The representation also contains additional entities for gear and circuit. Depending on what type inputgear, secondgear, switch, and div10 are, their meanings change. As attributes, each one is a property of the gear or circuit. For example, the gear has two attributes, inputgear and secondgear. The circuit has two attributes, switch and circuit. As functions inputgear, secondgear, switch, and div10 become quantities of the gear and circuit. In this example, the functions inputgear and secondgear now map to the numerical quantities “torque from inputgear” and “torque from secondgear,” For the circuit the quantities map to logical quantity “switch engaged” and the numerical quantity “current count on the divide by 10 counter.” SME processes these differently. It does not allow attributes to match unless they are part of a higher-order relation, but it does allow functions to match, even if they are not part of such a relation. It allows functions to match because they indirectly refer to entities and thus should be treated like relations that involve no entities. However, as next section shows, the intern rules assign lower weights to matches between functions than to matches between relations. The reason SME does not match attributes is because it is trying to create connected knowledge based on relationships and thus satisfy the systematicity principle. For example, if both a clock and a car have inputgear attributes, SME will not mark them as similar. If it did, it would be making a match between the clock and car based on their appearance — not on the relationships between them. When the additional predicates in p3 and p4 are functions, the results from matching p3 and p4 are similar to the results from p1 and p2 except there is an additional match between gear and circuit and the values for the match hypotheses between (inputgear gear) and (switch circuit), and (secondgear gear) and (div10 circuit), are lower. The next section describes the reason for this in more detail. If the inputgear, secondgear, switch, and div10 are attributes instead of entities, SME does not find matches between any of the attributes. It finds matches only between the transmit predicates and between torque and signal. Additionally, the structural-evaluation scores for the remaining two matches decrease. In order to get the two predicates to match, p3 would need to be replaced by p5, which is demonstrated below. transmit torque (inputgear gear) (div10 gear) (p5) Since the true-analogy rule set identifies that the div10 attributes are the same between p5 and p4 and because the div10 attributes are both part of the higher-relation match between torque and signal, SME makes a match between (div10 gear) and (div10 circuit) — which leads to a match between gear and circuit. Being part of a higher-order match is a requiremen
AI Overviews
AI Overviews is an artificial intelligence (AI) feature integrated into Google Search that produces AI-generated summaries of search results. The feature has been criticized for its inaccuracy and for reducing website traffic. == History and development == AI Overviews were first introduced as part of Google's Search Generative Experience (SGE), which was unveiled at the Google I/O conference in May 2023. In May 2024 at Google I/O 2024, the feature was rebranded as AI Overviews and launched in the United States. The introduction of AI Overviews was seen as a strategic move to compete with other generative AI advancements, including OpenAI's ChatGPT. By August 2024, AI Overviews was rolled out to several other countries, including the United Kingdom, India, Japan, Brazil, Mexico, and Indonesia, with support for multiple languages. In October 2024, Google expanded the feature globally, making it available in over 100 countries. In December 2024, Botify x Demandsphere released findings stating that when AI Overviews and featured snippets appear together on the search engine results page, they take up approximately 67.1% of the screen on desktop and 75.7% on mobile. Even if content is ranking in the #1 position, it may not be visible to consumers if other visual elements on the results page are more prominent. In March 2025, Google started testing an "AI Mode", where the search results page is AI-generated. The company was also considering adding advertisements to the AI Mode, as they already exist in AI Overviews. As of May 2025, AI Overviews are available in over 200 countries and territories and in more than 40 languages. As of March 2026, Google AI Overviews appear on more than 48% of total Google Search queries, compared to just 6.49% in the previous year (58% year-over-year growth). == Functionality == The AI Overviews feature uses large language models to generate summaries from web content. The overviews are designed to be concise, providing a snapshot of relevant information about the queried topic. Google allows users to adjust the language complexity in summaries, offering both simplified and detailed options. The overviews also include links to sources. According to a June 2025 study by Semrush, the most cited source is Quora, followed by Reddit. == Reception == The feature has faced criticism for inaccuracies, including instances where erroneous or nonsensical content was generated. Depending on what is searched for, the overview may also consist of hallucinated content, such as when searching for idioms that do not exist. In May 2024, Google temporarily restricted the AI tool after it provided suggestions that were seen as nonsensical and harmful, such as telling users to eat rocks or apply glue on pizza. Concerns were also raised by content publishers, who feared a decline in web traffic as users relied on the summaries instead of visiting source websites. A Google patent from 2026 raised the concern of webmasters that Google could entirely replace the landing page of websites by an AI optimized copy of the website in its results. There is also apprehension about the ethical implications of AI-driven content aggregation, including its impact on intellectual property rights and the visibility of smaller content providers. The European Commission announced in December 2025 that they were investigating whether AI Overviews breached European competition law. In response, Google has stated its commitment to improve content validation and refine the algorithms used to filter unreliable information. Google implemented measures to prioritize link placement within AI Overviews, aiming to balance user convenience with the needs of content creators. In January 2026, Google restricted AI Overviews on certain health-related searches following an investigation by The Guardian. == Lawsuits == On February 24, 2025, Chegg sued Alphabet over the AI Overviews feature, claiming that it was leading to students preferring "low-quality, unverified AI summaries", thus violating antitrust law. Chegg also said it was considering either a sale or a take-private transaction. In September 2025, Penske Media Corporation, the publisher of Rolling Stone and The Hollywood Reporter, sued Google, claiming that AI Overviews illegally regurgitate content from their websites and drive off potential site visitors by always appearing on top of the search results while leaving little incentive to see the linked sources. The company stated that "the future of digital media and [...] its integrity [...] is threatened by Google's current actions", alleging that 20% of searches that link to Penske-owned websites show AI Overviews and that the figure is expected to rise. Google spokesperson José Castañeda called the claims "meritless" and stated that "AI Overviews send traffic to a greater diversity of sites." In 2026, Canadian musician Ashley MacIsaac filed a lawsuit against Google claiming that the AI Overview feature had wrongly stated that MacIsaac had been convicted of numerous criminal offences and was on the sex offender registry. He claims this incorrect information led to the cancellation of a December 2025 gig organized by the Sipekne'katik First Nation.
Morphological antialiasing
Morphological antialiasing (MLAA) is a spatial anti-aliasing technique used in real-time computer graphics. It reduces artifacts, such as jaggies, when representing a high-resolution image at a lower resolution. MLAA is a post-process filtering which detects borders in the resulting image and then finds specific patterns in these. Anti-aliasing is achieved by blending pixels in these borders, according to the pattern they belong to and their position within the pattern. Introduced in 2009, MLAA was an early and influential example of anti-aliasing techniques done in post-processing, which makes them suitable for deferred shading. A similar method in this class is fast approximate anti-aliasing (FXAA). Temporal anti-aliasing, also a post-process, has become the most common anti-aliasing method for real-time rendering and video games. Enhanced subpixel morphological antialiasing, or SMAA, is an image-based GPU-based implementation of MLAA developed by Universidad de Zaragoza and Crytek.
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.
Phase stretch transform
Phase stretch transform (PST) is a computational approach to signal and image processing. One of its utilities is for feature detection and classification. PST is related to time stretch dispersive Fourier transform. It transforms the image by emulating propagation through a diffractive medium with engineered 3D dispersive property (refractive index). The operation relies on symmetry of the dispersion profile and can be understood in terms of dispersive eigenfunctions or stretch modes. PST performs similar functionality as phase-contrast microscopy, but on digital images. PST can be applied to digital images and temporal (time series) data. It is a physics-based feature engineering algorithm. == Operation principle == Here the principle is described in the context of feature enhancement in digital images. The image is first filtered with a spatial kernel followed by application of a nonlinear frequency-dependent phase. The output of the transform is the phase in the spatial domain. The main step is the 2-D phase function which is typically applied in the frequency domain. The amount of phase applied to the image is frequency dependent, with higher amount of phase applied to higher frequency features of the image. Since sharp transitions, such as edges and corners, contain higher frequencies, PST emphasizes the edge information. Features can be further enhanced by applying thresholding and morphological operations. PST is a pure phase operation whereas conventional edge detection algorithms operate on amplitude. == Physical and mathematical foundations of phase stretch transform == Photonic time stretch technique can be understood by considering the propagation of an optical pulse through a dispersive fiber. By disregarding the loss and non-linearity in fiber, the non-linear Schrödinger equation governing the optical pulse propagation in fiber upon integration reduces to: E o ( z , t ) = 1 2 π ∫ − ∞ ∞ E ~ i ( 0 , ω ) ⋅ e − i β 2 z ω 2 2 ⋅ e i ω t d ω {\displaystyle E_{o}(z,t)={\frac {1}{2\pi }}\int _{-\infty }^{\infty }{\tilde {E}}_{i}(0,\omega )\cdot e^{\frac {-i\beta _{2}z\omega ^{2}}{2}}\cdot e^{i\omega {t}}\,d\omega } (1) where β 2 {\displaystyle \beta _{2}} = GVD parameter, z is propagation distance, E o ( z , t ) {\displaystyle E_{o}(z,t)} is the reshaped output pulse at distance z and time t. The response of this dispersive element in the time-stretch system can be approximated as a phase propagator as presented in H ( ω ) = e i φ ( ω ) = e i ∑ m = 0 ∞ φ m ( ω ) = ∏ m = 0 ∞ H m ( ω ) {\displaystyle H(\omega )=e^{i\varphi (\omega )}=e^{i\sum _{m=0}^{\infty }\varphi _{m}(\omega )}=\prod _{m=0}^{\infty }H_{m}(\omega )} (2) Therefore, Eq. 1 can be written as following for a pulse that propagates through the time-stretch system and is reshaped into a temporal signal with a complex envelope given by E o ( t ) = 1 2 π ∫ − ∞ ∞ E ~ i ( ω ) ⋅ H ( ω ) ⋅ e i ω t d ω {\displaystyle E_{o}(t)={\frac {1}{2\pi }}\int _{-\infty }^{\infty }{\tilde {E}}_{i}(\omega )\cdot H(\omega )\cdot e^{i\omega t}\,d\omega } (3) The time stretch operation is formulated as generalized phase and amplitude operations, S { E i ( t ) } = ∫ − ∞ + ∞ F { E i ( t ) } ⋅ e i φ ( ω ) ⋅ L ~ ( ω ) ⋅ e i ω t d ω {\displaystyle \mathbb {S} \{E_{i}(t)\}=\int _{-\infty }^{+\infty }{\mathcal {F}}\{E_{i}(t)\}\cdot e^{i\varphi (\omega )}\cdot {\tilde {L}}(\omega )\cdot e^{i\omega {t}}d\omega } (4) where e i φ ( ω ) {\displaystyle e^{i\varphi (\omega )}} is the phase filter and L ~ ( ω ) {\displaystyle {\tilde {L}}(\omega )} is the amplitude filter. Next the operator is converted to discrete domain, S { E i [ n ] } = 1 N ∑ u = 0 N − 1 F F T { E i ( n ) } ⋅ K ~ ( u ) ⋅ L ~ ( u ) ⋅ e i 2 π N u n {\displaystyle \mathbb {S} \{E_{i}[n]\}={\frac {1}{N}}\sum _{u=0}^{N-1}FFT\{E_{i}(n)\}\cdot {\tilde {K}}(u)\cdot {\tilde {L}}(u)\cdot e^{i{\frac {2\pi }{N}}un}} (5) where u {\displaystyle u} is the discrete frequency, K ~ ( u ) {\displaystyle {\tilde {K}}(u)} is the phase filter, L ~ ( u ) {\displaystyle {\tilde {L}}(u)} is the amplitude filter and FFT is fast Fourier transform. The stretch operator S { } {\displaystyle \mathbb {S} \{\}} for a digital image is then S { E i [ n , m ] } = 1 M N ∑ v = 0 N − 1 ∑ u = 0 M − 1 F F T 2 { E i ( n , m ) } ⋅ K ~ ( u , v ) ⋅ L ~ ( u , v ) ⋅ e i 2 π M u m ⋅ e i 2 π N v n {\displaystyle \mathbb {S} \{E_{i}[n,m]\}={\frac {1}{MN}}\sum _{v=0}^{N-1}\sum _{u=0}^{M-1}FFT^{2}\{E_{i}(n,m)\}\cdot {\tilde {K}}(u,v)\cdot {\tilde {L}}(u,v)\cdot e^{i{\frac {2\pi }{M}}um}\cdot e^{i{\frac {2\pi }{N}}vn}} (6) In the above equations, E i [ n , m ] {\displaystyle E_{i}[n,m]} is the input image, n {\displaystyle n} and m {\displaystyle m} are the spatial variables, F F T 2 {\displaystyle FFT^{2}} is the two-dimensional fast Fourier transform, and u {\displaystyle u} and v {\displaystyle v} are spatial frequency variables. The function K ~ ( u , v ) {\displaystyle {\tilde {K}}(u,v)} is the warped phase kernel and the function L ~ ( u , v ) {\displaystyle {\tilde {L}}(u,v)} is a localization kernel implemented in frequency domain. PST operator is defined as the phase of the Warped Stretch Transform output as follows P S T { E i [ n , m ] } ≜ ∡ { S { E i [ x , y ] } } {\displaystyle PST\{E_{i}[n,m]\}\triangleq \measuredangle \{\mathbb {S} \{E_{i}[x,y]\}\}} (7) where ∡ { } {\displaystyle \measuredangle \{\}} is the angle operator. == PST kernel implementation == The warped phase kernel K ~ ( u , v ) {\displaystyle {\tilde {K}}(u,v)} can be described by a nonlinear frequency dependent phase K ~ ( u , v ) = e i φ ( u , v ) {\displaystyle {\tilde {K}}(u,v)=e^{i\varphi (u,v)}} While arbitrary phase kernels can be considered for PST operation, here we study the phase kernels for which the kernel phase derivative is a linear or sublinear function with respect to frequency variables. A simple example for such phase derivative profiles is the inverse tangent function. Consider the phase profile in the polar coordinate system φ ( u , v ) = φ polar ( r , θ ) = φ polar ( r ) {\displaystyle \varphi (u,v)=\varphi _{\text{polar}}(r,\theta )=\varphi _{\text{polar}}(r)} From d φ ( r ) d r = tan − 1 ( r ) {\displaystyle {\frac {d\varphi (r)}{dr}}=\tan ^{-1}(r)} we have φ ( r ) = r tan − 1 ( r ) − 1 2 log ( r 2 + 1 ) {\displaystyle \varphi (r)=r\tan ^{-1}(r)-{\frac {1}{2}}\log(r^{2}+1)} Therefore, the PST kernel is implemented as φ ( r ) = S ⋅ ( W r ) ⋅ tan − 1 ( W r ) − 1 2 log ( 1 + ( W r ) 2 ) ( W r max ) ⋅ tan − 1 ( W r max ) − 1 2 log ( 1 + ( W r max ) 2 ) {\displaystyle \varphi (r)=S\cdot {\frac {(Wr)\cdot \tan ^{-1}(Wr)-{\frac {1}{2}}\log(1+(Wr)^{2})}{(Wr_{\max })\cdot \tan ^{-1}(Wr_{\max })-{\frac {1}{2}}\log(1+(Wr_{\max })^{2})}}} where S {\displaystyle S} and W {\displaystyle W} are real-valued numbers related to the strength and warp of the phase profile == Applications == PST has been used for edge detection in biological and biomedical images as well as synthetic-aperture radar (SAR) image processing, as well as detail and feature enhancement for digital images. PST has also been applied to improve the point spread function for single molecule imaging in order to achieve super-resolution. The transform exhibits intrinsic superior properties compared to conventional edge detectors for feature detection in low contrast visually impaired images. The PST function can also be performed on 1-D temporal waveforms in the analog domain to reveal transitions and anomalies in real time. == Open source code release == On February 9, 2016, a UCLA Engineering research group has made public the computer code for PST algorithm that helps computers process images at high speeds and "see" them in ways that human eyes cannot. The researchers say the code could eventually be used in face, fingerprint, and iris recognition systems for high-tech security, as well as in self-driving cars' navigation systems or for inspecting industrial products. The Matlab implementation for PST can also be downloaded from Matlab Files Exchange. However, it is provided for research purposes only, and a license must be obtained for any commercial applications. The software is protected under a US patent. The code was then significantly refactored and improved to support GPU acceleration. In May 2022, it became one algorithm in PhyCV: the first physics-inspired computer vision library.
Foveated rendering
Foveated rendering is a rendering technique which uses an eye tracker integrated with a virtual reality headset to reduce the rendering workload by greatly reducing the image quality in the peripheral vision (outside of the zone gazed by the fovea). A less sophisticated variant called fixed foveated rendering doesn't utilise eye tracking and instead assumes a fixed focal point. == History == Research into foveated rendering dates back at least to 1991. At Tech Crunch Disrupt SF 2014, Fove unveiled a headset featuring foveated rendering. This was followed by a successful kickstarter in May 2015. At CES 2016, SensoMotoric Instruments (SMI) demoed a new 250 Hz eye tracking system and a working foveated rendering solution. It resulted from a partnership with camera sensor manufacturer Omnivision who provided the camera hardware for the new system. In July 2016, Nvidia demonstrated during SIGGRAPH a new method of foveated rendering claimed to be invisible to users. In February 2017, Qualcomm announced their Snapdragon 835 Virtual Reality Development Kit (VRDK) which includes foveated rendering support called Adreno Foveation. == Use == According to chief scientist Michael Abrash at Oculus, utilising foveated rendering in conjunction with sparse rendering and deep learning image reconstruction has the potential to require an order of magnitude fewer pixels to be rendered in comparison to a full image. Later, these results have been demonstrated and published. In December 2019, fixed foveated rendering support was added to the Oculus Quest SDK. A number of VR headsets have included on-board eye tracking to provide support for foveated rendering, including HTC's Vive Pro Eye (2019), Meta Quest Pro (2022), PlayStation VR2 (2023), and Apple Vision Pro (2024). In 2025, Valve announced the upcoming Steam Frame headset, which applies a variation of the technique known as "foveated streaming" for wireless streaming from a PC to the headset; the method similarly uses variance in bit rate, and is performed at the encoder level rather than the software level.
Opponent process
The opponent process is a hypothesis of color vision that states that the human visual system interprets information about color by processing signals from the three types of photoreceptor cells in an antagonistic manner. The three types of cones are called L, M, and S. The names stand for "Long wavelength sensitive,” "middle wavelength sensitive," and "short wavelength sensitive." The opponent-process theory implicates three opponent channels: L versus M, S versus (L+M), and a luminance channel (+ versus -). These cone-opponent mechanisms were at one time thought to be the neural substrate for a psychological theory called Hering's Opponent Colors Theory, which calls for three psychologically important opponent color processes: red versus green, blue versus yellow, and black versus white (luminance). The Opponent Colors Theory is named for the German physiologist Ewald Hering who proposed the idea in the late 19th century. However, it has been argued that Hering’s Opponent Colors Theory lacks adequate phenomenological and empirical support, and may not be a necessary feature of normal human color experience. Correspondingly, considerable physiological and behavioral evidence proves that the physiological cone opponent mechanisms do not constitute the neurobiological basis for Hering's Opponent Colors Theory. == Color theory == === Complementary colors === When staring at a bright color for a while (e.g. red), then looking away at a white field, an afterimage is perceived, such that the original color will evoke its complementary color (cyan, in the case of red input). When complementary colors are combined or mixed, they "cancel each other out" and become neutral (white or gray). That is, complementary colors are never perceived as a mixture; there is no "greenish red" or "yellowish blue", despite claims to the contrary. The strongest color contrast that a color can have is its complementary color. Complementary colors may also be called "opposite colors" and they were originally considered the primary evidence in support of Hering's Opponent Colors Theory. There are two fatal problems with this evidence. First, the complement of red is not green, as called for by Hering's theory; it is bluish-green. And second, there exists a complementary color for every color, so there is nothing special about the set of complementary pairs picked out by Hering's theory. === Unique hues === The colors that define the extremes for each opponent channel are called unique hues, as opposed to composite (mixed) hues. Ewald Hering first defined the unique hues as red, green, blue, and yellow, and based them on the concept that these colors could not be simultaneously perceived. For example, a color cannot appear both red and green. These definitions have been experimentally refined and are represented today by average hue angles of 353° (carmine red), 128° (cobalt green), 228° (cobalt blue), 58° (yellow). The unique hues are a defining feature of many psychological color spaces, but there is substantial evidence showing that the unique hues are not hard wired in the nervous system, contrary to the stipulations of Hering's Opponent Colors Theory. Unique hues can differ between individuals and are often used in psychophysical research to measure variations in color perception due to color-vision deficiencies or color adaptation. While there is considerable inter-subject variability when defining unique hues experimentally, an individual's unique hues are very consistent, to within a few nanometers of wavelength. == Physiological basis == === Relation to LMS color space === The trichromatic theory is in conflict with Hering's Opponent Colors Theory, although it is compatible with a physiological opponent process that compares the outputs of the different classes of cone types. The poles of these cone opponent mechanisms do not correspond to the unique hues of Hering's Opponent Colors Theory and unlike the unique hues, have no privilege in color perception. Most humans have three different cone cells in their retinas that facilitate trichromatic color vision. Colors are determined by the proportional excitation of these three cone types, i.e. their quantum catch. The levels of excitation of each cone type are the parameters that define LMS color space. To calculate the opponent process tristimulus values from the LMS color space, the cone excitations must be compared: The luminous (achromatic) opponent channel is a weighted sum of all three cone cells (plus the rod cells in some conditions). The red–green opponent channel is equal to the difference of the L- and M-cones. The blue–yellow opponent channel is equal to the difference of the S-cone and the average/weighted sum of the L- and M-cones. Most mammals have no L cone (the primate L cone arose from a gene duplication of the M cone opsin gene). These mammals still show two kinds of opponent channels in their retinal ganglion cells: the achromatic channel and the blue-yellow opponency channel. === Cone opponent mechanisms are encoded in the retina === The output of different types of cones are compared by cells in the retina including retina bipolar cells (which compare signals from L and M cones) and bistratified retinal ganglion cells (which compare S cone signals with L and M cone signals). The output of bipolar cells is relayed to the visual cortex by the retinal ganglion cells (RGCs) by way of a thalamic relay station called the lateral geniculate nucleus (LGN) of the thalamus. Much of the scientific knowledge of retinal ganglion cell physiology was obtained by neural recordings of cells in the LGN. The cone-opponent mechanisms in the retina and LGN represent a fundamental physiological opponent process but do not represent the unique hues (or Hering's Opponent Colors Theory). For example, the colors that best elicit responses of the bistratified S-(L+M)-opponent neurons are best described as purplish (or lavender) and lime-green, not "blue" and "yellow". The neurons are sometimes referred to as "blue–yellow" neurons, but this is a historical artifact dating to the time when it was thought that Hering's Opponent Colors Theory was hardwired by the retina and the mismatch between the colors to which they are optimally tuned and Hering's Opponent Colors was overlooked. Cone opponent mechanisms exist in the retinas of many mammals, including monkeys, mice, and cats. In primates, the LGN contains three major classes of layers: Magnocellular layers (M, large-cell) – responsible largely for the luminance channel Parvocellular layers (P, small-cell) – responsible largely for red–green opponency Koniocellular layers (K) – responsible largely for blue–yellow opponency, poor spatial resolution, long latency Other mammals such as cats also have three cell types denoted as X (magno), Y (parvo), and W (konio). The W type is beyond most doubt homologous to the primate K type. There are some subtle differences between the M and X types as well as the Y and P types to make the correspondence unclear. === Advantage === Transmitting information in opponent-channel color space could be advantageous over transmitting it in LMS color space ("raw" signals from each cone type). There is some overlap in the wavelengths of light to which the three types of cones (L for long-wave, M for medium-wave, and S for short-wave light) respond, so it is more efficient for the visual system (from a perspective of dynamic range) to record differences between the responses of cones, rather than each type of cone's individual response. Hurvich and Jameson argued that the use of opponent-channel color space would increase color contrast, making the information easier to process by later stages of vision. === Color blindness === Color blindness can be classified by the cone cell that is affected (protan, deutan, tritan) or by the opponent channel that is affected (red–green or blue–yellow). In either case, the channel can either be inactive (in the case of dichromacy) or have a lower dynamic range (in the case of anomalous trichromacy). For example, individuals with deuteranopia see little difference between the red and green unique hues. == History == Johann Wolfgang von Goethe first studied the physiological effect of opposed colors in his Theory of Colours in 1810. Goethe arranged his color wheel symmetrically "for the colours diametrically opposed to each other in this diagram are those which reciprocally evoke each other in the eye. Thus, yellow demands purple; orange, blue; red, green; and vice versa: Thus again all intermediate gradations reciprocally evoke each other." Ewald Hering proposed opponent color theory in 1892. He thought that the colors red, yellow, green, and blue are special in that any other color can be described as a mix of them, and that they exist in opposite pairs. That is, either red or green is perceived and never greenish-red: Even though yellow is a mixture of red and green in the RGB color theory, humans