AI Face Time

AI Face Time — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Super-resolution imaging

Super-resolution imaging (SR) is a class of techniques that improve the resolution of an imaging system. In optical SR the diffraction limit of systems is transcended, while in geometrical SR the resolution of digital imaging sensors is enhanced. In some radar and sonar imaging applications (e.g. magnetic resonance imaging (MRI), high-resolution computed tomography), subspace decomposition-based methods (e.g. MUSIC) and compressed sensing-based algorithms (e.g., SAMV) are employed to achieve SR over standard periodogram algorithm. Super-resolution imaging techniques are used in general image processing and in super-resolution microscopy. == Super-resolution principles == Several concepts are fundamental to super-resolution imaging: Diffraction limit: the capacity of an optical instrument to reproduce the details of an object in an image has limits that are imposed by laws of physics: the diffraction equations in the wave theory of light, or the uncertainty principle for photons in quantum mechanics. Information transfer can never be increased beyond this boundary, but packets outside the limits can be cleverly swapped for (or multiplexed with) some inside it. Super-resolution microscopy does not so much “break” as “circumvent” the diffraction limit. New procedures probing electro-magnetic disturbances at the molecular level (in the so-called near field) remain fully consistent with Maxwell's equations. Spatial frequency domain: A succinct expression of the diffraction limit is given in the spatial frequency domain. In Fourier optics light distributions are expressed as superpositions of a series of grating light patterns in a range of fringe widths - these widths represent the spatial frequencies. It is generally taught that diffraction theory stipulates an upper limit, the cut-off spatial-frequency, beyond which pattern elements fail to be transferred into the optical image, i.e., are not resolved. But in fact what is set by diffraction theory is the width of the passband, not a fixed upper limit. No laws of physics are broken when a spatial frequency band beyond the cut-off spatial frequency is swapped for one inside it: this has long been implemented in dark-field microscopy. Nor are information-theoretical rules broken when superimposing several bands, disentangling them in the received image needs assumptions of object invariance during multiple exposures, i.e., the substitution of one kind of uncertainty for another. Information: When the term super-resolution is used in techniques based on the inference of object details using a statistical treatment of the image within standard resolution limits (for example, averaging multiple exposures), it involves an exchange of one kind of information (extracting signal from noise) for another (the assumption that the target has remained invariant). Recent breakthroughs incorporate quantum-transformer hybrids into super-resolution, such as QUIET‑SR, a 2025 model that employs shifted quantum window attention within a transformer to enhance image detail while respecting diffraction and information-theory limits Similarly, frequency-integrated transformers (e.g., FIT) enrich super-resolution by explicitly combining spatial and frequency-domain information via FFT-based attention, improving reconstruction across scales Resolution and localization: True resolution involves the distinction of whether a target, e.g. a star or a spectral line, is single or double, ordinarily requiring separable peaks in the image. When a target is known to be single, its location can be determined with higher precision than the image width by finding the centroid (center of gravity) of its image light distribution. The word ultra-resolution had been proposed for this process but it did not catch on, and the high-precision localization procedure is typically referred to as super-resolution. == Techniques == === Optical or diffractive super-resolution === Substituting spatial-frequency bands: Though the bandwidth allowable by diffraction is fixed, it can be positioned anywhere in the spatial-frequency spectrum. Dark-field illumination in microscopy is an example. See also aperture synthesis. ==== Multiplexing spatial-frequency bands ==== An image is formed using the normal passband of the optical device. Then, some known light structure (for example, a set of light fringes) is superimposed on the target. The image now contains components resulting from the combination of the target and the superimposed light structure, e.g. moiré fringes, and carries information about target detail which simple unstructured illumination does not. The “superresolved” components, however, need disentangling to be revealed. For an example, see structured illumination (figure to left). ==== Multiple parameter use within traditional diffraction limit ==== If a target has no special polarization or wavelength properties, two polarization states or non-overlapping wavelength regions can be used to encode target details, one in a spatial-frequency band inside the cut-off limit the other beyond it. Both would use normal passband transmission but are then separately decoded to reconstitute target structure with extended resolution. ==== Probing near-field electromagnetic disturbance ==== Super-resolution microscopy is generally discussed within the realm of conventional optical imagery. However, modern technology allows the probing of electromagnetic disturbance within molecular distances of the source, which has superior resolution properties. See also evanescent waves and the development of the new super lens. === Geometrical or image-processing super-resolution === ==== Multi-exposure image noise reduction ==== When an image is degraded by noise, the resolution may be improved by averaging multiple exposures. See example on the right. ==== Single-frame deblurring ==== Known defects in a given imaging situation, such as defocus or aberrations, can sometimes be mitigated in whole or in part by suitable spatial-frequency filtering of even a single image. Such procedures all stay within the diffraction-mandated passband, and do not extend it. ==== Sub-pixel image localization ==== The location of a single source can be determined by computing the "center of gravity" (centroid) of the light distribution extending over several adjacent pixels (see figure on the left). Provided that there is enough light, this can be achieved with arbitrary precision, very much better than pixel width of the detecting apparatus and the resolution limit for the decision of whether the source is single or double. This technique, which requires the presupposition that all the light comes from a single source, is at the basis of what has become known as super-resolution microscopy, e.g. stochastic optical reconstruction microscopy (STORM), where fluorescent probes attached to molecules give nanoscale distance information. It is also the mechanism underlying visual hyperacuity. ==== Bayesian induction beyond traditional diffraction limit ==== Some object features, though beyond the diffraction limit, may be known to be associated with other object features that are within the limits and hence contained in the image. Then conclusions can be drawn, using statistical methods, from the available image data about the presence of the full object. The classical example is Toraldo di Francia's proposition of judging whether an image is that of a single or double star by determining whether its width exceeds the spread from a single star. This can be achieved at separations well below the classical resolution bounds, and requires the prior limitation to the choice "single or double?" The approach can take the form of extrapolating the image in the frequency domain, by assuming that the object is an analytic function, and that we can exactly know the function values in some interval. This method is severely limited by the ever-present noise in digital imaging systems, but it can work for radar, astronomy, microscopy or magnetic resonance imaging. More recently, a fast single image super-resolution algorithm based on a closed-form solution to ℓ 2 − ℓ 2 {\displaystyle \ell _{2}-\ell _{2}} problems has been proposed and demonstrated to accelerate most of the existing Bayesian super-resolution methods significantly. == Aliasing == Geometrical SR reconstruction algorithms are possible if and only if the input low resolution images have been under-sampled and therefore contain aliasing. Because of this aliasing, the high-frequency content of the desired reconstruction image is embedded in the low-frequency content of each of the observed images. Given a sufficient number of observation images, and if the set of observations vary in their phase (i.e. if the images of the scene are shifted by a sub-pixel amount), then the phase information can be used to separate the aliased high-frequency content from the true low-frequency content, and the full-resolution image can be accurate
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Candace Sidner

Candace Lee (Candy) Sidner is an American computer scientist whose research has applied artificial intelligence and natural language processing to problems in personal information management, intelligent user interfaces, and human–robot interaction. She is a research professor of computer science at the Worcester Polytechnic Institute, and a former president of the Association for Computational Linguistics. == Education and career == Sidner majored in mathematics at Kalamazoo College, graduating in 1971. She earned a master's degree in computer science at the University of Pittsburgh in 1975, and completed a Ph.D. in computer science in 1979 at the Massachusetts Institute of Technology. Her dissertation, Towards A Computational Theory of Definite Anaphora Comprehension in English Discourse, was supervised by Jonathan Allen. She worked as a researcher for Bolt Beranek and Newman from 1979 to 1989, and continued to work in industry for the Digital Equipment Corporation (1989 to 1993), the Lotus Development Corporation (1993 to 2000), Mitsubishi Electric Research Laboratories (2000 to 2007), and BAE Systems (2007 to 2010). She took her present position as a research professor at the Worcester Polytechnic Institute in 2009. She served as president of the Association for Computational Linguistics in 1989. == Recognition == Sidner was named a Fellow of the Association for the Advancement of Artificial Intelligence in 1991. In 2013, she was named a Fellow of the Association for Computational Linguistics, "for seminal contributions to discourse focus and collaborative dialog".
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AI Copywriting Tools Reviews: What Actually Works in 2026

Shopping for the best AI copywriting tool? An AI copywriting tool is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI copywriting tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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Self-verifying finite automaton

In automata theory, a self-verifying finite automaton (SVFA) is a special kind of a nondeterministic finite automaton (NFA) with a symmetric kind of nondeterminism introduced by Hromkovič and Schnitger. Generally, in self-verifying nondeterminism, each computation path is concluded with any of the three possible answers: yes, no, and I do not know. For each input string, no two paths may give contradictory answers, namely both answers yes and no on the same input are not possible. At least one path must give answer yes or no, and if it is yes then the string is considered accepted. SVFA accept the same class of languages as deterministic finite automata (DFA) and NFA but have different state complexity. == Formal definition == An SVFA is represented formally by a 6-tuple, A=(Q, Σ, Δ, q0, Fa, Fr) such that (Q, Σ, Δ, q0, Fa) is an NFA, and Fa, Fr are disjoint subsets of Q. For each word w = a1a2 … an, a computation is a sequence of states r0,r1, …, rn, in Q with the following conditions: r0 = q0 ri+1 ∈ Δ(ri, ai+1), for i = 0, …, n−1. If rn ∈ Fa then the computation is accepting, and if rn ∈ Fr then the computation is rejecting. There is a requirement that for each w there is at least one accepting computation or at least one rejecting computation but not both. == Results == Each DFA is a SVFA, but not vice versa. Jirásková and Pighizzini proved that for every SVFA of n states, there exists an equivalent DFA of g ( n ) = Θ ( 3 n / 3 ) {\displaystyle g(n)=\Theta (3^{n/3})} states. Furthermore, for each positive integer n, there exists an n-state SVFA such that the minimal equivalent DFA has exactly g ( n ) {\displaystyle g(n)} states. Other results on the state complexity of SVFA were obtained by Jirásková and her colleagues.
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Deep image prior

Deep image prior is a type of convolutional neural network used to enhance a given image with no prior training data other than the image itself. A neural network is randomly initialized and used as prior to solve inverse problems such as noise reduction, super-resolution, and inpainting. Image statistics are captured by the structure of a convolutional image generator rather than by any previously learned capabilities. == Method == === Background === Inverse problems such as noise reduction, super-resolution, and inpainting can be formulated as the optimization task x ∗ = m i n x E ( x ; x 0 ) + R ( x ) {\displaystyle x^{}=min_{x}E(x;x_{0})+R(x)} , where x {\displaystyle x} is an image, x 0 {\displaystyle x_{0}} a corrupted representation of that image, E ( x ; x 0 ) {\displaystyle E(x;x_{0})} is a task-dependent data term, and R(x) is the regularizer. Deep neural networks learn a generator/decoder x = f θ ( z ) {\displaystyle x=f_{\theta }(z)} which maps a random code vector z {\displaystyle z} to an image x {\displaystyle x} . The image corruption method used to generate x 0 {\displaystyle x_{0}} is selected for the specific application. === Specifics === In this approach, the R ( x ) {\displaystyle R(x)} prior is replaced with the implicit prior captured by the neural network (where R ( x ) = 0 {\displaystyle R(x)=0} for images that can be produced by a deep neural networks and R ( x ) = + ∞ {\displaystyle R(x)=+\infty } otherwise). This yields the equation for the minimizer θ ∗ = a r g m i n θ E ( f θ ( z ) ; x 0 ) {\displaystyle \theta ^{}=argmin_{\theta }E(f_{\theta }(z);x_{0})} and the result of the optimization process x ∗ = f θ ∗ ( z ) {\displaystyle x^{}=f_{\theta ^{}}(z)} . The minimizer θ ∗ {\displaystyle \theta ^{}} (typically a gradient descent) starts from a randomly initialized parameters and descends into a local best result to yield the x ∗ {\displaystyle x^{}} restoration function. ==== Overfitting ==== A parameter θ may be used to recover any image, including its noise. However, the network is reluctant to pick up noise because it contains high impedance while useful signal offers low impedance. This results in the θ parameter approaching a good-looking local optimum so long as the number of iterations in the optimization process remains low enough not to overfit data. === Deep Neural Network Model === Typically, the deep neural network model for deep image prior uses a U-Net like model without the skip connections that connect the encoder blocks with the decoder blocks. The authors in their paper mention that "Our findings here (and in other similar comparisons) seem to suggest that having deeper architecture is beneficial, and that having skip-connections that work so well for recognition tasks (such as semantic segmentation) is highly detrimental." == Applications == === Denoising === The principle of denoising is to recover an image x {\displaystyle x} from a noisy observation x 0 {\displaystyle x_{0}} , where x 0 = x + ϵ {\displaystyle x_{0}=x+\epsilon } . The distribution ϵ {\displaystyle \epsilon } is sometimes known (e.g.: profiling sensor and photon noise) and may optionally be incorporated into the model, though this process works well in blind denoising. The quadratic energy function E ( x , x 0 ) = | | x − x 0 | | 2 {\displaystyle E(x,x_{0})=||x-x_{0}||^{2}} is used as the data term, plugging it into the equation for θ ∗ {\displaystyle \theta ^{}} yields the optimization problem m i n θ | | f θ ( z ) − x 0 | | 2 {\displaystyle min_{\theta }||f_{\theta }(z)-x_{0}||^{2}} . === Super-resolution === Super-resolution is used to generate a higher resolution version of image x. The data term is set to E ( x ; x 0 ) = | | d ( x ) − x 0 | | 2 {\displaystyle E(x;x_{0})=||d(x)-x_{0}||^{2}} where d(·) is a downsampling operator such as Lanczos that decimates the image by a factor t. === Inpainting === Inpainting is used to reconstruct a missing area in an image x 0 {\displaystyle x_{0}} . These missing pixels are defined as the binary mask m ∈ { 0 , 1 } H × V {\displaystyle m\in \{0,1\}^{H\times V}} . The data term is defined as E ( x ; x 0 ) = | | ( x − x 0 ) ⊙ m | | 2 {\displaystyle E(x;x_{0})=||(x-x_{0})\odot m||^{2}} (where ⊙ {\displaystyle \odot } is the Hadamard product). The intuition behind this is that the loss is computed only on the known pixels in the image, and the network is going to learn enough about the image to fill in unknown parts of the image even though the computed loss doesn't include those pixels. This strategy is used to remove image watermarks by treating the watermark as missing pixels in the image. === Flash–no-flash reconstruction === This approach may be extended to multiple images. A straightforward example mentioned by the author is the reconstruction of an image to obtain natural light and clarity from a flash–no-flash pair. Video reconstruction is possible but it requires optimizations to take into account the spatial differences. == Implementations == A reference implementation rewritten in Python 3.6 with the PyTorch 0.4.0 library was released by the author under the Apache 2.0 license: deep-image-prior A TensorFlow-based implementation written in Python 2 and released under the CC-SA 3.0 license: deep-image-prior-tensorflow A Keras-based implementation written in Python 2 and released under the GPLv3: machine_learning_denoising == Example == See Astronomy Picture of the Day (APOD) of 2024-02-18
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Laws of Form

Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, written by August 1967 and published in 1969. The book straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems: The primary arithmetic (described in Chapter 4 of LoF), whose models include Boolean arithmetic; The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean logic, and the classical propositional calculus; Equations of the second degree (Chapter 11), whose interpretations include finite automata and Alonzo Church's Restricted Recursive Arithmetic (RRA). "Boundary algebra" is a Meguire (2011) term for the union of the primary algebra and the primary arithmetic. Laws of Form sometimes loosely refers to the "primary algebra" as well as to LoF. == Contents == The preface states that the work was first explored in 1959, and Spencer Brown cites Bertrand Russell as being supportive of his endeavour. He also thanks J. C. P. Miller of University College London for helping with the proofreading and offering other guidance. In 1963 Spencer Brown was invited by Harry Frost, staff lecturer in the physical sciences at the department of Extra-Mural Studies of the University of London, to deliver a course on the mathematics of logic. LoF emerged from work in electronic engineering its author did around 1960. Key ideas of the LOF were first outlined in his 1961 manuscript Design with the Nor, which remained unpublished until 2021, and further refined during subsequent lectures on mathematical logic he gave under the auspices of the University of London's extension program. LoF has appeared in several editions. The second series of editions appeared in 1972 with the "Preface to the First American Edition", which emphasised the use of self-referential paradoxes, and the most recent being a 1997 German translation. LoF has never gone out of print. LoF's mystical and declamatory prose and its love of paradox make it a challenging read for all. Spencer-Brown was influenced by Ludwig Wittgenstein and R. D. Laing. LoF also echoes a number of themes from the writings of Charles Sanders Peirce, Bertrand Russell, and Alfred North Whitehead. The work has had curious effects on some classes of its readership; for example, on obscure grounds, it has been claimed that the entire book is written in an operational way, giving instructions to the reader instead of telling them what "is", and that in accordance with G. Spencer-Brown's interest in paradoxes, the only sentence that makes a statement that something is, is the statement which says no such statements are used in this book. Furthermore, the claim asserts that except for this one sentence the book can be seen as an example of E-Prime. What prompted such a claim, is obscure, either in terms of incentive, logical merit, or as a matter of fact, because the book routinely and naturally uses the verb to be throughout, and in all its grammatical forms, as may be seen both in the original and in quotes shown below. == Reception == Ostensibly a work of formal mathematics and philosophy, LoF became something of a cult classic: it was praised by Heinz von Foerster when he reviewed it for the Whole Earth Catalog. Those who agree point to LoF as embodying an enigmatic "mathematics of consciousness", its algebraic symbolism capturing an (perhaps even "the") implicit root of cognition: the ability to "distinguish". LoF argues that primary algebra reveals striking connections among logic, Boolean algebra, and arithmetic, and the philosophy of language and mind. Stafford Beer wrote in a review for Nature in 1969, "When one thinks of all that Russell went through sixty years ago, to write the Principia, and all we his readers underwent in wrestling with those three vast volumes, it is almost sad". Banaschewski (1977) argues that the primary algebra is nothing but new notation for Boolean algebra. Indeed, the two-element Boolean algebra 2 can be seen as the intended interpretation of the primary algebra. Yet the notation of the primary algebra: Fully exploits the duality characterizing not just Boolean algebras but all lattices; Highlights how syntactically distinct statements in logic and 2 can have identical semantics; Dramatically simplifies Boolean algebra calculations, and proofs in sentential and syllogistic logic. Moreover, the syntax of the primary algebra can be extended to formal systems other than 2 and sentential logic, resulting in boundary mathematics. LoF has influenced, among others, Heinz von Foerster, Louis Kauffman, Niklas Luhmann, Humberto Maturana, Francisco Varela and William Bricken. Some of these authors have modified the primary algebra in a variety of interesting ways. LoF claimed that certain well-known mathematical conjectures of very long standing, such as the four color theorem, Fermat's Last Theorem, and the Goldbach conjecture, are provable using extensions of the primary algebra. Spencer-Brown eventually circulated a purported proof of the four color theorem, but it was met with skepticism. == The form (Chapter 1) == The symbol: Also called the "mark" or "cross", is the essential feature of the Laws of Form. In Spencer-Brown's inimitable and enigmatic fashion, the Mark symbolizes the root of cognition, i.e., the dualistic Mark indicates the capability of differentiating a "this" from "everything else but this". In LoF, a Cross denotes the drawing of a "distinction", and can be thought of as signifying the following, all at once: The act of drawing a boundary around something, thus separating it from everything else; That which becomes distinct from everything by drawing the boundary; Crossing from one side of the boundary to the other. All three ways imply an action on the part of the cognitive entity (e.g., person) making the distinction. As LoF puts it: "The first command: Draw a distinction can well be expressed in such ways as: Let there be a distinction, Find a distinction, See a distinction, Describe a distinction, Define a distinction, Or: Let a distinction be drawn". (LoF, Notes to chapter 2) The counterpoint to the Marked state is the Unmarked state, which is simply nothing, the void, or the un-expressable infinite represented by a blank space. It is simply the absence of a Cross. No distinction has been made and nothing has been crossed. The Marked state and the void are the two primitive values of the Laws of Form. The Cross can be seen as denoting the distinction between two states, one "considered as a symbol" and another not so considered. From this fact arises a curious resonance with some theories of consciousness and language. Paradoxically, the Form is at once Observer and Observed, and is also the creative act of making an observation. LoF (excluding back matter) closes with the words: ...the first distinction, the Mark and the observer are not only interchangeable, but, in the form, identical. C. S. Peirce came to a related insight in the 1890s; see § Related work. == The primary arithmetic (Chapter 4) == The syntax of the primary arithmetic goes as follows. There are just two atomic expressions: The empty Cross ; All or part of the blank page (the "void"). There are two inductive rules: A Cross may be written over any expression; Any two expressions may be concatenated. The semantics of the primary arithmetic are perhaps nothing more than the sole explicit definition in LoF: "Distinction is perfect continence". Let the "unmarked state" be a synonym for the void. Let an empty Cross denote the "marked state". To cross is to move from one value, the unmarked or marked state, to the other. We can now state the "arithmetical" axioms A1 and A2, which ground the primary arithmetic (and hence all of the Laws of Form): "A1. The law of Calling". Calling twice from a state is indistinguishable from calling once. To make a distinction twice has the same effect as making it once. For example, saying "Let there be light" and then saying "Let there be light" again, is the same as saying it once. Formally: = {\displaystyle \ =} "A2. The law of Crossing". After crossing from the unmarked to the marked state, crossing again ("recrossing") starting from the marked state returns one to the unmarked state. Hence recrossing annuls crossing. Formally: = {\displaystyle \ =} In both A1 and A2, the expression to the right of '=' has fewer symbols than the expression to the left of '='. This suggests that every primary arithmetic expression can, by repeated application of A1 and A2, be simplified to one of two states: the marked or the unmarked state. This is indeed the case, and the result is the expression's "simplification". The two fundamental metatheorems of the primary arithmetic state that: Every finite expression has a unique simplification. (T3 in LoF); Starting from an initial marked or unmarked state, "complicating" an expression by a finite number of repeated application of A1 and A2 cannot yield
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How to Choose an AI Logo Maker

Trying to pick the best AI logo maker? An AI logo maker is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI logo maker slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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Emergent (software)

Emergent (formerly PDP++) is a biologically-based neural simulation software that is primarily intended for creating models of the brain and cognitive processes. Development initially began in 1995 at Carnegie Mellon University, and as of 2014, continues at the University of Colorado at Boulder. The 3.x release of the software, which was known as PDP++, is featured in the textbook Computational Explorations in Cognitive Neuroscience. == Features == Emergent features a modular design, based on the principles of object-oriented programming. It runs on Microsoft Windows, Darwin / macOS and Linux. C-Super-Script (variously, CSS and C^C), a built-in C++-like interpreted scripting language, allows access to virtually all simulator objects and can initiate all the same actions as the GUI, and more. Version 4 and upward features a full 3D environment for visualizations, based on Qt and Open Inventor. Robotics simulations are made possible by integration with the Open Dynamics Engine. A plugin system allows for expanding the software in many ways. Version 5 introduced parallel threading support, numerous speed improvements, a help browser featuring an interface to the project's Wiki and auto-generated documentation, undo and redo using diffs and a definable undo depth. In addition, 5.0.2 introduced a built-in plugin source code editor, and plugins can now be compiled from the main interface, enabling full development of plugins within Emergent. Emergent also provides an implementation of Leabra which was developed by Randall C. O'Reilly in his PhD thesis.
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Supersampling

Supersampling or supersampling anti-aliasing (SSAA) is a spatial anti-aliasing method, i.e. a method used to remove aliasing (jagged and pixelated edges, colloquially known as "jaggies") from images rendered in computer games or other computer programs that generate imagery. Aliasing occurs because unlike real-world objects, which have continuous smooth curves and lines, a computer screen shows the viewer a large number of small squares. These pixels all have the same size, and each one has a single color. A line can only be shown as a collection of pixels, and therefore appears jagged unless it is perfectly horizontal or vertical. The aim of supersampling is to reduce this effect. Color samples are taken at several instances inside the pixel (not just at the center as normal)—hence the term "supersampling"—and an average color value is calculated. This can for example be achieved by rendering the image at a much higher resolution than the one being displayed, then shrinking it to the desired size, using the extra pixels for calculation, with the result being a downsampled image with smoother transitions from one line of pixels to another along the edges of objects, but each pixel could also be supersampled using other strategies (see the Supersampling patterns section). The number of samples determines the quality of the output. == Motivation == Aliasing is manifested in the case of 2D images as moiré pattern and pixelated edges, colloquially known as "jaggies". Common signal processing and image processing knowledge suggests that to achieve perfect elimination of aliasing, proper spatial sampling at the Nyquist rate (or higher) after applying a 2D Anti-aliasing filter is required. As this approach would require a forward and inverse fourier transformation, computationally less demanding approximations like supersampling were developed to avoid domain switches by staying in the spatial domain ("image domain"). == Method == === Computational cost and adaptive supersampling === Supersampling is computationally expensive because it requires much greater video card memory and memory bandwidth, since the amount of buffer used is several times larger. A way around this problem is to use a technique known as adaptive supersampling, where only pixels at the edges of objects are supersampled. Initially only a few samples are taken within each pixel. If these values are very similar, only these samples are used to determine the color. If not, more are used. The result of this method is that a higher number of samples are calculated only where necessary, thus improving performance. === Supersampling patterns === When taking samples within a pixel, the sample positions have to be determined in some way. Although the number of ways in which this can be done is infinite, there are a few ways which are commonly used. ==== Grid ==== The simplest algorithm. The pixel is split into several sub-pixels, and a sample is taken from the center of each. It is fast and easy to implement. Although, due to the regular nature of sampling, aliasing can still occur if a low number of sub-pixels is used. ==== Random ==== Also known as stochastic sampling, it avoids the regularity of grid supersampling. However, due to the irregularity of the pattern, samples end up being unnecessary in some areas of the pixel and lacking in others. ==== Poisson disk ==== The Poisson disk sampling algorithm places the samples randomly, but then checks that any two are not too close. The end result is an even but random distribution of samples. The naive "dart throwing" algorithm is extremely slow for large data sets, which once limited its applications for real-time rendering. However, many fast algorithms now exist to generate Poisson disk noise, even those with variable density. The Delone set provides a mathematical description of such sampling. ==== Jittered ==== A modification of the grid algorithm to approximate the Poisson disk. A pixel is split into several sub-pixels, but a sample is not taken from the center of each, but from a random point within the sub-pixel. Congregation can still occur, but to a lesser degree. ==== Rotated grid ==== A 2×2 grid layout is used but the sample pattern is rotated to avoid samples aligning on the horizontal or vertical axis, greatly improving antialiasing quality for the most commonly encountered cases. For an optimal pattern, the rotation angle is arctan (⁠1/2⁠) (about 26.6°) and the square is stretched by a factor of ⁠√5/2⁠, making it also a 4-queens solution.
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The Best Free AI Headshot Generator for Beginners

Shopping for the best AI headshot generator? An AI headshot generator is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI headshot generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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AI Headshot Generators Reviews: What Actually Works in 2026

Looking for the best AI headshot generator? An AI headshot generator is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI headshot generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Android Auto

Android Auto is a mobile app developed by Google to mirror features of a smartphone (or other Android device) on a car's dashboard information and entertainment head unit. Once an Android device is paired with the car's head unit, the system can mirror some apps on the vehicle's display. Supported apps include GPS mapping and navigation, music playback, SMS, telephone, and Web search. The system supports both touchscreen and button-controlled head units. Hands-free operation through voice commands is available and recommended to reduce driver distraction. Android Auto is part of the Open Automotive Alliance, a joint effort of 28 automobile manufacturers, with Nvidia as tech supplier, available in 36 countries. == History == Android Auto was revealed at Google I/O 2014. The app was released to the public on March 19, 2015. In November 2016, Google implemented an app that would run the Android Auto UI on the mobile device. In July 2019, Android Auto received its first major UI rework, which among other changes, brought an app drawer to Android Auto for the first time. Google also announced that the app's ability to be used on a phone would be discontinued in favor of Google Assistant's drive mode. In December 2020, Google announced the expansion of Android Auto to 36 additional countries in Europe, Indonesia, and more. In April 2021, Android Auto launched in Belgium, Denmark, Netherlands, Norway, Portugal, and Sweden. Google announced in May 2022 a user interface redesign for Android Auto, codenamed CoolWalk, which aims to simplify the app's usage, and make it more adaptable to screens of different orientations and aspect ratios. The redesign incorporates a new split-screen layout, where Google Maps can be displayed alongside a music player. CoolWalk was originally slated to launch in Q3 2022. In June 2022, Android Auto no longer ran directly on a mobile device; the app permitting this was decommissioned, in favor of a Driving Mode built into the Google Assistant app for a similar purpose. In November 2022, the CoolWalk user interface was released in Android Auto's beta program. == Functionality == Android Auto is software that can be utilized from an Android mobile device, acting as a vehicle's dashboard head unit. Once the user's Android device is connected to the vehicle, the head unit will serve as an external display for the Android device, presenting supported software in a car-specific user interface provided by the Android Auto app. In Android Auto's first iterations, the device was required to be connected via USB to the car. For some time, starting in November 2016, Google added the option to run Android Auto as a regular app on an Android device, allowing users to choose whether to use Android Auto on a personal phone or tablet, rather than on a compatible automotive head unit. This app was decommissioned in June 2022 in favor of a Driving Mode built into the Google Assistant app. At CES 2018, Google confirmed that the Google Assistant would be coming to Android Auto later in the year. An Android Auto SDK has been released, allowing third parties to modify their apps to work with Android Auto; initially, only APIs for music and messaging apps were available. == Head unit support == In May 2015, Hyundai became the first manufacturer to offer Android Auto support, making it first available in the 2015 Hyundai Sonata. Automobile manufacturers that will offer Android Auto support in their cars include Abarth, Acura, Alfa Romeo, Aston Martin, Audi, Bentley, Buick, BMW, BYD, Cadillac, Chevrolet, Chrysler, Citroën, Dodge, Ferrari, Fiat, Ford, GMC, Genesis, Holden, Honda, Hyundai, Infiniti, Jaguar Land Rover, Jeep, Kia, Lamborghini, Lexus, Lincoln, Mahindra and Mahindra, Maserati, Maybach, Mazda, Mercedes-Benz, Mitsubishi, Nissan, Opel, Peugeot, Porsche, RAM, Renault, SEAT, Škoda, SsangYong, Subaru, Suzuki, Tata Motors Cars, Toyota, Volkswagen and Volvo. Additionally, aftermarket car-audio systems supporting Android Auto add the technology into host vehicles, including Pioneer, Kenwood, Panasonic, and Sony. == Criticism == In May 2019, Italy filed an antitrust complaint targeting Android Auto, citing a Google policy of allowing third-parties to only offer media and messaging apps on the platform, preventing Enel from offering an app for locating vehicle charging stations. Google announced a new SDK, to be released to select partners in August 2020 and made generally available by the end of the year. == Availability == As of December 2025, Android Auto is available in 46 countries:
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Neural processing unit

A neural processing unit (NPU), also known as an AI accelerator or deep learning processor, is a class of specialized hardware accelerator or computer system designed to accelerate artificial intelligence and machine learning applications, including artificial neural networks and computer vision. == Use == Their purpose is either to efficiently execute already trained AI models (inference) or to train AI models. NPUs can be more efficient in terms of speed or power consumption. NPU applications include algorithms for robotics, Internet of things, and data-intensive or sensor-driven tasks. They are often manycore or spatial designs and focus on low-precision arithmetic, novel dataflow architectures, or in-memory computing capability. As of 2024, a widely used datacenter-grade AI integrated circuit chip, the Nvidia H100 GPU, contains tens of billions of MOSFETs. === Consumer devices === AI accelerators are used in Apple silicon, Qualcomm, Samsung, Huawei, and Google Tensor smartphone processors. Vision processing units are accelerators specialized for machine vision algorithms such as CNN (convolutional neural networks) and SIFT (scale-invariant feature transform). They are used in devices that need to keep track of objects visually such as AR headsets and drones. It is more recently (circa 2017) added to processors from Apple and (circa 2022) to processors from Intel and AMD. All models of Intel Meteor Lake processors have a built-in versatile processor unit (VPU) for accelerating inference for computer vision and deep learning. On consumer devices, the NPU is intended to be small, power-efficient, but reasonably fast when used to run small models. To do this they are designed to support low-bitwidth operations using data types such as INT4, INT8, FP8, and FP16. A common metric is trillions of operations per second (TOPS). Although TOPS does not explicitly specify the kind of operations, it is typically INT8 additions and multiplications. === Datacenters === Accelerators are used in cloud computing servers: e.g., tensor processing units (TPU) for Google Cloud Platform, and Trainium and Inferentia chips for Amazon Web Services. Many vendor-specific terms exist for devices in this category, and it is an emerging technology without a dominant design. Since the late 2010s, graphics processing units designed by companies such as Nvidia and AMD often include AI-specific hardware in the form of dedicated functional units for low-precision matrix-multiplication operations. These GPUs are commonly used as AI accelerators, both for training and inference. === Scientific computation === Although NPUs are tailored for low-precision (e.g., FP16, INT8) matrix multiplication operations, they can be used to emulate higher-precision matrix multiplications in scientific computing. As modern GPUs place much focus on making the NPU part fast, using emulated FP64 (Ozaki scheme) on NPUs can potentially outperform native FP64. This has been demonstrated using FP16-emulated FP64 on NVIDIA TITAN RTX and using INT8-emulated FP64 on NVIDIA consumer GPUs and the A100 GPU. Consumer GPUs especially benefited as they have limited FP64 hardware capacity, showing a 6× speedup. Since CUDA Toolkit 13.0 Update 2, cuBLAS automatically uses INT8-emulated FP64 matrix multiplication of the equivalent precision if it is faster than native. This is in addition to the FP16-emulated FP32 feature introduced in version 12.9. == Programming == An operating system or a higher-level library may provide application programming interfaces such as TensorFlow with LiteRT Next (Android), CoreML (iOS, macOS) or DirectML (Windows). Formats such as ONNX are used to represent trained neural networks. Consumer CPU-integrated NPUs are accessible through vendor-specific APIs. AMD (Ryzen AI), Intel (OpenVINO), Apple silicon (CoreML), and Qualcomm (SNPE) each have their own APIs, which can be built upon by a higher-level library. GPUs generally use existing GPGPU pipelines such as CUDA and OpenCL adapted for lower precisions and specialized matrix-multiplication operations. Vulkan is also being used. Custom-built systems such as the Google TPU use private interfaces. There are a large number of separate underlying acceleration APIs and compilers/runtimes in use in the AI field, causing a great increase in software development effort due to the many combinations involved. As of 2025, the open standard organization Khronos Group is pursuing standardization of AI-related interfaces to reduce the amount of work needed. Khronos is working on three separate fronts: expansion of data types and intrinsic operations in OpenCL and Vulkan, inclusion of compute graphs in SPIR-V, and a NNEF/SkriptND file format for describing a neural network.
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Noémie Elhadad

Noémie Elhadad is an American data scientist who is an associate professor of biomedical informatics at the Columbia University Vagelos College of Physicians and Surgeons. As of 2022, she serves as the chair of the Department of Biomedical Informatics. Her research considers machine learning in bioinformatics, natural language processing and medicine. == Early life and education == Elhadad studied computer software engineering at École nationale supérieure d'électronique, informatique, télécommunications, mathématique et mécanique de Bordeaux (ENSEIRB). She completed her doctoral research at Columbia University. She was based in the Department of Computer Science, where she developed patient-focused text summaries of clinical literature. == Research and career == Elhadad joined the faculty at the City College of New York. In 2007 she joined the Department of Biomedical Informatics at Columbia University. She was made Chair of the Health Analytics Center at the Columbia Data Science Institute in 2013. Her research considers how clinical data, electronic health records and patient-generated data can enhance access to information for researchers, patients and physicians. She developed an artificial intelligence tool that supported patients in the NewYork-Presbyterian Hospital. Elhadad is interested in using data to advance women's health. She led the Citizen Endo Project that looks to comprehensively describe how patients experience endometriosis. It was built using principles of citizen science, using patient testimonials from focus groups in New York City and data aggregation. She created the app, Phendo, which asks patients about their experience of the disease. The name Phendo is a portmanteau of phenotyping endometriosis. Elhadad was announced as chair of the Department of Biomedical Informatics in December 2022. == Selected publications == Caruana, Rich; Lou, Yin; Gehrke, Johannes; Koch, Paul; Sturm, Marc; Elhadad, Noemie (August 10, 2015). "Intelligible Models for HealthCare". Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, NY, USA: ACM. pp. 1721–1730. doi:10.1145/2783258.2788613. ISBN 9781450336642. S2CID 14190268. Chaitanya Shivade; Preethi Raghavan; Eric Fosler-Lussier; Peter J Embi; Noemie Elhadad; Stephen B Johnson; Albert M Lai (November 7, 2013). "A review of approaches to identifying patient phenotype cohorts using electronic health records". Journal of the American Medical Informatics Association. 21 (2): 221–230. doi:10.1136/AMIAJNL-2013-001935. ISSN 1067-5027. PMC 3932460. PMID 24201027. Wikidata Q37598951. Shivade, Chaitanya; Raghavan, Preethi; Fosler-Lussier, Eric; Embi, Peter J; Elhadad, Noemie; Johnson, Stephen B; Lai, Albert M (March 2014). "A review of approaches to identifying patient phenotype cohorts using electronic health records". Journal of the American Medical Informatics Association. 21 (2): 221–230. doi:10.1136/amiajnl-2013-001935. ISSN 1067-5027. PMC 3932460. PMID 24201027. == Personal life == Elhadad suffers from endometriosis.
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AI Presentation Makers: Free vs Paid (2026)

Curious about the best AI presentation maker? An AI presentation maker is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI presentation maker slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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