Optical braille recognition

Optical braille recognition is technology to capture and process images of braille characters into natural language characters. It is used to convert braille documents for people who cannot read them into text, and for preservation and reproduction of the documents. == History == In 1984, a group of researchers at the Delft University of Technology designed a braille reading tablet, in which a reading head with photosensitive cells was moved along set of rulers to capture braille text line-by-line. In 1988, a group of French researchers at the Lille University of Science and Technology developed an algorithm, called Lectobraille, which converted braille documents into plain text. The system photographed the braille text with a low-resolution CCD camera, and used spatial filtering techniques, median filtering, erosion, and dilation to extract the braille. The braille characters were then converted to natural language using adaptive recognition. The Lectobraille technique had an error rate of 1%, and took an average processing time of seven seconds per line. In 1993, a group of researchers from the Katholieke Universiteit Leuven developed a system to recognize braille that had been scanned with a commercially available scanner. The system, however, was unable to handle deformities in the braille grid, so well-formed braille documents were required. In 1999, a group at the Hong Kong Polytechnic University implemented an optical braille recognition technique using edge detection to translate braille into English or Chinese text. In 2001, Murray and Dais created a handheld recognition system, that scanned small sections of a document at once. Because of the small area scanned at once, grid deformation was less of an issue, and a simpler, more efficient algorithm was employed. In 2003, Morgavi and Morando designed a system to recognize braille characters using artificial neural networks. This system was noted for its ability to handle image degradation more successfully than other approaches. == Challenges == Many of the challenges to successfully processing braille text arise from the nature of braille documents. Braille is generally printed on solid-color paper, with no ink to produce contrast between the raised characters and the background paper. However, imperfections in the page can appear in a scan or image of the page. Many documents are printed inter-point, meaning they are double-sided. As such, the depressions of the braille of one side appear interlaid with the protruding braille of the other side. == Techniques == Some optical braille recognition techniques attempt to use oblique lighting and a camera to reveal the shadows of the depressions and protrusions of the braille. Others make use of commercially available document scanners.

Vision transformer

A vision transformer (ViT) is a transformer designed for computer vision. A ViT decomposes an input image into a series of patches (rather than text into tokens), serializes each patch into a vector, and maps it to a smaller dimension with a single matrix multiplication. These vector embeddings are then processed by a transformer encoder as if they were token embeddings. ViTs were designed as alternatives to convolutional neural networks (CNNs) in computer vision applications. They have different inductive biases, training stability, and data efficiency. Compared to CNNs, ViTs are less data efficient, but have higher capacity. Some of the largest modern computer vision models are ViTs, such as one with 22B parameters. Subsequent to its publication, many variants were proposed, with hybrid architectures with both features of ViTs and CNNs. ViTs have found application in image recognition, image segmentation, weather prediction, and autonomous driving. == History == Transformers were introduced in Attention Is All You Need (2017), and have found widespread use in natural language processing. A 2019 paper applied ideas from the Transformer to computer vision. Specifically, they started with a ResNet, a standard convolutional neural network used for computer vision, and replaced all convolutional kernels by the self-attention mechanism found in a Transformer. It resulted in superior performance. However, it is not a Vision Transformer. In 2020, an encoder-only Transformer was adapted for computer vision, yielding the ViT, which reached state of the art in image classification, overcoming the previous dominance of CNN. The masked autoencoder (2022) extended ViT to work with unsupervised training. The vision transformer and the masked autoencoder, in turn, stimulated new developments in convolutional neural networks. Subsequently, there was cross-fertilization between the previous CNN approach and the ViT approach. In 2021, some important variants of the Vision Transformers were proposed. These variants are mainly intended to be more efficient, more accurate or better suited to a specific domain. Two studies improved efficiency and robustness of ViT by adding a CNN as a preprocessor. The Swin Transformer achieved state-of-the-art results on some object detection datasets such as COCO, by using convolution-like sliding windows of attention mechanism, and the pyramid process in classical computer vision. == Overview == The basic architecture, used by the original 2020 paper, is as follows. In summary, it is a BERT-like encoder-only Transformer. The input image is of type R H × W × C {\displaystyle \mathbb {R} ^{H\times W\times C}} , where H , W , C {\displaystyle H,W,C} are height, width, channel (RGB). It is then split into square-shaped patches of type R P × P × C {\displaystyle \mathbb {R} ^{P\times P\times C}} . For each patch, the patch is pushed through a linear operator, to obtain a vector ("patch embedding"). The position of the patch is also transformed into a vector by "position encoding" (the paper tried no embedding, 1D embedding, 2D embedding, and relative embedding: 1D was adopted). The two vectors are added, then pushed through several Transformer encoders. The attention mechanism in a ViT repeatedly transforms representation vectors of image patches, incorporating more and more semantic relations between image patches in an image. This is analogous to how in natural language processing, as representation vectors flow through a transformer, they incorporate more and more semantic relations between words, from syntax to semantics. The above architecture turns an image into a sequence of vector representations. To use these for downstream applications, an additional head needs to be trained to interpret them. For example, to use it for classification, one can add a shallow MLP on top of it that outputs a probability distribution over classes. The original paper uses a linear-GeLU-linear-softmax network. == Variants == === Original ViT === The original ViT was an encoder-only Transformer supervise-trained to predict the image label from the patches of the image. As in the case of BERT, it uses a special token in the input side, and the corresponding output vector is used as the only input of the final output MLP head. The special token is an architectural hack to allow the model to compress all information relevant for predicting the image label into one vector. Transformers found their initial applications in natural language processing tasks, as demonstrated by language models such as BERT and GPT-3. By contrast the typical image processing system uses a convolutional neural network (CNN). Well-known projects include Xception, ResNet, EfficientNet, DenseNet, and Inception. Transformers measure the relationships between pairs of input tokens (words in the case of text strings), termed attention. The cost is quadratic in the number of tokens. For images, the basic unit of analysis is the pixel. However, computing relationships for every pixel pair in a typical image is prohibitive in terms of memory and computation. Instead, ViT computes relationships among pixels in various small sections of the image (e.g., 16x16 pixels), at a drastically reduced cost. The sections (with positional embeddings) are placed in a sequence. The embeddings are learnable vectors. Each section is arranged into a linear sequence and multiplied by the embedding matrix. The result, with the position embedding is fed to the transformer. === Architectural improvements === ==== Pooling ==== After the ViT processes an image, it produces some embedding vectors. These must be converted to a single class probability prediction by some kind of network. In the original ViT and Masked Autoencoder, they used a dummy [CLS] token, in emulation of the BERT language model. The output at [CLS] is the classification token, which is then processed by a LayerNorm-feedforward-softmax module into a probability distribution. Global average pooling (GAP) does not use the dummy token, but simply takes the average of all output tokens as the classification token. It was mentioned in the original ViT as being equally good. Multihead attention pooling (MAP) applies a multiheaded attention block to pooling. Specifically, it takes as input a list of vectors x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} , which might be thought of as the output vectors of a layer of a ViT. The output from MAP is M u l t i h e a d e d A t t e n t i o n ( Q , V , V ) {\displaystyle \mathrm {MultiheadedAttention} (Q,V,V)} , where q {\displaystyle q} is a trainable query vector, and V {\displaystyle V} is the matrix with rows being x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} . This was first proposed in the Set Transformer architecture. Later papers demonstrated that GAP and MAP both perform better than BERT-like pooling. A variant of MAP was proposed as class attention, which applies MAP, then feedforward, then MAP again. Re-attention was proposed to allow training deep ViT. It changes the multiheaded attention module. === Masked Autoencoder === The Masked Autoencoder took inspiration from denoising autoencoders and context encoders. It has two ViTs put end-to-end. The first one ("encoder") takes in image patches with positional encoding, and outputs vectors representing each patch. The second one (called "decoder", even though it is still an encoder-only Transformer) takes in vectors with positional encoding and outputs image patches again. ==== Training ==== During training, input images (224px x 224 px in the original implementation) are split along a designated number of lines on each axis, producing image patches. A certain percentage of patches are selected to be masked out by mask tokens, while all others are retained in the image. The network is tasked with reconstructing the image from the remaining unmasked patches. Mask tokens in the original implementation are learnable vector quantities. A linear projection with positional embeddings is then applied to the vector of unmasked patches. Experiments varying mask ratio on networks trained on the ImageNet-1K dataset found 75% mask ratios achieved high performance on both finetuning and linear-probing of the encoder's latent space. The MAE processes only unmasked patches during training, increasing the efficiency of data processing in the encoder and lowering the memory usage of the transformer. A less computationally-intensive ViT is used for the decoder in the original implementation of the MAE. Masked patches are added back to the output of the encoder block as mask tokens and both are fed into the decoder. A reconstruction loss is computed for the masked patches to assess network performance. ==== Prediction ==== In prediction, the decoder architecture is discarded entirely. The input image is split into patches by the same algorithm as in training, but no patches are masked out. A linear projection wi

Mike Little

Mike Little (born 12 May 1962) is an English web developer and writer. He is the co-founder of the free and open source web publishing software WordPress. == Biography == Mike Little was born in Manchester, England in 1962 to a Nigerian father, who was a mathematics lecturer and musician, and an English mother who worked as a primary school teacher. Little was placed into foster care when he was four months of age, and was later adopted by the same family. He grew up on a council estate in Brinnington, Stockport, and was educated at Stockport School. In 2003, Little and Matt Mullenweg started working on a project in which they built on b2/cafelog and later named it WordPress, releasing the first version on 27 May 2003. Little states that, despite not being invited to join his co-founder's for-profit business Automattic, he and Mullenweg remain on good terms. He clarified: "I don’t want it to sound like he cheated me out of something or ripped me off in some way. He didn’t." In June 2013, Little was awarded the SAScon's "Outstanding Contribution to Digital" award for his part in co-founding and developing WordPress. Little has been described as "modest" and living in "virtual anonymity". He has one daughter. He identifies as a follower of Stoicism and a humanist, and in 2021, he became a patron of charity Humanists UK.

Downloadable content

Downloadable content (DLC) is additional content created for an already released video game, distributed through the Internet by the game's publisher. It can be added for no extra cost or as a form of video game monetization, enabling the publisher to gain additional revenue from a title after it has been purchased, often using a microtransaction system. DLC can range from cosmetic content, such as skins, to new in-game content, like characters, levels, modes, and larger expansions that may contain a mix of such content as a continuation of the base game. In some games, multiple DLCs (including future DLC not yet released) may be bundled as part of a "season pass"—typically at a discount rather than purchasing each DLC individually. While the Dreamcast was the first home console to support DLC (albeit in a limited form due to hardware and internet connection limitations), Microsoft's Xbox helped popularize the concept. Since the seventh generation of video game consoles, DLC has been a prevalent feature of major video game platforms with internet connectivity. == Etymology == Since the popularization of microtransactions in online distribution platforms such as Steam, the term DLC has become a synonymous for any form of paid content in video games, regardless of whether they constitute the download of new content. Furthermore, this led to the creation of the oxymoronic term "on-disc DLC" for content included on the game's original files but locked behind a paywall. == History == === Precursors to DLC === The earliest form of downloadable content were offerings of full games, such as on the Atari 2600's GameLine service, which allowed users to download games using a telephone line. A similar service, Sega Channel, allowed for the downloading of games to the Sega Genesis over a cable line. While the GameLine and Sega Channel services allowed for the distribution of entire titles, they did not provide downloadable content for existing titles. Expansion packs were sold at retail for some PC games, which featured content such as additional levels, characters, or maps for a base game. They often required an installation of the original game in order to function, but some games (such as Half-Life) had "standalone" expansions, which were essentially spin-off games that reused engine code and assets from the original game. === On consoles === The Dreamcast was the first console to feature online support as a standard; DLC was available, though limited in size due to the narrowband connection and the 200 block limit of the Visual Memory Unit memory card. These online features were still considered a breakthrough in video games. With the release of the Xbox, Microsoft was the second company to implement downloadable content. Many Xbox titles, including Splinter Cell, Halo 2, and Ninja Gaiden, offered varying amounts of extra content, available for download through the Xbox Live service. Most of this content was available free. With the advent of the GameCube, Nintendo was the third company to implement downloadable content. Many GameCube titles offered varying amounts of extra content from Game Boy Advance titles with the GameCube – Game Boy Advance link cable. All of this content was available free. The Xbox 360 (2005) included more robust support for digital distribution, including DLC downloads and purchases, via its Xbox Live Marketplace service. Microsoft believed that publishers would benefit by offering small pieces of content at a small cost ($1 to $5), rather than full expansion packs (~$20), as this would allow players to pick and chose what content they desired, providing revenue to the publishers. Microsoft also utilized a digital currency known as "Microsoft Points" for transactions, which could also be purchased through physical gift cards to avoid the banking fees associated with the small price points. The PlayStation 3 (2006) adopted the same approach with their downloadable hub, the PlayStation Store. Sony planned on having the bulk of its content be purchased separately via many separate online microtransactions for PlayStation Network titles, including Gran Turismo HD Concept and Gran Turismo 5 Prologue. The Wii (2006) featured a sparser amount of downloadable content on their Wii Shop Channel, the bulk of which is accounted for by digital distribution of emulated Nintendo titles from previous generations. Music video games, such as titles from the Guitar Hero and Rock Band franchises, took significant advantage of downloadable content as a means of offering new songs to be played in-game. Harmonix claimed that Guitar Hero II would feature "more online content than anyone has ever seen in a game to this date." Rock Band features the largest number of downloadable items of any console video game, with a steady number of new songs that were added weekly between 2007 and 2013. Acquiring all the downloadable content for Rock Band would, as of July 12, 2012, cost $5,880.10. === On personal computers === As the popularity and speed of internet connections rose, so did the popularity of using the internet for digital distribution of media. User-created game mods and maps were distributed exclusively online, as they were mainly created by people without the infrastructure capable of distributing the content through physical media. In 1997, Cavedog offered a new unit every month as free downloadable content for their real-time strategy computer game Total Annihilation. Later PC digital distribution platforms, such as Games for Windows Marketplace and Steam, would add support for DLC in a similar manner to consoles. === On handhelds === Nokia phones of the late 1990s and early 2000s shipped with side-scrolling shooter Space Impact, available on various models. With the introduction of WAP in 2000, additional downloadable content for the game, with extra levels, became available. The Nintendo Wi-Fi Connection service on the Nintendo DS could be used to obtain a form of DLC for certain games, such as Picross DS—where players could download puzzle "packs" of classic puzzles from previous Picross series games (such as Mario's Picross). as well as downloadable user generated content. Due to the Nintendo DS's use of cartridges and lack of dedicated storage, most "DLC" for DS games was limited in scope, or in some cases (such as Professor Layton and the Curious Village and Moero! Nekketsu Rhythm Damashii Osu! Tatakae! Ouendan 2), was already part of the game's data on the cartridge, and merely unlocked. Its successor, the Nintendo 3DS, natively supported the purchase of DLC for supported titles via Nintendo eShop. Starting with iPhone OS 3, downloadable content became available for the platform via applications bought from the App Store. While this ability was initially only available to developers for paid applications, Apple eventually allowed for developers to offer this in free applications as well in October 2009. == On-disc DLC == In some cases, a purchased DLC may not actually download new content to the device, but merely consists of data used to enable associated content that is already present within the game's data. DLC of this nature revealed via data mining is typically referred to as "on-disc DLC" or PULC (premium unlockable content). This practice has sometimes been considered controversial, with publishers being accused of using what is effectively a microtransaction to lock access to content that was already contained within the game as sold at retail. Data relating to future DLC may be included on-disc or downloaded during updates for technical reasons as well, either to ensure online multiplayer compatibility for existing content between players who have not yet purchased the new DLC, or as dormant support code for planned content that is still in development at the time of the release. == Monetization == Downloadable content is often offered for a price. Since Facebook games popularized the business model of microtransactions, some have criticized downloadable content as being overpriced and an incentive for developers to leave items out of the initial release, with The Elder Scrolls IV: Oblivion's horse armor DLC having faced a mixed reception upon its release for that reason. However, by 2009, the Horse Armor DLC was one of the top ten content packs that Bethesda had sold, which justified the DLC model for future games. Where a normal software disc may allow its license sold or traded, DLC is generally locked to a specific user's account and does not come with the ability to transfer that license to another user. In addition to individual content downloads, video game publishers sometimes offer a "season pass", which allows users to pre-order a selection of upcoming content over a specific time period, and ensuring the customer's ability to immediately obtain the content upon release. As users do not have the ability to fully preview the content before their purchase, there is a chance that the content of a season

Algorithmic amplification

Algorithmic amplification is the process by which automated ranking and recommendation systems on digital platforms increase the visibility of certain content beyond its initial audience. Major platforms including Facebook, YouTube, TikTok, and X (formerly Twitter) use such systems to determine what appears in users' feeds and search results. The term is used in research on social media and digital media regulation to describe how platform design choices influence the distribution of online information. Unlike chronological feeds, algorithmic systems evaluate content using signals such as engagement rates, viewing duration, and predicted relevance to individual users. Content that performs strongly on these metrics may be promoted to progressively larger audiences through feeds, search rankings, or autoplay systems. The process is distinct from content moderation, which involves removing, labelling, or restricting content under platform rules, although the two can interact in practice. The concept is closely connected to the attention economy. Research has linked algorithmic amplification to the spread of misinformation and the circulation of political content, as well as to effects on young users' mental health. The scale and direction of those effects remain debated, in part because independent researchers have limited access to the internal workings of platform recommendation systems. Governments in the European Union, United Kingdom, United States, and China have pursued differing regulatory approaches to recommendation algorithms. The EU's Digital Services Act and the UK's Online Safety Act 2023 impose obligations on large platforms related to recommendation system transparency and risk, while China became the first country to enact binding legislation specifically targeting such systems. Internal documents and whistleblower testimony reported by the BBC in 2026 described how competitive pressure between Meta and TikTok led to trade-offs between engagement and user safety in the design of their recommendation systems. == Terminology == The term algorithmic amplification is used in media studies, platform governance scholarship and regulatory literature to describe how automated systems influence the distribution of content beyond what organic user sharing alone would produce. It is distinct from viral spread, which refers primarily to user-driven sharing behaviour, and from algorithmic bias, which describes systematic errors or unfairness in algorithmic outputs. The related term algorithmic curation is used for the broader process of selecting and ordering content, of which amplification is one possible outcome. The phrase also appears in regulatory and legislative discussion of recommendation systems. The European Union's Digital Services Act (DSA) identifies recommendation systems as a potential source of systemic risk, and the term appears frequently in academic and policy commentary on the regulation. In the United States, proposals including the Filter Bubble Transparency Act and the Kids Online Safety Act (KOSA) have used it to frame requirements around recommendation system transparency. In the United Kingdom, the House of Commons Science, Innovation and Technology Committee used the term in a 2025 report on how recommendation algorithms contributed to the spread of misinformation during the 2024 Southport riots. A Joint Declaration on AI and Freedom of Expression adopted in October 2025 by four international freedom of expression mandate holders, including the UN Special Rapporteur on Freedom of Opinion and Expression and the OSCE Representative on Freedom of the Media, stated that recommender systems and other AI-powered curation tools exert "a large hidden influence and gatekeeper role" over what information people access and consume. == Background == Early internet platforms typically displayed content in reverse-chronological order or through keyword-based search systems. Although the term is most often applied to social media, the underlying logic predates social media itself. A 2021 overview traced the origins of modern recommendation systems to the early 1990s, when they were first used experimentally for personal email and information filtering. The 1992 Tapestry mail system and the 1994 GroupLens news filtering system were early milestones before recommendation systems spread into e-commerce and other online services. As user bases and content volumes grew during the 2000s, major platforms including Google, YouTube, and Facebook developed machine-learning systems to personalise content delivery and prioritise material predicted to generate engagement. Facebook introduced its News Feed in 2006, which gradually shifted from chronological presentation towards algorithmically ranked content. YouTube altered its recommendation system in 2012 to prioritise watch time rather than clicks, a change the platform said was prompted by concerns that click-based metrics encouraged misleading thumbnails and low-quality videos. TikTok, launched internationally in 2018, adopted a model in which its primary content surface, the For You feed, is driven almost entirely by algorithmic recommendation rather than by a user's social graph. An internal document obtained by The New York Times in 2021 showed that the platform's algorithm optimised for retention and time spent, using signals such as watch duration, replays, likes, and comments to score and rank videos. Algorithmic recommendation also became central to platforms outside social media. Spotify's personalised features, including Discover Weekly, Release Radar, and Home recommendations, use behavioural signals and inferred "taste profiles" to surface tracks and artists beyond a listener's existing library. An ethnographic study of music curators at streaming platforms described this blend of algorithmic and human editorial selection as an "algo-torial" model of gatekeeping. Amazon adopted item-based collaborative filtering for product recommendations in 1998, and its recommendation engine has been described as one of the earliest large-scale deployments of recommendation technology in e-commerce. The same dynamics operate on adult content platforms. Law professor Amy Adler has argued that from 2007 onwards the pornography industry migrated to algorithm-driven streaming platforms, most of which are controlled by a single near-monopoly company, Aylo (formerly MindGeek). These platforms use algorithmic search engines, suggestions, rigid categorisation of content, and AI-driven search term optimisation in ways that produce the same distorting effects found on mainstream speech platforms, including filter bubbles, feedback loops, and the tendency of algorithmic recommendations to alter individual preferences. == Mechanisms == Recommendation systems commonly combine collaborative filtering, which predicts a user's preferences from the behaviour of similar users, with machine-learning models that predict which content a user is likely to engage with from their prior activity. In a common two-stage design, a platform first generates a set of candidate items from a large content pool and then ranks them using a scoring model with objectives such as predicted engagement or user satisfaction. Small changes in ranking criteria can shift exposure at scale, particularly when applied repeatedly across multiple browsing sessions. These systems typically rely on signals including engagement rates, viewing duration, click-through rates, and network relationships between users. Modern recommendation pipelines continuously update predictions as new behavioural data arrives, allowing platforms to adjust rankings in near real time. Users' revealed preferences, expressed through behaviour such as clicks and viewing time, do not always align with their stated preferences, expressed through explicit feedback such as surveys or content controls. Popularity signals can create feedback dynamics in which early engagement increases the likelihood that content will be shown to additional users. Experimental research on online cultural markets has demonstrated how such feedback processes can produce unequal visibility outcomes even when initial differences in content quality are small. == Beneficial and public-interest uses == Recommendation systems can help users navigate large volumes of content by surfacing material predicted to match their interests or needs, which can improve discoverability on platforms with large content libraries. In public health communication, platforms can help health authorities distribute timely information at scale, though the same recommendation systems also risk amplifying misinformation alongside official guidance. Sociologist Zeynep Tufekci has argued that the shift from independent blogs to large centralised platforms transferred gatekeeping power from traditional media to corporate algorithms. In the case of the Egyptian uprising of 2011, she noted that ordinary users

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.

Signal-to-crosstalk ratio

The signal-to-crosstalk ratio at a specified point in a circuit is the ratio of the power of the wanted signal to the power of the unwanted signal from another channel. The signals are adjusted in each channel so that they are of equal power at the zero transmission level point in their respective channels. The signal-to-crosstalk ratio is usually expressed in dB.