Ordered dithering is any image dithering algorithm which uses a pre-set threshold map tiled across an image. It is commonly used to display a continuous image on a display of smaller color depth. For example, Microsoft Windows uses it in 16-color graphics modes. With the most common "Bayer" threshold map, the algorithm is characterized by noticeable crosshatch patterns in the result. == Threshold map == The algorithm reduces the number of colors by applying a threshold map M to the pixels displayed, causing some pixels to change color, depending on the distance of the original color from the available color entries in the reduced palette. The first threshold maps were designed by hand to minimise the perceptual difference between a grayscale image and its two-bit quantisation for up to a 4x4 matrix. An optimal threshold matrix is one that for any possible quantisation of color has the minimum possible texture so that the greatest impression of the underlying feature comes from the image being quantised. It can be proven that for matrices whose side length is a power of two there is an optimal threshold matrix. The map may be rotated or mirrored without affecting the effectiveness of the algorithm. This threshold map (for sides with length as power of two) is also known as a Bayer matrix or, when unscaled, an index matrix. For threshold maps whose dimensions are a power of two, the map can be generated recursively via: M 2 n = 1 ( 2 n ) 2 [ 4 M n 4 M n + 2 J n 4 M n + 3 J n 4 M n + J n ] = J 2 ⊗ M n + 1 n 2 M 2 ⊗ J n , {\displaystyle \mathbf {M} _{2n}={\frac {1}{(2n)^{2}}}{\begin{bmatrix}4\mathbf {M} _{n}&4\mathbf {M} _{n}+2\mathbf {J} _{n}\\4\mathbf {M} _{n}+3\mathbf {J} _{n}&4\mathbf {M} _{n}+\mathbf {J} _{n}\end{bmatrix}}=\mathbf {J} _{2}\otimes \mathbf {M} _{n}+{\frac {1}{n^{2}}}\mathbf {M} _{2}\otimes \mathbf {J} _{n},} where J n {\displaystyle \mathbf {J} _{n}} are n × n {\displaystyle n\times n} matrices of ones and ⊗ {\displaystyle \otimes } is the Kronecker product. While the metric for texture that Bayer proposed could be used to find optimal matrices for sizes that are not a power of two, such matrices are uncommon as no simple formula for finding them exists, and relatively small matrix sizes frequently give excellent practical results (especially when combined with other modifications to the dithering algorithm). This function can also be expressed using only bit arithmetic: M(i, j) = bit_reverse(bit_interleave(bitwise_xor(i, j), i)) / n ^ 2 == Pre-calculated threshold maps == Rather than storing the threshold map as a matrix of n {\displaystyle n} × n {\displaystyle n} integers from 0 to n 2 {\displaystyle n^{2}} , depending on the exact hardware used to perform the dithering, it may be beneficial to pre-calculate the thresholds of the map into a floating point format, rather than the traditional integer matrix format shown above. For this, the following formula can be used: Mpre(i,j) = Mint(i,j) / n^2 This generates a standard threshold matrix. for the 2×2 map: this creates the pre-calculated map: Additionally, normalizing the values to average out their sum to 0 (as done in the dithering algorithm shown below) can be done during pre-processing as well by subtracting 1⁄2 of the largest value from every value: Mpre(i,j) = Mint(i,j) / n^2 – 0.5 maxValue creating the pre-calculated map: == Algorithm == The ordered dithering algorithm renders the image normally, but for each pixel, it offsets its color value with a corresponding value from the threshold map according to its location, causing the pixel's value to be quantized to a different color if it exceeds the threshold. For most dithering purposes, it is sufficient to simply add the threshold value to every pixel (without performing normalization by subtracting 1⁄2), or equivalently, to compare the pixel's value to the threshold: if the brightness value of a pixel is less than the number in the corresponding cell of the matrix, plot that pixel black, otherwise, plot it white. This lack of normalization slightly increases the average brightness of the image, and causes almost-white pixels to not be dithered. This is not a problem when using a gray scale palette (or any palette where the relative color distances are (nearly) constant), and it is often even desired, since the human eye perceives differences in darker colors more accurately than lighter ones, however, it produces incorrect results especially when using a small or arbitrary palette, so proper normalization should be preferred. In other words, the algorithm performs the following transformation on each color c of every pixel: c ′ = n e a r e s t _ p a l e t t e _ c o l o r ( c + r × ( M ( x mod n , y mod n ) − 1 / 2 ) ) {\displaystyle c'=\mathrm {nearest\_palette\_color} {\mathopen {}}\left(c+r\times \left(M(x{\bmod {n}},y{\bmod {n}})-1/2\right){\mathclose {}}\right)} where M(i, j) is the threshold map on the i-th row and j-th column, c′ is the transformed color, and r is the amount of spread in color space. Assuming an RGB palette with 23N evenly distanced colors where each color (a triple of red, green and blue values) is represented by an octet from 0 to 255, one would typically choose r ≈ 255 N {\textstyle r\approx {\frac {255}{N}}} . (1⁄2 is again the normalizing term.) Because the algorithm operates on single pixels and has no conditional statements, it is very fast and suitable for real-time transformations. Additionally, because the location of the dithering patterns always stays the same relative to the display frame, it is less prone to jitter than error-diffusion methods, making it suitable for animations. Because the patterns are more repetitive than error-diffusion method, an image with ordered dithering compresses better. Ordered dithering is more suitable for line-art graphics as it will result in straighter lines and fewer anomalies. The values read from the threshold map should preferably scale into the same range as the minimal difference between distinct colors in the target palette. Equivalently, the size of the map selected should be equal to or larger than the ratio of source colors to target colors. For example, when quantizing a 24 bpp image to 15 bpp (256 colors per channel to 32 colors per channel), the smallest map one would choose would be 4×2, for the ratio of 8 (256:32). This allows expressing each distinct tone of the input with different dithering patterns. === A variable palette: pattern dithering === == Non-Bayer approaches == The above thresholding matrix approach describes the Bayer family of ordered dithering algorithms. A number of other algorithms are also known; they generally involve changes in the threshold matrix, which changes the distribution of the "noise" introduced by all kinds of dithering (the difference between the original image and the dithered image). === Halftone === Halftone dithering performs a form of clustered dithering, creating a look similar to halftone patterns, using a specially crafted matrix. === Void and cluster === The Void and cluster algorithm uses a pre-generated blue noise as the matrix for the dithering process. The blue noise matrix keeps the Bayer's good high frequency content, but with a more uniform coverage of all the frequencies involved shows a much lower amount of patterning. The "voids-and-cluster" method gets its name from the matrix generation procedure, where a black image with randomly initialized white pixels is gaussian-blurred to find the brightest and darkest parts, corresponding to voids and clusters. After a few swaps have evenly distributed the bright and dark parts, the pixels are numbered by importance. It takes significant computational resources to generate the blue noise matrix: on a modern computer a 64×64 matrix requires a couple seconds using the original algorithm. This algorithm can be extended to make animated dither masks which also consider the axis of time. This is done by running the algorithm in three dimensions and using a kernel which is a product of a two-dimensional gaussian kernel on the XY plane, and a one-dimensional Gaussian kernel on the Z axis. === Simulated Annealing === Simulated annealing can generate dither masks by starting with a flat histogram and swapping values to optimize a loss function. The loss function controls the spectral properties of the mask, allowing it to make blue noise or noise patterns meant to be filtered by specific filters. The algorithm can also be extended over time for animated dither masks with chosen temporal properties.
Kruti
Kruti is a multilingual AI agent and chatbot developed by the Indian company Ola Krutrim. It is designed to perform real-world tasks for users, such as booking taxis and ordering food, by integrating directly with various online services. It is notable for its ability to understand and respond in multiple Indian languages. Developed by a team founded by Bhavish Aggarwal, Kruti functions as an "agentic" AI, meaning it can reason, plan, and execute multi-step tasks to fulfill a user's request. The backend technology combines several open-source large language models with Ola's proprietary Krutrim V2 model. The system was developed to work primarily on smartphones, addressing the Indian market's specific needs, including language diversity and potential bandwidth constraints. Kruti was officially released in June 2025, replacing an earlier chatbot from the company that was also named Krutrim. Initially supporting 13 languages, the company plans to expand its capabilities to 22 Indian languages. == Background == Kruti is an improved version of Ola's Krutrim chatbot, which was first launched in 2023 and was intended to be replaced by Kruti. It was officially released on 12 June 2025 as an upgrade to passive chatbots, with support for text and voice in 13 Indian languages. As an agentic AI, it can execute tasks with customization and reasoning, providing adaptive answers based on user preferences and past interactions. Kruti is optimized for smartphone usage and designed to accommodate bandwidth constraints and usage patterns in India. To ensure scalability and cost-effective performance, it combines various open-source large language models with Ola's own Krutrim V2, which has 12 billion parameters. Its speech recognition is built to identify regional Indian languages, dialects, and accents. Due to its integration with numerous apps and services, Kruti is context-aware and can proactively complete tasks. Initially connected only with Ola ecosystem services, Krutrim intends to expand and incorporate various Indian services into Kruti, with the goal of adding services from Blinkit, Swiggy, and Uber with respective voice command support. On 20 June 2025, Krutrim acquired the AI platform BharatSah‘AI’yak to increase its involvement in government, education, and agriculture projects. This acquisition will allow Kruti to assist in broadening the scope of BharatSah'AI'yak's work on India-centric, vernacular retrieval-augmented generation AI bots. == Development == Kruti is designed to perform tasks with minimal user input, accepting documents, images, and text, without requiring users to switch between applications. Its agentic framework breaks queries into sub-tasks executed by multiple agents working sequentially or concurrently, with reported accuracy exceeding 90%. Kruti connects to company databases and APIs via the Model Context Protocol and presents responses as summaries, tables, or narratives adapted to user behaviour. The system supports payments via credit/debit cards and UPI. The underlying stack, which includes foundation models and AI training and inference systems, is intended to support adaptation across sectors such as healthcare, education, and finance. Ola Cabs and the Open Network for Digital Commerce have begun integrating Kruti into their platforms pending broader reliability testing.
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Powerset (company)
Powerset was an American company based in San Francisco, California, that, in 2006, was developing a natural language search engine for the Internet. On July 1, 2008, Powerset was acquired by Microsoft for an estimated $100 million (~$143 million in 2024). Powerset was working on building a natural language search engine that could find targeted answers to user questions (as opposed to keyword based search). For example, when confronted with a question like "Which U.S. state has the highest income tax?", conventional search engines ignore the question phrasing and instead do a search on the keywords "state", "highest", "income", and "tax". Powerset on the other hand, attempts to use natural language processing to understand the nature of the question and return pages containing the answer. The company was in the process of "building a natural language search engine that reads and understands every sentence on the Web". The company has licensed natural language technology from PARC, the former Xerox Palo Alto Research Center. On May 11, 2008, the company unveiled a tool for searching a fixed subset of English Wikipedia using conversational phrases rather than keywords. Acquisition by Microsoft: One significant milestone in Powerset's history was its acquisition by Microsoft on July 1, 2008, for an estimated $100 million. This acquisition was part of Microsoft's broader strategy to enhance its search capabilities and compete more effectively with other search engine providers, particularly Google. Natural Language Search Engine: Powerset's primary focus was on developing a natural language search engine capable of understanding and interpreting user queries in a more human-like manner. Instead of simply matching keywords, Powerset aimed to comprehend the meaning behind the words, allowing for more accurate and contextually relevant search results. Technology and Partnerships: Powerset had licensed natural language technology from PARC, the Xerox Palo Alto Research Center. This technology likely played a crucial role in the development of Powerset's NLP capabilities. Wikipedia Search Tool: In May 2008, Powerset unveiled a search tool that allowed users to search a fixed subset of English Wikipedia using conversational phrases rather than traditional keywords. This demonstrated the potential of Powerset's NLP technology in providing more precise and relevant search results. == Powerlabs == In a form of beta testing, Powerset opened an online community called Powerlabs on September 17, 2007. Business Week said: "The company hopes the site will marshal thousands of people to help build and improve its search engine before it goes public next year." Said The New York Times: "[Powerset Labs] goes far beyond the 'alpha' or 'beta' testing involved in most software projects, when users put a new product through rigorous testing to find its flaws. Powerset doesn’t have a product yet, but rather a collection of promising natural language technologies, which are the fruit of years of research at Xerox PARC." Powerlabs' initial search results are taken from Wikipedia. == Notable people == Barney Pell (born March 18, 1968, in Hollywood, California) was co-founder and CEO of Powerset. Pell received his Bachelor of Science degree in symbolic systems from Stanford University in 1989, where he graduated Phi Beta Kappa and was a National Merit Scholar. Pell received a PhD in computer science from Cambridge University in 1993, where he was a Marshall Scholar. He has worked at NASA, as chief strategist and vice president of business development at StockMaster.com (acquired by Red Herring in March, 2000) and at Whizbang! Labs. Prior to joining Powerset, Pell was an Entrepreneur-in-Residence at Mayfield Fund, a venture capital firm in Silicon Valley. Pell is also a founder of Moon Express, Inc., a U.S. company awarded a $10M commercial lunar contract by NASA and a competitor in the Google Lunar X PRIZE. Steve Newcomb was the COO and co-founder of Powerset. Prior to joining Powerset, he was a co-founder of Loudfire, General Manager at Promptu, and was on the board of directors at Jaxtr. He left Powerset in October 2007 to form Virgance, a social startup incubator. Lorenzo Thione (born in Como, Italy) was the product architect and co-founder of Powerset. Prior to joining Powerset, he worked at FXPAL in natural language processing and related research fields. Thione earned his master's degree in software engineering from the University of Texas at Austin. Ronald Kaplan, former manager of research in Natural Language Theory and Technology at PARC, served as the company's CTO and CSO. Ryan Ferrier is a member of the founding team of Powerset. He managed personnel and internal operations. After 2008 he went on to co-found Serious Business, which made Facebook applications and was later bought by Zynga. Another Powerset alumnus, Alex Le, became CTO of Serious Business and went on to become an executive producer at Zynga when it bought the company. Siqi Chen founded a stealth startup in mobile computing after leaving Powerset. Tom Preston-Werner worked at Powerset and left after the acquisition to found GitHub. == Investors == Powerset attracted a wide range of investors, many of whom had considerable experience in the venture capital field. The company received $12.5 million (~$18.2 million in 2024) in Series A funding during November 2007, co-led by the venture capital firms Foundation Capital and The Founders Fund. Among the better-known investors: Esther Dyson, founding chairman of ICANN, founder of the newsletter Release 1.0 and editor at Cnet Peter Thiel, founder and former CEO of PayPal Luke Nosek, founder of PayPal Todd Parker. Managing Partner, Hidden River Ventures Reid Hoffman, executive vice president of PayPal and founder of LinkedIn First Round Capital, seed-stage venture firm
How to Choose an AI Art Generator
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