Floyd–Steinberg Dithering
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Floyd–Steinberg Dithering
Floyd–Steinberg dithering is an image dithering algorithm first published in 1976 by Robert W. Floyd and Louis Steinberg. It is commonly used by image manipulation software, for example when an image is converted into GIF format that is restricted to a maximum of 256 colors. Implementation The algorithm achieves dithering using error diffusion, meaning it pushes (adds) the residual quantization error of a pixel onto its neighboring pixels, to be dealt with later. It spreads the debt out according to the distribution (shown as a map of the neighboring pixels): : \begin & & * & \frac & \ldots \\ \ldots & \frac & \frac & \frac & \ldots \\ \end The pixel indicated with a star (*) indicates the pixel currently being scanned, and the blank pixels are the previously-scanned pixels. The algorithm scans the image from left to right, top to bottom, quantizing pixel values one by one. Each time ...
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Michelangelo's David - Floyd-Steinberg
Michelangelo di Lodovico Buonarroti Simoni (; 6 March 1475 – 18 February 1564), known as Michelangelo (), was an Italian sculptor, painter, architect, and poet of the High Renaissance. Born in the Republic of Florence, his work was inspired by models from classical antiquity and had a lasting influence on Western art. Michelangelo's creative abilities and mastery in a range of artistic arenas define him as an archetypal Renaissance man, along with his rival and elder contemporary, Leonardo da Vinci. Given the sheer volume of surviving correspondence, sketches, and reminiscences, Michelangelo is one of the best-documented artists of the 16th century. He was lauded by contemporary biographers as the most accomplished artist of his era. Michelangelo achieved fame early; two of his best-known works, the ''Pietà'' and ''David'', were sculpted before the age of thirty. Although he did not consider himself a painter, Michelangelo created two of the most influential frescoes in ...
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Dithering
Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images. Dither is routinely used in processing of both digital audio and video data, and is often one of the last stages of mastering audio to a CD. A common use of dither is converting a grayscale image to black and white, such that the density of black dots in the new image approximates the average gray level in the original. Etymology The term ''dither'' was published in books on analog computation and hydraulically controlled guns shortly after World War II. Though he did not use the term ''dither'', the concept of dithering to reduce quantization patterns was first applied by Lawrence G. Roberts in his 1961 MIT master's thesis and 1962 article. By 1964 dither was being used in the modern sense described in this article. The technique was in use at least as early as 1915, though not under the name ''dither''. In digital p ...
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Robert W
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honour, praise, renown" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe it entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including English, German, Dutch, Norwegian, Swedish, Scots, Danish, and Icelandic. It can be use ...
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Louis Steinberg
Louis may refer to: * Louis (coin) * Louis (given name), origin and several individuals with this name * Louis (surname) * Louis (singer), Serbian singer * HMS ''Louis'', two ships of the Royal Navy See also Derived or associated terms * Lewis (other) * Louie (other) * Luis (other) * Louise (other) * Louisville (other) * Louis Cruise Lines * Louis dressing, for salad * Louis Quinze, design style Associated names * * Chlodwig, the origin of the name Ludwig, which is translated to English as "Louis" * Ladislav and László - names sometimes erroneously associated with "Louis" * Ludovic, Ludwig, Ludwick, Ludwik Ludwik () is a Polish given name. Notable people with the name include: * Ludwik Czyżewski, Polish WWII general * Ludwik Fleck (1896–1961), Polish medical doctor and biologist * Ludwik Gintel (1899–1973), Polish-Israeli Olympic soccer player ...
, names sometimes translated to English as "Louis" {{disambiguation ...
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Error Diffusion
Error diffusion is a type of halftoning in which the quantization residual is distributed to neighboring pixels that have not yet been processed. Its main use is to convert a multi-level image into a binary image, though it has other applications. Unlike many other halftoning methods, error diffusion is classified as an area operation, because what the algorithm does at one location influences what happens at other locations. This means buffering is required, and complicates parallel processing. Point operations, such as ordered dither, do not have these complications. Error diffusion has the tendency to enhance edges in an image. This can make text in images more readable than in other halftoning techniques. Early history Richard Howland Ranger received United States patent 1790723 for his invention, "Facsimile system." The patent, which issued in 1931, describes a system for transmitting images over telephone or telegraph lines, or by radio.Richard Howland Ranger, Facsimile ...
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Quantization Error
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer. Example For example, rounding a real number x to the nearest integer value forms a very basic type of quantizer – a ''uniform'' one. A typical (''mid-tread'') uni ...
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Pixel
In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest point in an all points addressable display device. In most digital display devices, pixels are the smallest element that can be manipulated through software. Each pixel is a sample of an original image; more samples typically provide more accurate representations of the original. The intensity of each pixel is variable. In color imaging systems, a color is typically represented by three or four component intensities such as red, green, and blue, or cyan, magenta, yellow, and black. In some contexts (such as descriptions of camera sensors), ''pixel'' refers to a single scalar element of a multi-component representation (called a ''photosite'' in the camera sensor context, although ''sensel'' is sometimes used), while in yet other contexts (like MRI) it may refer to a set of component intensities for a spatial position. Etymology The w ...
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Boustrophedon Transform
In mathematics, the boustrophedon transform is a procedure which maps one sequence to another. The transformed sequence is computed by an "addition" operation, implemented as if filling a triangular array in a boustrophedon (zigzag- or serpentine-like) manner—as opposed to a "Raster Scan" sawtooth-like manner. Definition The boustrophedon transform is a numerical, sequence-generating transformation, which is determined by an "addition" operation. Generally speaking, given a sequence: (a_0, a_1, a_2, \ldots), the boustrophedon transform yields another sequence: (b_0, b_1, b_2, \ldots), where b_0 is likely defined equivalent to a_0. The entirety of the transformation itself can be visualized (or imagined) as being constructed by filling-out the triangle as shown in Figure 1. Boustrophedon Triangle To fill-out the numerical Isosceles triangle (Figure 1), you start with the input sequence, (a_0, a_1, a_2, \ldots), and place one value (from the input sequence) per row, using ...
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Pseudocode
In computer science, pseudocode is a plain language description of the steps in an algorithm or another system. Pseudocode often uses structural conventions of a normal programming language, but is intended for human reading rather than machine reading. It typically omits details that are essential for machine understanding of the algorithm, such as variable declarations and language-specific code. The programming language is augmented with natural language description details, where convenient, or with compact mathematical notation. The purpose of using pseudocode is that it is easier for people to understand than conventional programming language code, and that it is an efficient and environment-independent description of the key principles of an algorithm. It is commonly used in textbooks and scientific publications to document algorithms and in planning of software and other algorithms. No broad standard for pseudocode syntax exists, as a program in pseudocode is not an executa ...
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Nearest Neighbor Search
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values. Formally, the nearest-neighbor (NN) search problem is defined as follows: given a set ''S'' of points in a space ''M'' and a query point ''q'' ∈ ''M'', find the closest point in ''S'' to ''q''. Donald Knuth in vol. 3 of ''The Art of Computer Programming'' (1973) called it the post-office problem, referring to an application of assigning to a residence the nearest post office. A direct generalization of this problem is a ''k''-NN search, where we need to find the ''k'' closest points. Most commonly ''M'' is a metric space and dissimilarity is expressed as a distance metric, which is symmetric and satisfies the triangle inequality. Even more common, ''M'' is taken ...
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Atkinson Dithering
Atkinson dithering is a variant of Floyd-Steinberg dithering designed by Bill Atkinson at Apple Computer, and used in the original Macintosh computer. Implementation The algorithm achieves dithering using error diffusion, meaning it pushes (adds) the residual quantization error of a pixel In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest point in an all points addressable display device. In most digital display devices, pixels are the smal ... onto its neighboring pixels, to be dealt with later. It spreads the debt out according to the distribution (shown as a map of the neighboring pixels): : \begin & & * & \frac & \frac \\ \ldots & \frac & \frac & \frac & \ldots \\ \ldots & & \frac & & \ldots \\ \end The pixel indicated with a star (*) indicates the pixel currently being scanned, and the blank pixels are the previously scanned pixels. The algorithm scans the image from lef ...
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Image Processing
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensional picture, that resembles a subject. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term “image” may refer specifically to a 2D image. An image does not have to use the entire visual system to be a visual representation. A popular example of this is of a greyscale image, which uses the visual system's sensitivity to brightness across all wavelengths, without taking into account different colors. A black and white visual representation of something is still an image, even though it does not make full use of the visual system's capabilities. Images are typically still, but in some cases can be moving or animated. Characteristics Images may be two or three-dimensional, such as a pho ...
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