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Adam7 Algorithm
Adam7 is an interlacing algorithm for raster images, best known as the interlacing scheme optionally used in PNG images. An Adam7 interlaced image is broken into seven subimages, which are defined by replicating this 8×8 pattern across the full image. The subimages are then stored in the image file in numerical order. Adam7 uses seven passes and operates in both dimensions, compared to only four passes in the vertical dimension used by GIF. This means that an approximation of the entire image can be perceived much more quickly in the early passes, particularly if interpolation algorithms such as bicubic interpolation are used. History Adam7 is named after Adam M. Costello, who suggested the method on February 2, 1995, and after the seven steps involved. It is a rearrangement of this five-pass scheme that had earlier been proposed by Lee Daniel Crocker: Alternative speculative proposals at the time included square spiral interlacing and using Peano curves, but these w ...
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Adam7 Passes
Disintegrin and metalloproteinase domain-containing protein 7 is a protein that in humans is encoded by the ADAM7 gene. ADAM7 is an 85-kDa enzyme that is a member of the transmembrane A disintegrin and metalloproteinase, ADAM (A Disintegrin and Metalloprotease) protein family. Members of this family are membrane-anchored proteins structurally related to snake venom disintegrins, and have been implicated in a variety of biological processes involving cell-cell and cell-extracellular matrix, matrix interactions, including fertilization, muscle development, and neurogenesis. ADAM7 is important for the maturation of sperm cells in mammals. ADAM7 is also denoted as: ADAM_7, ADAM-7, EAPI, GP-83, and GP83. Function The functions of ADAM7 directly relate to sperm maturation and fertilization. Sperm are immobile until traversing the epididymis, in which the sperm interact with many proteins secreted by epithelial cells of the epididymis. Lacking protease activity, ADAM7 may play role ...
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Adam7 Interlacing Representation
Disintegrin and metalloproteinase domain-containing protein 7 is a protein that in humans is encoded by the ADAM7 gene. ADAM7 is an 85-kDa enzyme that is a member of the transmembrane ADAM (A Disintegrin and Metalloprotease) protein family. Members of this family are membrane-anchored proteins structurally related to snake venom disintegrins, and have been implicated in a variety of biological processes involving cell-cell and cell-matrix interactions, including fertilization, muscle development, and neurogenesis. ADAM7 is important for the maturation of sperm cells in mammals. ADAM7 is also denoted as: ADAM_7, ADAM-7, EAPI, GP-83, and GP83. Function The functions of ADAM7 directly relate to sperm maturation and fertilization. Sperm are immobile until traversing the epididymis, in which the sperm interact with many proteins secreted by epithelial cells of the epididymis. Lacking protease activity, ADAM7 may play roles in protein-protein interactions and cell adhesion process ...
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Interlacing (bitmaps)
In computing, interlacing (also known as interleaving) is a method of encoding a bitmap image such that a person who has partially received it sees a degraded copy of the entire image. When communicating over a slow communications link, this is often preferable to seeing a perfectly clear copy of one part of the image, as it helps the viewer decide more quickly whether to abort or continue the transmission. Interlacing is supported by the following formats, where it is optional: * GIF interlacing stores the lines in the order 0,8,16,\dots,(8n),\ 4, 12, \dots, (8n+4),\ 2,6,10,14,\dots,(4n+2),\ 1,3,5,7,9,\dots,(2n+1). * PNG uses the Adam7 algorithm, which interlaces in both the vertical and horizontal direction. * TGA uses two optional interlacing algorithms: **Two-way: 0,2,4,\dots,(2n),\ 1,3,\dots,(2n+1), **And four-way: 0,4,8,\dots,(4n),\ 1,5,\dots,(4n+1),\ 2,6,\dots,\ (4n+2),3,7,\dots,(4n+3). * JPEG, JPEG 2000, and JPEG XR (actually using a frequency decomposition hierar ...
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Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ...
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Raster Image
upright=1, The Smiley, smiley face in the top left corner is a raster image. When enlarged, individual pixels appear as squares. Enlarging further, each pixel can be analyzed, with their colors constructed through combination of the values for red, green and blue. In computer graphics and digital photography, a raster graphic represents a two-dimensional picture as a rectangular matrix or grid of square pixels, viewable via a computer display, paper, or other display medium. A raster is technically characterized by the width and height of the image in pixels and by the number of bits per pixel. Raster images are stored in image files with varying dissemination, production, generation, and acquisition formats. The printing and prepress industries know raster graphics as contones (from ''continuous tones''). In contrast, line art is usually implemented as vector graphics in digital systems. Many raster manipulations map directly onto the mathematical formalisms of linear alg ...
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Portable Network Graphics
Portable Network Graphics (PNG, officially pronounced , colloquially pronounced ) is a raster-graphics file format that supports lossless data compression. PNG was developed as an improved, non-patented replacement for Graphics Interchange Format (GIF) — unofficially, the initials PNG stood for the recursive acronym "PNG's not GIF". PNG supports palette-based images (with palettes of 24-bit RGB or 32-bit RGBA colors), grayscale images (with or without an alpha channel for transparency), and full-color non-palette-based RGB or RGBA images. The PNG working group designed the format for transferring images on the Internet, not for professional-quality print graphics; therefore non-RGB color spaces such as CMYK are not supported. A PNG file contains a single image in an extensible structure of ''chunks'', encoding the basic pixels and other information such as textual comments and integrity checks documented in RFC 2083. PNG files use the file extension PNG or png and hav ...
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Bicubic Interpolation
In mathematics, bicubic interpolation is an extension of cubic interpolation (not to be confused with cubic spline interpolation, a method of applying cubic interpolation to a data set) for interpolating data points on a two-dimensional regular grid. The interpolated surface (meaning the kernel shape, not the image) is smoother than corresponding surfaces obtained by bilinear interpolation or nearest-neighbor interpolation. Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing, bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in image resampling, when speed is not an issue. In contrast to bilinear interpolation, which only takes 4 pixels (2×2) into account, bicubic interpolation considers 16 pixels (4×4). Images resampled with bicubic interpolation can have different interpolation artifacts, depending on the b and c values chosen. Computation ...
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Lee Daniel Crocker
Lee Daniel Crocker (born July 3, 1963) is an American computer programmer. He is best known for rewriting the software upon which Wikipedia runs, to address scalability problems. This software, originally known as "Phase III", went live in July 2002 and became the foundation of what is now called MediaWiki. MediaWiki's code repository was still named "phase3" until the move from Subversion to Git in March 2012. He is a co-author of the PNG specification, and was also involved in the creation of the GIF and JPEG image file formats. He invented the per-scanline variable pre-filtering compression method used by PNG, the sum-of-abs heuristic used by many encoding programs, and proposed an early version of the Adam7 algorithm, using 5 passes rather than 7. In 1998, he was one of the 23 original creators of the "Transhumanist Declaration". As of 1999, he was a member of the Extropians futurist society. In June 2010, Crocker and others won the USENIX Advanced Computing Technical Assoc ...
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Peano Curve
In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous function from the unit interval onto the unit square, however it is not injective. Peano was motivated by an earlier result of Georg Cantor that these two sets have the same cardinality. Because of this example, some authors use the phrase "Peano curve" to refer more generally to any space-filling curve. Construction Peano's curve may be constructed by a sequence of steps, where the ''i''th step constructs a set ''Si'' of squares, and a sequence ''Pi'' of the centers of the squares, from the set and sequence constructed in the previous step. As a base case, ''S''0 consists of the single unit square, and ''P''0 is the one-element sequence consisting of its center point. In step ''i'', each square ''s'' of ''S''''i'' − 1 is partitioned into nine smaller equal squares, and its center point ''c'' is replace ...
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Discrete Wavelet Transform
In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency ''and'' location information (location in time). Examples Haar wavelets The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of 2^n numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum. This process is repeated recursively, pairing up the sums to prove the next scale, which leads to 2^n-1 differences and a final sum. Daubechies wavelets The most commonly used set of discrete wavelet transforms was formulated by the Belgian mathematician Ingrid Daubechies in 1988. This formulation is based on the use of recurrence relations to generate progressively finer discrete samplings o ...
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Haar Wavelet
In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal basis. The Haar sequence is now recognised as the first known wavelet basis and extensively used as a teaching example. The Haar sequence was proposed in 1909 by Alfréd Haar. Haar used these functions to give an example of an orthonormal system for the space of square-integrable functions on the unit interval  , 1 The study of wavelets, and even the term "wavelet", did not come until much later. As a special case of the Daubechies wavelet, the Haar wavelet is also known as Db1. The Haar wavelet is also the simplest possible wavelet. The technical disadvantage of the Haar wavelet is that it is not continuous, and therefore not differentiable. This property can, however, be an advantage for the a ...
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Downsample
In digital signal processing, downsampling, compression, and decimation are terms associated with the process of ''resampling'' in a multi-rate digital signal processing system. Both ''downsampling'' and ''decimation'' can be synonymous with ''compression'', or they can describe an entire process of bandwidth reduction (filtering) and sample-rate reduction. When the process is performed on a sequence of samples of a ''signal'' or a continuous function, it produces an approximation of the sequence that would have been obtained by sampling the signal at a lower rate (or density, as in the case of a photograph). ''Decimation'' is a term that historically means the '' removal of every tenth one''. But in signal processing, ''decimation by a factor of 10'' actually means ''keeping'' only every tenth sample. This factor multiplies the sampling interval or, equivalently, divides the sampling rate. For example, if compact disc audio at 44,100 samples/second is ''decimated'' by a factor of 5 ...
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