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Fractal Transform
The fractal transform is a technique invented by Michael Barnsley ''et al.'' to perform lossy image compression. This first practical fractal compression system for digital images resembles a vector quantization system using the image itself as the codebook. Fractal transform compression Start with a digital image A1. Downsample it by a factor of 2 to produce image A2. Now, for each block B1 of 4x4 pixels in A1, find the corresponding block B2 in A2 most similar to B1, and then find the grayscale or RGB offset and gain from A2 to B2. For each destination block, output the positions of the source blocks and the color offsets and gains. Fractal transform decompression Starting with an empty destination image A1, repeat the following algorithm several times: Downsample A1 down by a factor of 2 to produce image A2. Then copy blocks from A2 to A1 as directed by the compressed data, multiplying by the respective gains and adding the respective color offsets. This algorithm is guara ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Barnsley
Michael Fielding Barnsley (born 1946) is a British mathematician, researcher and an entrepreneur who has worked on fractal compression; he holds several patents on the technology. He received his Ph.D. in theoretical chemistry from University of Wisconsin–Madison in 1972 and BA in mathematics from Oxford in 1968. In 1987 he founded Iterated Systems Incorporated, and in 1988 he published a book entitled ''Fractals Everywhere'' and in 2006 ''SuperFractals''. He has also published these scientific papers: "Existence and Uniqueness of Orbital Measures", "Theory and Applications of Fractal Tops", "A Fractal Valued Random Iteration Algorithm and Fractal Hierarchy", "V-variable fractals and superfractals", "Fractal Transformations" and "Ergodic Theory, Fractal Tops and Colour Stealing". He is also credited for discovering the collage theorem. Iterated Systems was initially devoted to fractal image compression (epitomised by the Barnsley fern), and later focused on image archive manag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lossy Data Compression
In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storing, handling, and transmitting content. The different versions of the photo of the cat on this page show how higher degrees of approximation create coarser images as more details are removed. This is opposed to Lossless compression, lossless data compression (reversible data compression) which does not degrade the data. The amount of data reduction possible using lossy compression is much higher than using lossless techniques. Well-designed lossy compression technology often reduces file sizes significantly before degradation is noticed by the end-user. Even when noticeable by the user, further data reduction may be desirable (e.g., for real-time communication or to reduce transmission times or storage needs). The most widely use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Compression
Image compression is a type of data compression applied to digital images, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data. Lossy and lossless image compression Image compression may be lossy or lossless. Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics. Lossy compression methods, especially when used at low bit rates, introduce compression artifacts. Lossy methods are especially suitable for natural images such as photographs in applications where minor (sometimes imperceptible) loss of fidelity is acceptable to achieve a substantial reduction in bit rate. Lossy compression that produces negligible differences may be called visually lossless. Methods for lossy compression: * Transfor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal Compression
Fractal compression is a lossy compression method for digital images, based on fractals. The method is best suited for textures and natural images, relying on the fact that parts of an image often resemble other parts of the same image. Fractal algorithms convert these parts into mathematical data called "fractal codes" which are used to recreate the encoded image. Iterated function systems Fractal image representation may be described mathematically as an iterated function system (IFS). For binary images We begin with the representation of a binary image, where the image may be thought of as a subset of \mathbb^2. An IFS is a set of contraction mappings ''ƒ''1,...,''ƒN'', :f_i:\mathbb^2\to \mathbb^2. According to these mapping functions, the IFS describes a two-dimensional set ''S'' as the fixed point of the Hutchinson operator :H(A)=\bigcup_^N f_i(A), \quad A \subset \mathbb^2. That is, ''H'' is an operator mapping sets to sets, and ''S'' is the unique set satisfying ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Quantization
Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms. The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for lossy data compression. It can also be used for lossy data correction and density estimation. Vector quantization is based on the competitive learning paradigm, so it is closely related to the self-organizing map model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image
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 ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grayscale
In digital photography, computer-generated imagery, and colorimetry, a grayscale image is one in which the value of each pixel is a single sample representing only an ''amount'' of light; that is, it carries only intensity information. Grayscale images, a kind of black-and-white or gray monochrome, are composed exclusively of shades of gray. The contrast ranges from black at the weakest intensity to white at the strongest. Grayscale images are distinct from one-bit bi-tonal black-and-white images, which, in the context of computer imaging, are images with only two colors: black and white (also called ''bilevel'' or '' binary images''). Grayscale images have many shades of gray in between. Grayscale images can be the result of measuring the intensity of light at each pixel according to a particular weighted combination of frequencies (or wavelengths), and in such cases they are monochromatic proper when only a single frequency (in practice, a narrow band of frequencies) is ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RGB Color Space
An RGB color space is any additive color space based on the RGB color model. An RGB color space is defined by chromaticity coordinates of the red, green, and blue additive primaries, the white point which is usually a standard illuminant, and the transfer function which is also known as the tone response curve (TRC) or gamma. Applying Grassmann's law of light additivity, a colorspace so defined can produce colors which are enclosed within the 2D triangle on the chromaticity diagram defined by those primary coordinates. The TRC and white point further define the possible colors, creating a volume in a 3D shape that never exceeds the triangular bounds. The primary colors are often specified in terms of their xyY chromaticity coordinates, though the uʹ,vʹ coordinates from the UCS chromaticity diagram may be used. Both xyY and uʹ,vʹ are derived from the CIE 1931 color space, a device independent space also known as XYZ which uses the 2° standard observer, an averaging of expe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear
Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships are ''nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. The word linear comes from Latin ''linearis'', "pertaining to or resembling a line". In mathematics In mathematics, a linear map or linear function ''f''(''x'') is a function that satisfies the two properties: * Additivity: . * Homogeneity of degree 1: for all α. These properties are known as the superposition principle. In this definition, ''x'' is not necessarily a real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resampling (bitmap)
In computer graphics and digital imaging, image scaling refers to the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement. When scaling a vector graphic image, the graphic primitives that make up the image can be scaled using geometric transformations, with no loss of image quality. When scaling a raster graphics image, a new image with a higher or lower number of pixels must be generated. In the case of decreasing the pixel number (scaling down) this usually results in a visible quality loss. From the standpoint of digital signal processing, the scaling of raster graphics is a two-dimensional example of sample-rate conversion, the conversion of a discrete signal from a sampling rate (in this case the local sampling rate) to another. Mathematical Image scaling can be interpreted as a form of image resampling or image reconstruction from the view of the Nyquist sampling theorem. According to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Compression
Image compression is a type of data compression applied to digital images, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data. Lossy and lossless image compression Image compression may be lossy or lossless. Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics. Lossy compression methods, especially when used at low bit rates, introduce compression artifacts. Lossy methods are especially suitable for natural images such as photographs in applications where minor (sometimes imperceptible) loss of fidelity is acceptable to achieve a substantial reduction in bit rate. Lossy compression that produces negligible differences may be called visually lossless. Methods for lossy compression: * Transfor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
