Logarithm of a matrixIn mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to Lie theory since when a matrix has a logarithm then it is in an element of a Lie group and the logarithm is the corresponding element of the vector space of the Lie algebra.
Comparison of vector graphics editorsA number of vector graphics editors exist for various platforms. Potential users of these editors will make a comparison of vector graphics editors based on factors such as the availability for the user's platform, the software license, the feature set, the merits of the user interface (UI) and the focus of the program. Some programs are more suitable for artistic work while others are better for technical drawings. Another important factor is the application's support of various vector and bitmap image formats for import and export.
Mathematical morphologyMathematical morphology (MM) is a theory and technique for the analysis and processing of geometrical structures, based on set theory, lattice theory, topology, and random functions. MM is most commonly applied to s, but it can be employed as well on graphs, surface meshes, solids, and many other spatial structures. Topological and geometrical continuous-space concepts such as size, shape, convexity, connectivity, and geodesic distance, were introduced by MM on both continuous and discrete spaces.
NumPyNumPy (pronounced ˈnʌmpaɪ () or sometimes ˈnʌmpi ()) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. The predecessor of NumPy, Numeric, was originally created by Jim Hugunin with contributions from several other developers. In 2005, Travis Oliphant created NumPy by incorporating features of the competing Numarray into Numeric, with extensive modifications.
ConvolutionIn mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function () that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see commutativity).
Corner detectionCorner detection is an approach used within computer vision systems to extract certain kinds of features and infer the contents of an image. Corner detection is frequently used in motion detection, , video tracking, image mosaicing, panorama stitching, 3D reconstruction and object recognition. Corner detection overlaps with the topic of interest point detection. A corner can be defined as the intersection of two edges. A corner can also be defined as a point for which there are two dominant and different edge directions in a local neighbourhood of the point.
Manipulation (psychology)In psychology, manipulation is defined as subterfuge designed to influence or control another, usually in a manner which facilitates one's personal aims. The methods used distort or orient the interlocutor's perception of reality, in particular through seduction, suggestion, persuasion and non-voluntary or consensual submission. Definitions for the term vary in which behavior is specifically included, influenced by both culture and whether referring to the general population or used in clinical contexts.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
Chebyshev filterChebyshev filters are analog or digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple (type I) or stopband ripple (type II). Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the operating frequency range of the filter, but they achieve this with ripples in the passband. This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials.
Crowd manipulationCrowd manipulation is the intentional or unwitting use of techniques based on the principles of crowd psychology to engage, control, or influence the desires of a crowd in order to direct its behavior toward a specific action. This practice is common to religion, politics and business and can facilitate the approval or disapproval or indifference to a person, policy, or product. The ethicality of crowd manipulation is commonly questioned. Crowd manipulation differs from propaganda—although they may reinforce one another to produce a desired result.
Image compressionImage compression is a type of data compression applied to s, 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. 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.
GIFThe Graphics Interchange Format (GIF; ɡɪf or dʒɪf , see pronunciation) is a bitmap that was developed by a team at the online services provider CompuServe led by American computer scientist Steve Wilhite and released on June 15, 1987. It is in widespread usage on the World Wide Web due to its wide support and portability between applications and operating systems. The format supports up to 8 bits per pixel for each image, allowing a single image to reference its own palette of up to 256 different colors chosen from the 24-bit RGB color space.
