AliasingIn signal processing and related disciplines, aliasing is the overlapping of frequency components resulting from a sample rate below the Nyquist frequency. This overlap results in distortion or artifacts when the signal is reconstructed from samples which causes the reconstructed signal to differ from the original continuous signal. Aliasing that occurs in signals sampled in time, for instance in digital audio or the stroboscopic effect, is referred to as temporal aliasing. Aliasing in spatially sampled signals (e.
Affine transformationIn Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments.
Affine spaceIn mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments. In an affine space, there is no distinguished point that serves as an origin. Hence, no vector has a fixed origin and no vector can be uniquely associated to a point.
Affine groupIn mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into itself. In the case of a Euclidean space (where the associated field of scalars is the real numbers), the affine group consists of those functions from the space to itself such that the image of every line is a line. Over any field, the affine group may be viewed as a matrix group in a natural way. If the associated field of scalars the real or complex field, then the affine group is a Lie group.
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.
Affine geometryIn mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance and angle. As the notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines. Therefore, Playfair's axiom (Given a line L and a point P not on L, there is exactly one line parallel to L that passes through P.) is fundamental in affine geometry.
Geometric transformationIn mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).
BandlimitingBandlimiting refers to a process which reduces the energy of a signal to an acceptably low level outside of a desired frequency range. Bandlimiting is an essential part of many applications in signal processing and communications. Examples include controlling interference between radio frequency communications signals, and managing aliasing distortion associated with sampling for digital signal processing. A bandlimited signal is, strictly speaking, a signal with zero energy outside of a defined frequency range.
PixelIn digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest addressable element in a dot matrix 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 or synthetic image; more samples typically provide more accurate representations of the original. The intensity of each pixel is variable.
Digital image processingDigital image processing is the use of a digital computer to process s through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over . It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the form of multidimensional systems.
Spatial anti-aliasingIn digital signal processing, spatial anti-aliasing is a technique for minimizing the distortion artifacts (aliasing) when representing a high-resolution image at a lower resolution. Anti-aliasing is used in digital photography, computer graphics, digital audio, and many other applications. Anti-aliasing means removing signal components that have a higher frequency than is able to be properly resolved by the recording (or sampling) device. This removal is done before (re)sampling at a lower resolution.
Nyquist rateIn signal processing, the Nyquist rate, named after Harry Nyquist, is a value (in units of samples per second or hertz, Hz) equal to twice the highest frequency (bandwidth) of a given function or signal. When the function is digitized at a higher sample rate (see ), the resulting discrete-time sequence is said to be free of the distortion known as aliasing. Conversely, for a given sample-rate the corresponding Nyquist frequency in Hz is one-half the sample-rate.
Reconstruction filterIn a mixed-signal system (analog and digital), a reconstruction filter, sometimes called an anti-imaging filter, is used to construct a smooth analog signal from a digital input, as in the case of a digital to analog converter (DAC) or other sampled data output device. The sampling theorem describes why the input of an ADC requires a low-pass analog electronic filter, called the anti-aliasing filter: the sampled input signal must be bandlimited to prevent aliasing (here meaning waves of higher frequency being recorded as a lower frequency).
Language acquisitionLanguage acquisition is the process by which humans acquire the capacity to perceive and comprehend language (in other words, gain the ability to be aware of language and to understand it), as well as to produce and use words and sentences to communicate. Language acquisition involves structures, rules, and representation. The capacity to use language successfully requires one to acquire a range of tools including phonology, morphology, syntax, semantics, and an extensive vocabulary.
Second-language acquisitionSecond-language acquisition (SLA), sometimes called second-language learning — otherwise referred to as L2 (language 2) acquisition, is the process by which people learn a second language. Second-language acquisition is also the scientific discipline devoted to studying that process. The field of second-language acquisition is regarded by some but not everybody as a sub-discipline of applied linguistics but also receives research attention from a variety of other disciplines, such as psychology and education.
Image resolutionImage resolution is the level of detail an holds. The term applies to digital images, film images, and other types of images. "Higher resolution" means more image detail. Image resolution can be measured in various ways. Resolution quantifies how close lines can be to each other and still be visibly resolved. Resolution units can be tied to physical sizes (e.g. lines per mm, lines per inch), to the overall size of a picture (lines per picture height, also known simply as lines, TV lines, or TVL), or to angular subtense.
Multisample anti-aliasingMultisample anti-aliasing (MSAA) is a type of spatial anti-aliasing, a technique used in computer graphics to remove jaggies. The term generally refers to a special case of supersampling. Initial implementations of full-scene anti-aliasing (FSAA) worked conceptually by simply rendering a scene at a higher resolution, and then downsampling to a lower-resolution output. Most modern GPUs are capable of this form of anti-aliasing, but it greatly taxes resources such as texture, bandwidth, and fillrate.
SupersamplingSupersampling or supersampling anti-aliasing (SSAA) is a spatial anti-aliasing method, i.e. a method used to remove aliasing (jagged and pixelated edges, colloquially known as "jaggies") from images rendered in computer games or other computer programs that generate imagery. Aliasing occurs because unlike real-world objects, which have continuous smooth curves and lines, a computer screen shows the viewer a large number of small squares. These pixels all have the same size, and each one has a single color.
Statistical language acquisitionStatistical language acquisition, a branch of developmental psycholinguistics, studies the process by which humans develop the ability to perceive, produce, comprehend, and communicate with natural language in all of its aspects (phonological, syntactic, lexical, morphological, semantic) through the use of general learning mechanisms operating on statistical patterns in the linguistic input. Statistical learning acquisition claims that infants' language-learning is based on pattern perception rather than an innate biological grammar.
DemosaicingA demosaicing (also de-mosaicing, demosaicking or debayering) algorithm is a used to reconstruct a full color image from the incomplete color samples output from an overlaid with a color filter array (CFA). It is also known as CFA interpolation or color reconstruction. Most modern digital cameras acquire images using a single image sensor overlaid with a CFA, so demosaicing is part of the required to render these images into a viewable format.
