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Nearest-neighbor Interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around (neighboring) that point. The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant. The algorithm is very simple to implement and is commonly used (usually along with mipmapping) in real-time 3D rendering to select color values for a textured surface. Connection to Voronoi diagram For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbour interpolati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piecewise Constant
In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. Definition and first consequences A function f\colon \mathbb \rightarrow \mathbb is called a step function if it can be written as :f(x) = \sum\limits_^n \alpha_i \chi_(x), for all real numbers x where n\ge 0, \alpha_i are real numbers, A_i are intervals, and \chi_A is the indicator function of A: :\chi_A(x) = \begin 1 & \text x \in A \\ 0 & \text x \notin A \\ \end In this definition, the intervals A_i can be assumed to have the following two properties: # The intervals are pairwise disjoint: A_i \cap A_j = \emptyset for i \neq j # The union of the intervals is the entire real line: \bigcup_^n A_i = \mathbb R. Indeed, if that is not the case to start with, a different set of intervals can be picked for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voronoi Diagram
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons. Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art. The simplest case In the simplest case, shown in the first picture, we are given a finite set of points in the Euclid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rounding
Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ with $, the fraction 312/937 with 1/3, or the expression with . Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as but is known to be accurate only to within a few hundred units is usually better stated as "about ". On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating-point representation with a fixed number of sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero-order Hold
The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval. It has several applications in electrical communication. Time-domain model A zero-order hold reconstructs the following continuous-time waveform from a sample sequence ''x'' 'n'' assuming one sample per time interval ''T'': x_(t)\,= \sum_^ x cdot \mathrm \left(\frac \right) where \mathrm(\cdot) is the rectangular function. The function \mathrm \left(\frac \right) is depicted in Figure 1, and x_(t) is the piecewise-constant signal depicted in Figure 2. Frequency-domain model The equation above for the output of the ZOH can also be modeled as the output of a linear time-invariant filter with impulse response equal to a rect function, and with input being a sequence of dirac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Scaling
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Neighbor Interpolation
image:Natural-neighbors-coefficients-example.png, 200px, Natural neighbor interpolation with Sibson weights. The area of the green circles are the interpolating weights, ''w''''i''. The purple-shaded region is the new Voronoi cell, after inserting the point to be interpolated (black dot). The weights represent the intersection areas of the purple-cell with each of the seven surrounding cells. Natural neighbor interpolation is a method of spatial interpolation, developed by Robin Sibson. The method is based on Voronoi diagram, Voronoi tessellation of a discrete set of spatial points. This has advantages over simpler methods of interpolation, such as nearest-neighbor interpolation, in that it provides a smoother approximation to the underlying "true" function. The basic equation is: :G(x)=\sum^n_ where G(x) is the estimate at x, w_i are the weights and f(x_i) are the known data at (x_i). The weights, w_i, are calculated by finding how much of each of the surrounding areas is "stolen" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coloured Voronoi 2D
Coloureds ( af, Kleurlinge or , ) refers to members of multiracial ethnic communities in Southern Africa who may have ancestry from more than one of the various populations inhabiting the region, including African, European, and Asian. South Africa's Coloured people are regarded as having some of the most diverse genetic background. Because of the vast combination of genetics, different families and individuals within a family may have a variety of different physical features. ''Coloured'' was a legally defined racial classification during apartheid referring to anyone not white or not a member of one the aboriginal groups of Africa on a cultural basis, which effectively largely meant those people of colour not speaking any indigenous languages. In the Western Cape, a distinctive Cape Coloured and affiliated Cape Malay culture developed. In other parts of Southern Africa, people classified as Coloured were usually the descendants of individuals from two distinct ethniciti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Texture Filtering
In computer graphics, texture filtering or texture smoothing is the method used to determine the texture color for a texture mapped pixel, using the colors of nearby texels (pixels of the texture). There are two main categories of texture filtering, magnification filtering and minification filtering. Depending on the situation texture filtering is either a type of reconstruction filter where sparse data is interpolated to fill gaps (magnification), or a type of anti-aliasing (AA), where texture samples exist at a higher frequency than required for the sample frequency needed for texture fill (minification). Put simply, filtering describes how a texture is applied at many different shapes, size, angles and scales. Depending on the chosen filter algorithm the result will show varying degrees of blurriness, detail, spatial aliasing, temporal aliasing and blocking. Depending on the circumstances filtering can be performed in software (such as a software rendering package) or in hardware ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Rendering
3D rendering is the 3D computer graphics process of converting 3D models into 2D images on a computer. 3D renders may include photorealistic effects or non-photorealistic styles. Rendering methods Rendering is the final process of creating the actual 2D image or animation from the prepared scene. This can be compared to taking a photo or filming the scene after the setup is finished in real life. Several different, and often specialized, rendering methods have been developed. These range from the distinctly non-realistic wireframe rendering through polygon-based rendering, to more advanced techniques such as: scanline rendering, ray tracing, or radiosity. Rendering may take from fractions of a second to days for a single image/frame. In general, different methods are better suited for either photorealistic rendering, or real-time rendering. Real-time Rendering for interactive media, such as games and simulations, is calculated and displayed in real time, at rates o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real-time Computing
Real-time computing (RTC) is the computer science term for hardware and software systems subject to a "real-time constraint", for example from event to system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines". Ben-Ari, Mordechai; "Principles of Concurrent and Distributed Programming", ch. 16, Prentice Hall, 1990, , page 164 Real-time responses are often understood to be in the order of milliseconds, and sometimes microseconds. A system not specified as operating in real time cannot usually ''guarantee'' a response within any timeframe, although ''typical'' or ''expected'' response times may be given. Real-time processing ''fails'' if not completed within a specified deadline relative to an event; deadlines must always be met, regardless of system load. A real-time system has been described as one which "controls an environment by receiving data, processing them, and returning the results sufficiently qui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
