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Anisotropic Diffusion
In image processing and computer vision, anisotropic diffusion, also called Perona–Malik diffusion, is a technique aiming at reducing image noise without removing significant parts of the image content, typically edges, lines or other details that are important for the interpretation of the image. Anisotropic diffusion resembles the process that creates a scale space, where an image generates a parameterized family of successively more and more blurred images based on a diffusion process. Each of the resulting images in this family are given as a convolution between the image and a 2D isotropic Gaussian filter, where the width of the filter increases with the parameter. This diffusion process is a ''linear'' and ''space-invariant'' transformation of the original image. Anisotropic diffusion is a generalization of this diffusion process: it produces a family of parameterized images, but each resulting image is a combination between the original image and a filter that depends o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Processing
An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a projection on a surface, activation of electronic signals, or digital displays; they can also be reproduced through mechanical means, such as photography, printmaking, or photocopying. Images can also be animated through digital or physical processes. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term ''image'' (or ''optical image'') refers specifically to the reproduction of an object formed by light waves coming from the object. A ''volatile image'' exists or is perceived only for a short period. This may be a reflection of an object by a mirror, a projection of a camera obscura, or a scene displayed on a cathode-ray tube. A ''fixed image'', also called a hard copy, is one that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. Mathematics In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noise Reduction
Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio. All signal processing devices, both analog and digital, have traits that make them susceptible to noise. Noise can be random with an even frequency distribution ( white noise), or frequency-dependent noise introduced by a device's mechanism or signal processing algorithms. In electronic systems, a major type of noise is ''hiss'' created by random electron motion due to thermal agitation. These agitated electrons rapidly add and subtract from the output signal and thus create detectable noise. In the case of photographic film and magnetic tape, noise (both visible and audible) is introduced due to the grain structure of the medium. In pho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Noise
Image noise is random variation of brightness or color information in images. It can originate in film grain and in the unavoidable shot noise of an ideal photon detector. In digital photography is usually an aspect of electronic noise, produced by the image sensor of a digital camera. The circuitry of a Image scanner, scanner can also contribute to the effect. Image noise is often (but not necessarily) an undesirable by-product of image capture that obscures the desired information. Typically the term “image noise” is used to refer to noise in 2D images, not 3D images. The original meaning of "noise" was "unwanted signal"; Noise (radio), unwanted electrical fluctuations in signals received by AM radios caused audible acoustic noise ("static"). By analogy, unwanted electrical fluctuations are also called "noise". Image noise can range from almost imperceptible specks on a digital photograph taken in good light, to Optical astronomy, optical and Radioastronomy, radioast ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat Equation
In mathematics and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the heat equation and its variants have been found to be fundamental in many parts of both pure and applied mathematics. Definition Given an open subset of and a subinterval of , one says that a function is a solution of the heat equation if : \frac = \frac + \cdots + \frac, where denotes a general point of the domain. It is typical to refer to as time and as spatial variables, even in abstract contexts where these phrases fail to have their intuitive meaning. The collection of spatial variables is often referred to simply as . For any given value of , the right-hand side of the equation is the Laplace operator, Laplacian of the function . As such, the heat equation is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge-preserving Smoothing
Edge-preserving smoothing or edge-preserving filtering is an image processing technique that smooths away noise or textures while retaining sharp edges. Examples are the median, bilateral, guided, anisotropic diffusion, and Kuwahara filters. Introduction In many applications, e.g., medical or satellite imaging, the edges are key features and thus must be preserved sharp and undistorted in smoothing/denoising. Edge-preserving filters are designed to automatically limit the smoothing at “edges” in images measured, e.g., by high gradient magnitudes. For example, the motivation for anisotropic diffusion (also called nonuniform or variable conductance diffusion) is that a Gaussian smoothed image is a single time slice of the solution to the heat equation, that has the original image as its initial conditions. Anisotropic diffusion includes a variable conductance term that is determined using the differential structure of the image, such that the heat does not propagate over the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge Detection
Edge or EDGE may refer to: Technology Computing * Edge computing, a network load-balancing system * Edge device, an entry point to a computer network * Adobe Edge, a graphical development application * Microsoft Edge, a web browser developed by Microsoft * Microsoft Edge Legacy, a discontinued web browser developed by Microsoft * EdgeHTML, the layout engine used in Microsoft Edge Legacy * ThinkPad Edge, a Lenovo laptop computer series marketed from 2010 * Silhouette edge, in computer graphics, a feature of a 3D body projected onto a 2D plane * Explicit data graph execution, a computer instruction set architecture Telecommunication(s) * EDGE (telecommunication), a 2G digital cellular communications technology * Edge Wireless, an American mobile phone provider * Motorola Edge series, a series of smartphones made by Motorola * Samsung Galaxy Note Edge, a phablet made by Samsung * Samsung Galaxy S7 Edge or Samsung Galaxy S6 Edge, smartphones made by Samsung * Ubuntu Edg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilateral Filter
A bilateral filter is a non-linear, edge-preserving, and noise-reducing smoothing filter for images. It replaces the intensity of each pixel with a weighted average of intensity values from nearby pixels. This weight can be based on a Gaussian distribution. Crucially, the weights depend not only on Euclidean distance of pixels, but also on the radiometric differences (e.g., variations in color intensity or depth). This dual dependency preserves sharp edges while suppressing noise. Definition The bilateral filter is defined as : I^\text(x) = \frac \sum_ I(x_i)f_r(\, I(x_i) - I(x)\, )g_s(\, x_i - x\, ), and normalization term, , is defined as : W_p = \sum_ where : I^\text is the filtered image; : I is the original input image to be filtered; : x are the coordinates of the current pixel to be filtered; : \Omega is the window centered in x, so x_i \in \Omega is another pixel; : f_r is the range kernel for smoothing differences in intensities (this function can be a Gaussi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat Equation
In mathematics and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the heat equation and its variants have been found to be fundamental in many parts of both pure and applied mathematics. Definition Given an open subset of and a subinterval of , one says that a function is a solution of the heat equation if : \frac = \frac + \cdots + \frac, where denotes a general point of the domain. It is typical to refer to as time and as spatial variables, even in abstract contexts where these phrases fail to have their intuitive meaning. The collection of spatial variables is often referred to simply as . For any given value of , the right-hand side of the equation is the Laplace operator, Laplacian of the function . As such, the heat equation is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inner Product
In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in \langle a, b \rangle. Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or ''scalar product'' of Cartesian coordinates. Inner product spaces of infinite dimension are widely used in functional analysis. Inner product spaces over the field of complex numbers are sometimes referred to as unitary spaces. The first usage of the concept of a vector space with an inner product is due to Giuseppe Peano, in 1898. An inner product naturally induces an associated norm, (denoted , x, and , y, in the pictu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient Descent
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a trajectory that maximizes that function; the procedure is then known as ''gradient ascent''. It is particularly useful in machine learning for minimizing the cost or loss function. Gradient descent should not be confused with local search algorithms, although both are iterative methods for optimization. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divergence
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters the volume in an infinitesimal neighborhood of each point. (In 2D this "volume" refers to area.) More precisely, the divergence at a point is the rate that the flow of the vector field modifies a volume about the point ''in the limit'', as a small volume shrinks down to the point. As an example, consider air as it is heated or cooled. The velocity of the air at each point defines a vector field. While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region. The divergence of the velocity field in that region would thus have a positive value. While the air is cooled and thus contracting, the divergence of the velocity has a negative value. Physical interpretation of divergence In physical terms, the divergence of a vector field is the extent to which the vector fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
