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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., range differences, such as color intensity, depth distance, etc.). This preserves sharp edges. 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 Gaussian function); : g ... [...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., range differences, such as color intensity, depth distance, etc.). This preserves sharp edges. 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 Gaussian function); : g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersampling
Supersampling 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. A line can only be shown as a collection of pixels, and therefore appears jagged unless it is perfectly horizontal or vertical. The aim of supersampling is to reduce this effect. Color samples are taken at several instances inside the pixel (not just at the center as normal), and an average color value is calculated. This is achieved by rendering the image at a much higher resolution than the one being displayed, then shrinking it to the desired size, using the extra pixels ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) 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). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution (f*g) differs from cross-correlation (f \star g) only in that either or is reflected about the y-axis in convolution; thus it is a cross-correlation of and , or and . For complex-valued fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Blur
In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician and scientist Carl Friedrich Gauss). It is a widely used effect in graphics software, typically to reduce image noise and reduce detail. The visual effect of this blurring technique is a smooth blur resembling that of viewing the image through a translucent screen, distinctly different from the bokeh effect produced by an out-of-focus lens or the shadow of an object under usual illumination. Gaussian smoothing is also used as a pre-processing stage in computer vision algorithms in order to enhance image structures at different scales—see scale space representation and scale space implementation. Mathematics Mathematically, applying a Gaussian blur to an image is the same as convolving the image with a Gaussian function. This is also known as a two-dimensional Weierstrass transform. By contrast, convolving by a circ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Filter
In electronics and signal processing mainly in digital signal processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would have infinite impulse response). Gaussian filters have the properties of having no overshoot to a step function input while minimizing the rise and fall time. This behavior is closely connected to the fact that the Gaussian filter has the minimum possible group delay. A Gaussian filter will have the best combination of suppression of high frequencies while also minimizing spatial spread, being the critical point of the uncertainty principle. These properties are important in areas such as oscilloscopes and digital telecommunication systems. Mathematically, a Gaussian filter modifies the input signal by convolution with a Gaussian function; this transformation is also known as the Weierstrass transform. Definition The one-dimensional Gaussian filter has an impulse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 d ... [...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] |
Beltrami Flow
In fluid dynamics, Beltrami flows are flows in which the vorticity vector \mathbf and the velocity vector \mathbf are parallel to each other. In other words, Beltrami flow is a flow where Lamb vector is zero. It is named after the Italian mathematician Eugenio Beltrami due to his derivation of the Beltrami vector field, while initial developments in fluid dynamics were done by the Russian scientist Ippolit S. Gromeka in 1881. Description Since the vorticity vector \boldsymbol and the velocity vector \mathbf are parallel to each other, we can write :\boldsymbol\times\mathbf=0, \quad \boldsymbol = \alpha(\mathbf,t) \mathbf, where \alpha(\mathbf,t) is some scalar function. One immediate consequence of Beltrami flow is that it can never be a planar or axisymmetric flow because in those flows, vorticity is always perpendicular to the velocity field. The other important consequence will be realized by looking at the incompressible vorticity equation :\frac + (\mathbf\cdot\nabla)\bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
G'MIC
G'MIC (GREYC's Magic for Image Computing) is a free and open-source framework for image processing. It defines a script language that allows the creation of complex macros. Originally usable only through a command line interface, it is currently mostly popular as a GIMP plugin, and is also included in Krita. G'MIC is dual-licensed under CECILL-2.1 or CECILL-C. Features G'MIC's graphical interface is notable for its noise removal filters, which came from an earlier project called GREYCstoration by the same authors. G'MIC offers many built-in commands for image processing, including basic mathematical manipulations, look up tables, and filtering operations. More complex macros and pipelines built out of those commands are defined in its library files. Interpreters Command line G'MIC is primarily a script language callable from a shell. For example, to display an image: gmic image.jpg This command displays the image contained in the file ''image.jpg'' and allows zooming in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-linear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GIMP
GIMP ( ; GNU Image Manipulation Program) is a free and open-source raster graphics editor used for image manipulation (retouching) and image editing, free-form drawing, transcoding between different image file formats, and more specialized tasks. It is not designed to be used for drawing, though some artists and creators have used it for such. GIMP is released under the GPL-3.0-or-later license and is available for Linux, macOS, and Microsoft Windows. History In 1995, Spencer Kimball and Peter Mattis began developing GIMP – originally named ''General Image Manipulation Program –'' as a semester-long project at the University of California, Berkeley for the eXperimental Computing Facility''.'' The acronym was coined first, with the letter ''G'' being added to ''-IMP'' as a reference to "the gimp" in the scene from the 1994 '' Pulp Fiction'' film. In 1996 was the initial public release of GIMP (0.54). The editor was quickly adopted and a community of contributors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adobe Photoshop
Adobe Photoshop is a raster graphics editor developed and published by Adobe Inc. for Windows and macOS. It was originally created in 1988 by Thomas and John Knoll. Since then, the software has become the industry standard not only in raster graphics editing, but in digital art as a whole. The software's name is often colloquially used as a verb (e.g. "to photoshop an image", " photoshopping", and "photoshop contest") although Adobe discourages such use. Photoshop can edit and compose raster images in multiple layers and supports masks, alpha compositing and several color models including RGB, CMYK, CIELAB, spot color, and duotone. Photoshop uses its own PSD and PSB file formats to support these features. In addition to raster graphics, Photoshop has limited abilities to edit or render text and vector graphics (especially through clipping path for the latter), as well as 3D graphics and video. Its feature set can be expanded by plug-ins; programs developed and distributed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
