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Image Gradient
An image gradient is a directional change in the intensity or color in an image. The gradient of the image is one of the fundamental building blocks in image processing. For example, the Canny edge detector uses image gradient for edge detection. In graphics software for digital image editing, the term gradient or color gradient is also used for a gradual blend of color which can be considered as an even gradation from low to high values, as used from white to black in the images to the right. Another name for this is ''color progression''. Mathematically, the gradient of a two-variable function (here the image intensity function) at each image point is a 2D vector with the components given by the derivatives in the horizontal and vertical directions. At each image point, the gradient vector points in the direction of largest possible intensity increase, and the length of the gradient vector corresponds to the rate of change in that direction. Since the intensity function of a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient2
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data
In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures. Data may be used as variables in a computational process. Data may represent abstract ideas or concrete measurements. Data is commonly used in scientific research, economics, and in virtually every other form of human organizational activity. Examples of data sets include price indices (such as consumer price index), unemployment rates, literacy rates, and census data. In this context, data represents the raw facts and figures which can be used in such a manner in order to capture the useful information out of it. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Variation Denoising
In signal processing, particularly image processing, total variation denoising, also known as total variation regularization or total variation filtering, is a noise removal process ( filter). It is based on the principle that signals with excessive and possibly spurious detail have high '' total variation'', that is, the integral of the absolute image gradient is high. According to this principle, reducing the total variation of the signal—subject to it being a close match to the original signal—removes unwanted detail whilst preserving important details such as edges. The concept was pioneered by L. I. Rudin, S. Osher, and E. Fatemi in 1992 and so is today known as the ''ROF model''. This noise removal technique has advantages over simple techniques such as linear smoothing or median filtering which reduce noise but at the same time smooth away edges to a greater or lesser degree. By contrast, total variation denoising is remarkably effective edge-preserving filter, i.e. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Derivatives
Image derivatives can be computed by using small convolution filters of size 2 × 2 or 3 × 3, such as the Laplacian, Sobel, Roberts and Prewitt operators. However, a larger mask will generally give a better approximation of the derivative and examples of such filters are Gaussian derivatives and Gabor filters. Sometimes high frequency noise needs to be removed and this can be incorporated in the filter so that the Gaussian kernel will act as a band pass filter. The use of Gabor filters in image processing has been motivated by some of its similarities to the perception in the human visual system. The pixel value is computed as a convolution : p'_u=\mathbf \ast G where \mathbf is the derivative kernel and G is the pixel values in a region of the image and \ast is the operator that performs the convolution. Sobel derivatives The derivative kernels, known as the Sobel operator are defined as follows, for the u and v directions respectively: : p'_u = \begi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Posterization
Posterization or posterisation of an image is the conversion of a continuous gradation of tone to several regions of fewer tones, causing abrupt changes from one tone to another. This was originally done with photographic processes to create posters. It can now be done photographically or with digital image processing, and may be deliberate or an unintended artifact of color quantization. Cause The effect may be created deliberately, or happen accidentally. For artistic effect, most image editing programs provide a posterization feature, or photographic processes may be used. Unwanted posterization, also known as color banding, banding, may occur when the color depth, sometimes called bit depth, is insufficient to accurately sample a continuous gradation of color tone. As a result, a continuous gradient appears as a series of discrete steps or bands of color — hence the name. When discussing fixed pixel displays, such as LCD and plasma televisions, this effect is referred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Color Banding
Colour banding is a subtle form of posterization in digital images, caused by the colour of each pixel being rounded to the nearest of the digital colour levels. While posterization is often done for artistic effect, colour banding is an undesired artifact. In 24-bit colour modes, 8 bits per channel is usually considered sufficient to render images in Rec. 709 or sRGB. However the eye can see the difference between the colour levels, especially when there is a sharp border between two large areas of adjacent color levels. This will happen with gradual gradients (like sunsets, dawns or clear blue skies), and also when blurring an image a large amount. Colour banding is more noticeable with fewer bits per pixel (BPP) at 16–256 colours (4–8 BPP), where there are fewer shades with a larger difference between them. Possible solutions include the introduction of dithering and increasing the number of bits per colour channel. Because the banding comes from limitati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient-domain Image Processing
Gradient domain image processing, also called Poisson image editing, is a type of digital image processing that operates on the differences between neighboring pixels, rather than on the pixel values directly. Mathematically, an image gradient represents the derivative of an image, so the goal of gradient domain processing is to construct a new image by integrating the gradient, which requires solving Poisson's equation. Overview Processing images in the gradient domain is a two-step process. The first step is to choose an image gradient. This is often extracted from one or more images and then modified, but it can be obtained through other means as well. For example, some researchers have explored the advantages of users painting directly in the gradient domain, while others have proposed sampling a gradient directly from a camera sensor. The second step is to solve Poisson's equation to find a new image that can produce the gradient from the first step. An exact solution often ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kernel (image Processing)
In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This is accomplished by doing a convolution between the kernel and an image. Details The general expression of a convolution is g(x,y)= \omega *f(x,y)=\sum_^a, where g(x,y) is the filtered image, f(x,y) is the original image, \omega is the filter kernel. Every element of the filter kernel is considered by -a \leq dx \leq a and -b \leq dy \leq b. Depending on the element values, a kernel can cause a wide range of effects. . The above are just a few examples of effects achievable by convolving kernels and images. Origin The origin is the position of the kernel which is above (conceptually) the current output pixel. This could be outside of the actual kernel, though usually it corresponds to one of the kernel elements. For a symmetric kernel, the origin is usually the center element. Convolution Convolution is the pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Differences
A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted \Delta is the operator that maps a function to the function \Delta /math> defined by :\Delta x)= f(x+1)-f(x). A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives. There are many similarities between difference equations and differential equations, specially in the solving methods. Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences. In numerical analysis, finite differences are widely used for approximating derivatives, and the term "fini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by It can be thought of as the rate of change of the function in the x-direction. Sometimes, for z=f(x, y, \ldots), the partial derivative of z with respect to x is denoted as \tfrac. Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: :f'_x(x, y, \ldots), \frac (x, y, \ldots). The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sobel Filter
The Sobel operator, sometimes called the Sobel–Feldman operator or Sobel filter, is used in image processing and computer vision, particularly within edge detection algorithms where it creates an image emphasising edges. It is named after Irwin Sobel and Gary Feldman, colleagues at the Stanford Artificial Intelligence Laboratory (SAIL). Sobel and Feldman presented the idea of an "Isotropic 3 × 3 Image Gradient Operator" at a talk at SAIL in 1968. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of the image intensity function. At each point in the image, the result of the Sobel–Feldman operator is either the corresponding gradient vector or the norm of this vector. The Sobel–Feldman operator is based on convolving the image with a small, separable, and integer-valued filter in the horizontal and vertical directions and is therefore relatively inexpensive in terms of computations. On the other hand, the gradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensity Image With Gradient Images
Intensity may refer to: In colloquial use * Strength (other) *Amplitude * Level (other) *Magnitude (other) In physical sciences Physics * Intensity (physics), power per unit area (W/m2) *Field strength of electric, magnetic, or electromagnetic fields (V/m, T, etc.) *Intensity (heat transfer), radiant heat flux per unit area per unit solid angle (W·m−2·sr−1) *Electric current, whose value is sometimes called ''current intensity'' in older books Optics *Radiant intensity, power per unit solid angle (W/sr) * Luminous intensity, luminous flux per unit solid angle (lm/sr or cd) *Irradiance, power per unit area (W/m2) Astronomy * Radiance, power per unit solid angle per unit projected source area (W·sr−1·m−2) Seismology *Mercalli intensity scale, a measure of earthquake impact * Japan Meteorological Agency seismic intensity scale, a measure of earthquake impact * Peak ground acceleration, a measure of earthquake acceleration (g or m/s2) Acous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
