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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 wiktionary:gradation, gradation from low to high values, and seen from black to white 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 (geometric), 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 direc ...
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Data
Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of data. Data are usually organized into structures such as tables that provide additional context and meaning, and 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 are commonly used in scientific research, economics, and virtually every other form of human organizational activity. Examples of data sets include price indices (such as the consumer price index), unemployment rates, literacy rates, and census data. In this context, data represent the raw facts and figures from which useful information can be extracted. Data are collected using technique ...
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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 ...
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Gradient-domain Image Processing
Gradient domain image processing, also called Poisson image editing, is a type of digital image processing that operates directly on the differences between neighboring pixels, rather than on the pixel values. 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 also be obtained through other means. 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 doe ...
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