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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 ...
Mathematically, the gradient of a two-variable function (here the image intensity function) is at each image point 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 ...
The gradient is obtained from an existing image and modified for image editing purposes. Various operators, such as finite difference or Sobel, can be used to find the gradient of a given image. This gradient can then be manipulated directly to produce several different effects when the resulting image is solved for.
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 ...
In mathematics, the structure tensor, also referred to as the second-moment matrix, is a matrix derived from the gradient of a function.It describes the distribution of the gradient in a specified neighborhood around a point and makes the information invariant to the observing coordinates.
Perlin noise is a procedural texture primitive, a type of gradient noise used by visual effects artists to increase the appearance of realism in computer graphics. The function has a pseudo-random appearance, yet all of its visual details are the same size. This property allows it to be readily controllable; multiple scaled copies of Perlin ...
and an external gradient is given by: G e ( f ) = f ⊕ b − f {\displaystyle G_{e}(f)=f\oplus b-f} . The internal and external gradients are "thinner" than the gradient, but the gradient peaks are located on the edges, whereas the internal and external ones are located at each side of the edges.
In Cartesian coordinates, the divergence of a continuously differentiable vector field = + + is the scalar-valued function: = = (, , ) (, , ) = + +.. As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge.