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Two types of gradients, with blue arrows to indicate the direction of the gradient. Light areas indicate higher pixel values A blue and green color 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.
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.
Two-dimensional slice through 3D Perlin noise at z = 0. Perlin noise is a type of gradient noise developed by Ken Perlin in 1983. It has many uses, including but not limited to: procedurally generating terrain, applying pseudo-random changes to a variable, and assisting in the creation of image textures.
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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 ...
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 ...
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.
Gradient vector flow (GVF), a computer vision framework introduced by Chenyang Xu and Jerry L. Prince, [1] [2] is the vector field that is produced by a process that smooths and diffuses an input vector field. It is usually used to create a vector field from images that points to object edges from a distance.