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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 .
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 ...
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. [1] However, a larger mask will generally give a better approximation of the derivative and examples of such filters are Gaussian derivatives [ 2 ] and Gabor filters . [ 3 ]
where x is the initial intensity value in the image, z is the computed derivative and i,j represent the location in the image. The results of this operation will highlight changes in intensity in a diagonal direction. One of the most appealing aspects of this operation is its simplicity; the kernel is small and contains only integers.
SSIM has also been used on the gradient of images, making it "G-SSIM". G-SSIM is especially useful on blurred images. [19] The modifications above can be combined. For example, 4-G-r* is a combination of 4-SSIM, G-SSIM, and r*. It is able to reflect radiologist preference for images much better than other SSIM variants tested. [20]
In mathematical morphology and digital image processing, a morphological gradient is the difference between the dilation and the erosion of a given image. It is an image where each pixel value (typically non-negative) indicates the contrast intensity in the close neighborhood of that pixel.
Displays a background using multiple colors which gradually phases from one color to another. Template parameters [Edit template data] Parameter Description Type Status Background color 1 1 First background color Suggested values #000000 Line optional Background color 2 2 Second background color Suggested values #000000 Line optional Background color 3 3 Third background color Suggested values ...
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.