5/20/2023 0 Comments Gradient math![]() The following image is the magnitude of the gradient:Īgain, in the above image the change in initial image is encoded in the gray level: here you see that white means an high change in the initial image while black means no change at all. ![]() You can now combine the two components in order to get the magnitude of the gradient and the orientation of the gradient. scanning the image from the top to the bottom: We can make analogous observations for the vertical component, it shows how the image change in the vertical direction, i.e. In the above image, the inner part of the disk and the background are at a mean grey level because there is no change inside the disk and in the background. So, in the above image you see the brighter value in the left part of the circle because it is in the left part of the initial image that you have the black to white transition that gives you the left edge of the disk similarly, in the above image you see the darker value in the right part of the circle because it is in the right part of the initial image that you have the white to black transition that gives you the right edge of the disk. ![]() It shows how much the gray levels in your image change in the horizontal direction (it is the direction of positive x, scanning the image from left to right), this change is "encoded" in the grey level of the image of the horizontal component: the mean grey level means no change, the bright levels mean change from a dark value to a bright value, the dark levels mean a change from a bright value to a dark value. The following images shows you the horizontal component: As Dima explained in his answer, you have two component of the gradient, an horizontal and a vertical component. You can compute an approximation of the gradient of this image. Here you find a simple initial image of a white disk on a black background: My answer is based on the answer of mevatron to this question. As explained by Dima in his answer, you should be familiar with the mathematical concept of gradient in order to better understand the gradient in the field of image processing.
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