Differentiation
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Differentiation in the spatial domain corresponds to the multiplication of the Fourier transform of the spatial function by the Fourier transform of gradient in the frequency domain. The first derivative in x direction causes the sharpening of the edges of the picture in x direction. The gradient in x direction detects sudden changes in this direction - that is why we see sharper the vertical edges. This image processing operation is used to extract edges. Finding edges is a basis for the object recognition, known as the segmentation process.