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] Sometimes high frequency noise needs to be removed and this can be incorporated in the filter so that the Gaussian kernel will act as a band pass filter.[4] The use of Gabor filters[5] in image processing has been motivated by some of its similarities to the perception in the human visual system.[6]
The pixel value is computed as a convolution
where is the derivative kernel and is the pixel values in a region of the image and is the operator that performs the convolution.
^Pratt, W.K., 2007. Digital image processing (4th ed.). John Wiley & Sons, Inc. pp. 465–522
^H. Bouma, A. Vilanova, J.O. Bescós, B.M.T.H. Romeny, F.A. Gerritsen, Fast and accurate gaussian derivatives based on b-splines, in: Proceedings of the 1st International Conference on Scale Space and Variational Methods in Computer Vision, Springer-Verlag, Berlin, Heidelberg, 2007, pp. 406–417.
^P. Moreno, A. Bernardino, J. Santos-Victor, Improving the sift descriptor with smooth derivative filters, Pattern Recognition Letters 30 (2009) 18–26.
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