Optimally isotropic Laplacian operator

Laplacian operators used in the literature for digital image processing are not rotationally invariant. We examine the anisotropy of 3 x 3 Laplacian operators for images quantized in square pixels, and find the operator which has the minimum overall anisotropy.

[1]  John C. Russ,et al.  The Image Processing Handbook , 2016, Microscopy and Microanalysis.

[2]  Bhabatosh Chanda,et al.  The equivalence of best plane fit gradient with Robert's, Prewitt's and Sobel's gradient for edge detection and a 4-neighbour gradient with useful properties , 1984 .

[3]  Olivier D. Faugeras,et al.  Robust and fast computation of unbiased intensity derivatives in images , 1992, ECCV.

[4]  Luis Alvarez Images and PDE's , 1996 .

[5]  Berthold K. P. Horn Robot vision , 1986, MIT electrical engineering and computer science series.

[6]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[7]  A. Rosenfeld,et al.  Optimum Laplacian for digital image processing , 1997, Proceedings of International Conference on Image Processing.

[8]  James B. Cole A nearly exact second-order finite difference time-domain wave propagation algorithm on a coarse grid , 1994 .

[9]  Gérard G. Medioni,et al.  Detection of Intensity Changes with Subpixel Accuracy Using Laplacian-Gaussian Masks , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[11]  Azriel Rosenfeld,et al.  Digital Picture Processing , 1976 .