Edge detection in 3D images using four gradient filters

We consider the problem of detecting edge surfaces (composed of voxels with high gradient variation) from a greyscale 3D image. This operation can be performed by a triplet of gradient filters in the three cardinal directions of space. We propose an alternative approach considering the four directions of the four diagonals of the unit cube, motivated by thinking of the cubic grid as a deformed BCC grid. We have four gradient filters instead of three, but the overall number of non-zero entries is smaller, therefore an optimized implementation performs edge detection in 70% of the time taken by the classic Sobel filters, with comparable effectiveness.