Laplacian operator is a basic tool for image processing. For an image with regular pixels, the Laplacian operator can be represented as a stencil in which constant weights are arranged spatially to indicate which picture cells they apply to. However, in a discrete spherical image the image pixels are irregular; thus, a stencil with constant weights is not suitable. In this paper a spherical Laplacian operator is derived from Gauss's theorem; which is suitable to images with irregular pixels. The effectiveness of the proposed discrete spherical Laplacian operator is shown by the experimental results.

One approach for image edge sharpening which includes a phase-only synthesis (POS) is presented. The technique presented here is the generalized version of the traditional Laplacian image enhancement. The utilizing of an internally dividing point between the POS and the Laplacian enhancement image makes this approach more flexible, more effective.