Generalized Laplacians and Curvatures for Image Analysis and Processing

Newly developed combinatorial Laplacians and curvature operators for grayscale, as well as color images are tested on 2D synthetic and natural images. This novel approach is based upon more general concepts developed by R. Forman and is inspired by the Bochner-Weitzeböck formula which is an essential identity in Riemannian Geometry. After the presentation of the operators as they operate on images we further demonstrate the implementation of them as diffusion kernels. The differences between the various Laplacians we define, are illustrated by these examples as each of the operators is shown to be adequate for different type of image processing tasks such as sharpening anomaly detection smoothing and denoising.