Hierarchical Laplacian and Its Spectrum in Ultrametric Image Processing

International audienceThe Laplacian of an image is one of the simplest and useful image processing tools which highlights regions of rapid intensity change and therefore it is applied for edge detection and contrast enhancement. This paper deals with the definition of the Laplacian operator on ultrametric spaces as well as its spectral representation in terms of the corresponding eigenfunctions and eigenvalues. The theory reviewed here provides the computational framework to process images or signals defined on a hierarchical representation associated to an ultrametric space. In particular, image regularization by ultrametric heat kernel filtering and image enhancement by hierarchical Laplacian are illustrated