Computational Geometry-Based Scale-Space and Modal Image Decomposition

In this paper a framework for defining scale-spaces, based on the computational geometry concepts of α-shapes, is proposed. In this approach, objects (curves or surfaces) of increasing convexity are computed by selective sub-sampling, from the original shape to its convex hull. The relationships with the Empirical Mode Decomposition (EMD), the curvature motion-based scale-space and some operators from mathematical morphology, are studied. Finally, we address the problem of additive image/signal decomposition in fluorescence video-microscopy. An image sequence is mainly considered as a collection of 1D temporal signals, each pixel being associated with its temporal intensity variation.