Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices

This paper proposes an efficient probabilistic method that computes combinatorial gradient fields for two dimensional image data. In contrast to existing algorithms, this approach yields a geometric Morse-Smale complex that converges almost surely to its continuous counterpart when the image resolution is increased. This approach is motivated using basic ideas from probability theory and builds upon an algorithm from discrete Morse theory with a strong mathematical foundation. While a formal proof is only hinted at, we do provide a thorough numerical evaluation of our method and compare it to established algorithms.Comment: 17 pages, 7 figure

An Hierarchical Labeling Technique for Interactive Computation of Watersheds

International audience—The watershed computation is a prevalent task in the geographical information systems. It is used, among other purposes, to forecast the pollutant concentration and its impact on the water quality. The algorithm to compute the watershed can be hard to parallelize and with the increasingly data growth, the need for parallel computation increases. In this paper we propose a new method to parallelize the watershed computation. Our algorithm is decomposed into two tasks, the parallel watershed segmentation into a hierarchy that allows in a second task to retrieve randomly large watersheds at run-time in interactive time