GPI Seminar Series: Laurent Najman

Laurent Najman, ESIEE Paris, Morphological shapings and Power watersheds
Wednesday February 20th, 15h30, Seminar Room D5-007

Morphological shapings and Power watersheds

Abstract:

Morphological shapings:
Connected operators are filtering tools that act by merging elementary regions of an image. A popular strategy is based on tree-based image representations: for example, one can compute a shape-based attribute on each node of the tree and keep only the nodes for which the attribute is sufficiently strong. This operation can be seen as a thresholding of the tree, seen as a graph whose nodes are weighted by the attribute. Rather than being satisfied with a mere thresholding, we propose to expand on this idea, and to apply connected filters on this latest graph. Consequently, the filtering is done not in the space of the image, but on the space of shapes build from the image. Such a processing is a generalization of the existing tree-based connected operators. Indeed, the framework includes classical existing connected operators by attributes. It also allows us to propose a class of novel connected operators from the leveling family, based on shape attributes. Finally, we also propose a novel class of self-dual connected operators that we call morphological shapings.

Power watersheds:
In this work, we extend a common framework for graph-based image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes. Introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework. We then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm, which we term power watershed. In particular when q = 2, the power watershed leads to a multilabel, scale and contrast invariant, unique global optimum obtained in practice in quasi-linear time. Placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation. Two examples of such applications are surface reconstruction and anisotropic diffusion.

Laurent Najman's short bio:
Laurent Najman received the Habilitation à Diriger les Recherches in 2006 from the University of Marne-la-Vallée, a Ph.D. of applied mathematics from Paris-Dauphine University in 1994 with the highest honour (Félicitations du Jury) and an “Ingénieur” degree from the Ecole des Mines de Paris in 1991. After earning his engineering degree, he worked in the Central Research Laboratories of Thomson-CSF for three years, working on some problems of infrared image segmentation using mathematical morphology. He then joined a start-up company named Animation Science in 1995, as director of research and development. The technology of particle systems for computer graphics and scientific visualisation, developed by the company under his technical leadership received several awards, including the “European Information Technology Prize 1997” awarded by the European Commission (Esprit programme) and by the European Council for Applied Science and Engineering and the “Hottest Products of the Year 1996” awarded by the Computer Graphics World journal. In 1998, he joined OCÉ Print Logic Technologies, as senior scientist. He worked there on various problem of image analysis dedicated to scanning and printing. In 2002, he joined the Informatics Department of ESIEE, Paris, where he is professor and a member of the Laboratoire d’Informatique Gaspard Monge, Université Paris-Est Marne-la-Vallée. His current research interest is discrete mathematical morphology and discrete optimization.