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The minimum barrier distance

Seminars
Date: Monday, June 10, 2013 11:00

Place: Auditório Jacy Monteiro, block B, Cidade Universitária  |  City: São Paulo, Brazil

ABSTRACT

The minimum barrier distance, MBD, is a pseudo-metric defined on a compact subset D of the n-dimensional Euclidean space R^n and whose values depend on a fixed map (an image) w from D into R. The MBD is defined as the minimal value of the barrier strength of a path between the points, which constitutes the length of the smallest interval containing all values of w along the path. As such, MBD has some resemblance to the geodesic distance and the the pass value (which is a variant of Rosenfeld's degree of connectivity).

In the talk we discuss the relation between the digital version of MBD and its continuous counterpart. This discussion will revolve around a problem of efficient computation of MBD. In particular, we describe linear time algorithm that calculates approximate MBD and a polynomial time algorithm that calculates exact MBD.

Finally, we notice that every generalized distance function can be naturally translated to an image segmentation algorithm. The algorithms that fall under such category include: Relative Fuzzy Connectedness, Watershed, and those associated with the minimum barrier and geodesic distance functions. In particular, we compare experimentally these four algorithms on the 2D and 3D natural and medical images with known ground truth and at varying level of noise, blur and inhomogeneity.

The talk is based on a joint work of Krzysztof Chris Ciesielski, Robin Strand, Punam K. Saha, and Filip Malmberg

SHORT BIOGRAPHY


Krzysztof Chris Ciesielski received his Master’s and PhD degrees in mathematics from Warsaw University, Poland, in 1981 and 1985, respectively. He works at West Virginia University since 1989. He is an author or coauthor of three books and over 100 research papers. Most of this work is in pure mathematics (analysis, topology, and set theory). However, since 2003 his research switched and concentrates mainly in medical imaging. He conducts his research in medical imaging mainly in the University of Pennsylvania, where he holds a position of Adjunct Professor.

 

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