ICIP 2016
Anaïs Badoual, EPFL STI LIB

Test Run • 20 September 2016 • BM 4 233

Abstract
Title 1: Local Refinement for 3D Deformable Parametric Surfaces Abstract: Biomedical image segmentation is an active field of research where deformable models have proved to be efficient. The geometric representation of such models determines their ability to approximate the shape of interest as well as the speed of convergence of related optimization algorithms. We present a new tensor-product parameterization of surfaces that offers the possibility of local refinement. The goal is to allocate additional degrees of freedom to the surface only where an increase in local detail is required. We introduce the possibility of locally increasing the number of control points by inserting basis functions at specific locations. Our approach is generic and relies on refinable functions, which satisfy the refinement relation. We show that the proposed method improves brain segmentation in 3D MRI images. Title 2: An Inner-Product Calculus for Periodic Functions and Curves Abstract: Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and L2 distances between such curves. In particular, we present formulas for the direct and exact evaluation of correlation matrices in the case of closed (i.e., periodic) parametric curves and periodic signals. We give simplifications for practical cases that involve B-splines. To illustrate this approach, we also propose a least-squares approximation scheme that is able to resample curves while minimizing aliasing artifacts. Another application is the exact calculation of the enclosed area.