Earth mover's morphing: Topology-free shape morphing using cluster-based EMD flows

Abstract

This paper describes a method for topology-free shape morphing based on region cluster-based Earth Mover's Distance (EMD) flows, since existing methods for closed curve/surface-based shape morphing are inapplicable to regions with different genera. First, the shape region is decomposed into a number of small clusters by Fuzzy C-Means clustering. Next, the EMD between the clusters of two key shapes is calculated and the resultant EMD flows are exploited as a weighted many-to-many correspondence among the clusters. Then, the fuzzy clusters are transported based on the EMD flows and a transition control parameter. Unlike the closed curve/surface-based methods, the morphs using cluster transportation are not guaranteed to be a binary image, and hence graph cut-based binary denoising is applied to a volumetric image of the two-dimensional position and the one-dimensional transition control parameter. The experiments demonstrate that the proposed method can perform morphing between shapes with different genera, such as walking silhouettes or alphabetical characters. © 2011 Springer-Verlag Berlin Heidelberg.