Planar Shape Analysis and Its Applications in Image-Based Inferences

Abstract

Shapes of boundaries can play an important role in characterizing objects in images. We describe an approach for statistical analysis of shapes of closed curves using ideas from differential geometry. A fundamental tool in this shape analysis is the construction and implementation of geodesic paths between shapes. We use geodesic paths to accomplish a variety of tasks, including the definition of a metric to compare shapes, the computation of intrinsic statistics for a set of shapes, and the definition of probability models on shape spaces. We demonstrate this approach using three applications: (i) automated clustering of objects in an image database according to their shapes, (ii) interpolation of heart-wall boundaries in echocardiographic image sequences, and (iii) a study of shapes of human silhouettes in infrared surveillance images.