UCLA Brain Mapping Center

Publications

Analysis of planar shapes using geodesic paths on shape spaces.

Klassen E; Srivastava A; Mio W; Joshi SH;
IEEE transactions on pattern analysis and machine intelligence. 2004-Mar; 26(372-83):3
 
For analyzing shapes of planar, closed curves, we propose differential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradient-based shooting method to solve for the tangent that connects any two shapes via a geodesic. Using the Surrey fish database, we demonstrate some applications of this approach: 1) interpolation and extrapolations of shape changes, 2) clustering of objects according to their shapes, 3) statistics on shape spaces, and 4) Bayesian extraction of shapes in low-quality images.
 
PMID: 15376883    doi: 10.1109/TPAMI.2004.1262333
 

BMAP Author