Estimating geodesic distances on locally linear patches

Geodesic distance estimation is one of the key steps in isometric data embedding. This paper presents a new method to improve the precision of geodesic distance estimation. Different from the previous methods, the new method enlarges the searching area for approximate geodesic curve from local neighborhood edges to locally linear patches, which naturally leads to more precise geodesic distance estimation. Experiment results evidently show the improvement brought by the new method.