An efficient surface mesh representation adaptive to local smoothness

The problem of fitting a mesh to a surface, whether defined analytically or by image data, requires consideration of accuracy and attendant computational cost. The accuracy of the surface fit depends on the size of mesh elements. Distributing large mesh elements to surface parts with low curvature and small ones to those with high curvature enables efficient use of mesh elements. In this paper, we propose an algorithm which adapts mesh size to local surface smoothness. Changes in mesh size are accomplished by adaptively adjusting thresholds for division and merger of mesh elements. The primary motivation for developing this algorithm is image segmentation using deformable models and the algorithm was implemented in that context. Tests on a synthetic shape demonstrate the extent to which the local surface smoothness affects the mesh size.