Deforming surface features lines in intrinsic coordinates

Significant local structure of terrain surfaces can be described by structural lines which are connected sets of points where the surface is approximately cylindrical, i.e., the ratio of the principal curvatures is large. At each point curvature is maximal in the curvature direction associated with the curvature with larger absolute value. These lines form the skeleton of the surface for constructing triangulated approximations. Significant structures are best identified at coarse scales but need to be deformed to fine scale before use. Standard snake algorithms using proximity in the image plane do not suffice. Earlier work used the maximal curvature field as an intrinsic (curvature) coordinate system. This leads to shrinkage of the open curves under internal forces. A better solution is to restrict the movement of the lines to the principal curvature directions forming an intrinsic coordinate system over the surface. We evaluate the results of deforming lines by utilizing the deformed lines as structural lines for triangulation. Points at coarse scale move along curvature lines to the proper location at fine scale. The resulting fine scale lines are better positioned for terrain representation than those derived from proximity alone and produce more compact triangulations.