Comparative study of surface matching algorithms

Airborne laser ranging systems provide a new source for determining surfaces. There is an increasing need to compare surfaces and to combine and merge surface data obtained with different sensors. This paper addresses the problem of determining the 3D transformation parameters between two sets of points describing the same physical surface. However, the two sets are in different reference systems and the points are not identical. We describe two mathematical models that are suitable to find optimal transformation parameters such that the differences between the two sets of surface descriptions become minimal. The first approach minimizes the remaining differences along the z-axis of one of the coordinate systems while the second approach minimizes the distances between points of one surface description to surface patches of the other surface, parallel to the corresponding surface normals. After deriving the mathematical models, the two methods are tested with synthetic data. The performance of both methods are investigated with different topographic configurations The experiments confirm the theoretical expectations that the transformation parameters can only be determined well if the surface has reasonable surface slopes with surface normals pointing in all different directions. If these conditions are not satisfied, the transformation problem becomes ill-posed and only a subset of the parameters can be determined. For surfaces with large slopes, the second method performs better because it minimizes distances along surface normals.