Comparison of smooth polynomial functional surfaces for use in alignment

摘要

Two functional surfaces can be compared through an integral that gives a measure of matching between the two surfaces. If each surface is represented as a polynomial function of two variables, the integral can be done mathematically. This leads to a dramatic decrease in the computing time required for the comparison of two surfaces. The alignment of two surfaces is the process of transforming one of the surfaces until the measure of matching between the transformed surface and the other surface is optimized. The reduction in the time for comparison leads to a reduction in the time required for alignment.