3‐D curve matching using splines

A machine vision algorithm to find the longest common subcurve of two 3‐D curves is presented. The curves are represented by splines fitted through sequences of sample points extracted from dense range data. The approximated 3‐D curves are transformed into 1‐D numerical strings of rotation and translation invariant shape signatures, based on a multiresolution representation of the curvature and torsion values of the space curves. The shape signature strings are matched using an efficient hashing technique that finds longest matching substrings. The results of the string matching stage are later verified by a robust, least‐squares, 3‐D curve matching technique, which also recovers the Euclidean transformation between the curves being matched. This algorithm is of average complexity O(n) where n is the number of the sample points on the two curves. The algorithm has applications in assembly and object recognition tasks. Results of assembly experiments are included.