Rigid body constrained noisy point pattern matching

Noisy pattern matching problems arise in many areas, e.g., computational vision, robotics, guidance and control, stereophotogrammetry, astronomy, genetics, and high-energy physics. Least-squares pattern matching over the Euclidean space Eⁿ for unordered sets of cardinalities p and q is commonly formulated as a combinatorial optimization problem having complexity p(p-1)···(p-q+1), q⩽p. Since p and q may be 10 ³ or larger in typical applications, less than satisfactory suboptimal methods are usually employed. A hybrid approach is described for solving the pattern matching problem under rigid motion constraints, which often apply. The method reduces the complexity to l₂₁·n⁴+l₁₂·p³, where l₁₂ and l₂₁ are the number of iterations required by steepest-ascent and singular value decomposition (SVD)-based procedures, respectively