Abstract
Least-squares pattern matching over the Euclidean space E/sup n/ for unordered sets of cardinality p is commonly formulated as a combinatorial optimization problem having complexity p times p!, p>>n. Since p may be 10/sup 3/ or larger in typical applications, less than satisfactory suboptimal methods are usually used. A powerful hybrid approach is described which casts the pattern matching problem in a differentiable setting using rigid motion constraints which often apply and reduces the complexity to l/sub 21/n/sup 4/+l/sub 12/p/sup 3/, where l/sub 12/ and l/sub 21/ are the number of iterations required by procedures based on steepest ascent and singular value decomposition (SVD), respectively.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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