The Frobenius metric in image registration: Technical report

Image registration involves estimating how one set of n-dimensional points is rotated, scaled, and translated into a second set of n-dimensional points. In practice, n is usually 2 or 3. We consider a Frobenius norm approach in which a point-to-point matching between the sets (if they are of the same cardinalities) and the corresponding transformation are determined. Two strategies are investigated: the pruned tree approach and the parametric linear programming approach. Various versions of tree pruning approach have been investigated by other authors, whereas the parametric programming method is believed to be new. It addresses several inherent problems of the tree pruning method. Both approaches determine the rotation after scale and translation are removed. In the pruned tree approach, possible matchings of two- or three- dimensional points are partially enumerated using a tree search; the tree is pruned according to criteria based on the metric. The parametric approach solves an assignment problem for a number of candidate rotations. Each evaluation results in the point-to-point correspondence; the optimal matching corresponds to the rotation that minimizes the associated cost function. This approach, which has O(k/sup 3/) worst case asymptotic complexity, is more tolerant of noise than the pruned tree approach and canmore » be readily extended to the cases where the sets to be registered are of different cardinalities. 27 refs., 8 figs., 5 tabs.« less