In this paper, we study the approximate point set matching (APSM) problem with minimum RMSD score under translation, rotation, and one-to-one correspondence in d-dimension. Since most of the previous works about APSM problems use similality scores that do not especially care about one-to-one correspondence between points, such as Hausdorff distance, we cannot easily apply previously proposed methods to our APSM problem. So, we focus on speed-up of exhaustive search algorithms that can find all approximate matches. First, we present an efficient branch-and-bound algorithm using a novel lower bound function of the minimum RMSD score for the enumeration version of APSM problem. Then, we modify this algorithm for the optimization version. Next, we present another algorithm that runs fast with high probability when a set of parameters are fixed. Experimental results on both synthetic datasets and real 3-D molecular datasets showed that our branch-and-bound algorithm achieved significant speed-up over the naive algorithm still keeping the advantage of generating all answers.

The purpose of this paper is to present the novel technique to solve the recognition errors in invariant range image multi-pose face recognition. The scale, center and pose error problems were solved by using the geometric transform. Range image face data (RIFD) was obtained from a laser range finder and was used in the model to generate multi-poses. Each pose data size was reduced by linear reduction. The reduced RIFD was transformed to the gradient face model for facial feature image extraction and also for matching using the Membership Matching Score model. Using this method, the results from the experiment are acceptable although the size of gradient face image data is quite small (659 elements). Three-Layer Matching Search was the algorithm designed to reduce the access timing to the most accurate and similar pose position. The proposed algorithm was tested using facial range images from 130 people with normal facial expressions and without eyeglasses. The results achieved the mean success rate of 95.67 percent of 12 degrees up/down and left/right (UDLR) and 88.35 percent of 24 degrees UDLR.