Non-rigid Point Matching Algorithm Research

Feature based registration problems frequently arise in the domains of medical imaging, computer vision and pattern recognition. Point features, represented basically by the point locations, are the simplest form of features. Point matching is to find the correspondence and transformation between two point sets. Point matching problem can be quite difficult because of three major factors: the existence of noise, outlier and complicated non-rigid mapping. This thesis discusses the cases where the transformations are affine or thin plate spline, and presents two practical point matching algorithms. The main contributions are as follows:Firstly, we improve the deterministic-annealing-based point-matching algorithms. The existing algorithms usually add damping term of the form .xlog.x into their objective function in order to control matching matrix's entropy. The shortcoming is that the two-way constraints need to be enforced by using Sinkhorn method. This is an iterated approximating method, and has the danger of lowering the accuracy of the matching result. We propose that the form of x(x-1) be used as barrier term, in doing so, we can use Karush-Kuhn-Tucker necessary conditions to solve for matching matrix, and the optimality of the result in each step is guaranteed. Experiments show that the algorithm is significantly better than the existing deterministic-annealing-based algorithms in terms of accuracy, robustness, and also has less computation.Secondly, two improvements are made in the fuzzy point-matching algorithms. The first is converting matching matrix's one-way constraints to two-way constraints, so the situation of modal point-set and target point-set having outliers can be dealt with now. The second is using deterministic annealing algorithm as optimizing framework, so as to realize overall optimization. Experiments show the effectiveness of the algorithm.