A path following algorithm for the graph matching problem

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four datasets: simulated graphs, QAPLib, retina vessel images and handwritten chinese characters. In all cases, the results are competitive with the state-of-the-art.Comment: 23 pages, 13 figures,typo correction, new results in sections 4,5,

Advances in Character Recognition

This book presents advances in character recognition, and it consists of 12 chapters that cover wide range of topics on different aspects of character recognition. Hopefully, this book will serve as a reference source for academic research, for professionals working in the character recognition field and for all interested in the subject

Automatic Reassembly Method of 3D Thin-wall Fragments Based on Derivative Dynamic Time Warping

In order to address the automatic virtual reassembling of 3D thin-wall fragments, this paper proposes a 3D fragment reassembly method based on derivative dynamic time warping. Firstly, a calculation method of discrete curvature and torsion is designed to solve the difficulty of calculating curvature and torsion of discrete data points and eliminate effectively the noise interferences in the calculation process. Then, it takes curvature and torsion as the feature descriptors of the curve, searches the candidate matching line segments by the derivative dynamic time warping (DDTW) method with the feature descriptors, and records the positions of the starting and ending points of each candidate matching segment. After that, it designs a voting mechanism with the geometric invariant as the constraint information to select further the optimal matching line segments. Finally, it adopts the least squares method to estimate the rotation and transformation matrices and uses the iterative closest point (ICP) method to complete the reassembly of fragments. The experimental results show that the reassembly error is less than 1mm and that the reassembly effect is good. The method can solve the 3D curve matching in case there are partial feature defects, and can achieve the virtual restoration of the broken thin-wall fragment model quickly and effectively