Robust contour matching via the order-preserving assignment problem

Abstract

Abstract-A common approach to determining corresponding points on two shapes is to compute the cost of each possible pairing of points and solve the assignment problem (weighted bipartite matching) for the resulting cost matrix. We consider the problem of solving for point correspondences when the shapes of interest are each defined by a single, closed contour. A modification of the standard assignment problem is proposed whereby the correspondences are required to preserve the ordering of the points induced from the shapes' contours. Enforcement of this constraint leads to significantly improved correspondences. Robustness with respect to outliers and shape irregularity is obtained by required only a fraction of feature points to be matched. Furthermore, the minimum matching size may be specified in advance. We present efficient dynamic programming algorithms to solve the proposed optimization problem. Experiments on the Brown and MPEG-7 shape databases demonstrate the effectiveness of the proposed method relative to the standard assignment problem.Index Terms-Assignment problem, contour matching, dynamic programming, MPEG-7 shape database, shape descriptors.

Design and perceptual validation of performance measures for salient object segmentation

“…Elastic matching methods [11,3,9,8,22,23] directly align two contours by determining a mapping between the points on the contours that minimizes a matching cost. Typically, the matching cost is based on two components: 1) dissimilarity of local properties of matched points, e.g., tangent orientations, and 2) dissimilarity of matched curve segments, i.e., the cost of deforming one curve segment (stretching, bending or compressing) to match the other curve segment.…”

Generalized Hough Transform for Shape Matching

“…Finally, we have compared the proposed system to some of the best considered contour matching methods [12], [14], [2].…”

IS-Match: Partial Shape Matching by Efficiently Solving an Order Preserving Assignment Problem

“…While most classical methods for pairwise clustering 32)-34) only consider symmetric similarity matrices, recent methods as e.g., affinity propagation clustering 35) also work in non-metric spaces. To prove the quality of the provided similarity scores of IS-Match and to find the best suited clustering algorithm we evaluated all combinations between three shape matching algorithms (Shape Context 10) , COPAP 12) and IS-Match) and three clustering algorithms (k-center clustering, hierarchical agglomerative clustering and affinity propagation clustering).…”

“…Although this reduces the problem, e.g., occlusions still lead to matching errors as it is illustrated in Fig. 1 for the shape context based COPAP framework 12) . These problems are handled well by purely local matching methods as e.g., proposed by Chen, et al 13) , which accurately measure local similarity, but in contrast fail to provide a strong global description for robust shape alignment.…”