Reliably measuring the similarity of two shapes or images (instances) is an important problem for various computer vision applications such as classification, recognition, and retrieval. While pairwise measures take advantage of the geometric differences between two instances to quantify their similarity, recent advances use relationships among the population of instances when quantifying pairwise measures. In this paper, we propose a novel method which refines pairwise similarity measures using population cues by examining the most similar instances shared by the compared shapes or images. We then use this refined measure to organize instances into disjoint components that consist of similar instances. Connectivity is then established between components to avoid hard constraints on what instances can be retrieved, improving retrieval performance. To evaluate the proposed method we conduct experiments on the well-known MPEG-7 and Swedish Leaf shape datasets as well as the Nister and Stewenius image dataset. We show that the proposed method is versatile, performing very well on its own or in concert with existing methods.

Shape correspondence, which aims at accurately identifying corresponding landmarks from a given population of shape instances, is a very challenging step in constructing a statistical shape model such as the Point Distribution Model. The state-of-the-art methods such as MDL and SPHARM are primarily focused on closed-surface shape correspondence. In this paper we develop a novel method aimed at identifying accurately corresponding landmarks on 3D open-surfaces with a closed boundary. In particular, we enforce explicit topology consistency on the identified landmarks to ensure that they form a simple, consistent triangle mesh to more accurately model the correspondence of the underlying continuous shape instances. The proposed method also ensures the correspondence of the boundary of the open surfaces. For our experiments, we test the proposed method by constructing a statistical shape model of the human diaphragm from 26 shape instances.

This paper introduces a new benchmark study to evaluate the performance of landmark-based shape correspondence used for statistical shape analysis. Different from previous shape-correspondence evaluation methods, the proposed benchmark first generates a large set of synthetic shape instances by randomly sampling a given statistical shape model that defines a ground-truth shape space. We then run a test shape-correspondence algorithm on these synthetic shape instances to identify a set of corresponded landmarks. According to the identified corresponded landmarks, we construct a new statistical shape model, which defines a new shape space. We finally compare this new shape space against the ground-truth shape space to determine the performance of the test shape-correspondence algorithm. In this paper, we introduce three new performance measures that are landmark independent to quantify the difference between the ground-truth and the newly derived shape spaces. By introducing a ground-truth shape space that is defined by a statistical shape model and three new landmark-independent performance measures, we believe the proposed benchmark allows for a more objective evaluation of shape correspondence than previous methods. In this paper, we focus on developing the proposed benchmark for 2D shape correspondence. However it can be easily extended to 3D cases.

Accurately identifying corresponded landmarks from a population of shape instances is the major challenge in constructing statistical shape models. In this paper, we address this landmark-based shape-correspondence problem for 3D cases by developing a highly efficient landmark-sliding algorithm. This algorithm is able to quickly refine all the landmarks in a parallel fashion by sliding them on the 3D shape surfaces. We use 3D thin-plate splines to model the shape-correspondence error so that the proposed algorithm is invariant to affine transformations and more accurately reflects the nonrigid biological shape deformations between different shape instances. In addition, the proposed algorithm can handle both open-and closed-surface shape, while most of the current 3D shape-correspondence methods can only handle genus-0 closed surfaces. We conduct experiments on 3D hippocampus data and compare the performance of the proposed algorithm to the state-of-the-art MDL and SPHARM methods. We find that, while the proposed algorithm produces a shape correspondence with a better or comparable quality to the other two, it takes substantially less CPU time. We also apply the proposed algorithm to correspond 3D diaphragm data which have an open-surface shape.