Abstract

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 corresponding landmarks. According to the identified corresponding 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 easily be extended to 3D cases.

Abstract

This paper introduces a new benchmark study of evaluating 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 specified ground-truth statistical shape model. We then run the test shape-correspondence algorithms on these synthetic shape instances to construct a new statistical shape model. We finally introduce a new measure to describe the difference between this newly constructed statistical shape model and the ground truth. This new measure is then used to evaluate the performance of the test shapecorrespondence algorithm. By introducing the ground-truth statistical shape model, we believe the proposed benchmark allows for a more objective evaluation of the shape correspondence than those that do not specify any ground truth. 

Abstract

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.