One of the key challenges in deformable shape modeling is the problem of estimating a meaningful average or mean shape from a set of unlabeled shapes. We present a new joint clustering and matching algorithm that is capable of computing such a mean shape from multiple shape samples which are represented by unlabeled point-sets. An iterative bootstrap process is used wherein multiple shape sample point-sets are nonrigidly deformed to the emerging mean shape, with subsequent estimation of the mean shape based on these nonrigid alignments. The process is entirely symmetric with no bias toward any of the original shape sample point-sets. We believe that this method can be especially useful for creating atlases of various shapes present in medical images. We have applied the method to create mean shapes from nine hand-segmented 2D corpus callosum data sets and 10 hippocampal 3D point-sets.

Deformable models are central to non-rigid motion analysis, shape matching and non-rigid medical image registration. Spline-based deformations are a very popular class of parameterizations of deformable models and have been heavily used in multiple domains. In a somewhat separate sub-field, weighted graphs are a frequently used object parameterization. Graph matching using weighted graph object parameterizations finds application in a spectrum ranging from rigid pose estimation to deformable object recognition. Here, we demonstrate a hitherto unsuspected relationship between spline-based deformable models and weighted graphs. It turns out that spline parameterizations in the kernel representation can be used to construct equivalent weighted graphs. With this connection established, we envision a cross-fertilization between these two seemingly disparate sub-fields of computer vision.

We present a new robust point matching algorithm (RPM) that can jointly estimate the correspondence and non-rigid transformations between two point-sets that may be of different sizes. The algorithm utilizes the soft assign for the correspondence and the thin-plate spline for the non-rigid mapping. Embedded within a deterministic annealing framework, the algorithm can automatically reject a fraction of the points as outliers. Experiments on both 2D synthetic point-sets with varying degrees of deformation, noise and outliers, and on real 3D sulcal point-sets (extracted from brain MRI) demonstrate the robustness of the algorithm.

We have developed a new mutual information-based registration method for matching unlabeled point features. In contrast to earlier mutual information-based registration methods, which estimate the mutual information using image intensity information, our approach uses the point feature location information. A novel aspect of our approach is the emergence of correspondence (between the two sets of features) as a natural by-product of joint density estimation. We have applied this algorithm to the problem of geometric alignment of primate autoradiographs. We also present preliminary results on three-dimensional robust matching of sulci derived from anatomical magnetic resonance images. Finally, we present an experimental comparison between the mutual information approach and other recent approaches which explicitly parameterize feature correspondence.

We present a novel method for the geometric alignment of autoradiographs of the brain. The method is based on finding the spatial mapping and the one-to-one correspondences (or homologies) between point features extracted from the images and rejecting non-homologies as outliers. In this way, we attempt to account for the local, natural and artifactual differences between the autoradiograph slices. We have used the resulting automated algorithm on a set of left prefrontal cortex autoradiograph slices, specifically demonstrated its ability to perform point outlier rejection, validated its robustness property using synthetically generated spatial mappings and provided an anecdotal visual comparison with the well-known iterated closest-point (ICP) algorithm. Visualization of a stack of aligned left prefrontal cortex autoradiograph slices is also provided.