Generalized L2-Divergence and Its Application to Shape Alignment

Abstract

This paper proposes a novel and robust approach to the groupwise point-sets registration problem in the presence of large amounts of noise and outliers. Each of the point sets is represented by a mixture of Gaussians and the point-sets registration is treated as a problem of aligning the multiple mixtures. We develop a novel divergence measure which is defined between any arbitrary number of probability distributions based on L2 distance, and we call this new divergence measure "Generalized L2-divergence". We derive a closed-form expression for the Generalized-L2 divergence between multiple Gaussian mixtures, which in turn leads to a computationally effcient registration algorithm. This new algorithm has an intuitive interpretation, is simple to implement and exhibits inherent statistical robustness. Experimental results indicate that our algorithm achieves very good performance in terms of both robustness and accuracy.

An Efficient and Robust Algorithm for Parallel Groupwise Registration of Bone Surfaces

“…Bone surfaces of wrists, segmented from CT data with a voxel size of 0.3 × 0.3 × 0.3 mm 3 , serve as an example test set. The negligible bias and registration error of about 0.12 mm for the proposed algorithm are similar to those in [5]. However, current point cloud registration algorithms usually have computational and memory costs that increase quadratically with the number of point clouds, whereas the proposed algorithm has linearly increasing costs, allowing the registration of a much larger number of shapes: 48 versus 8, on the hardware used.…”

“…The method fits an evolving mean shape to each of the example point clouds thereby minimizing the total deformation. The registration algorithm alternates between a computationally expensive, but parallelizable, deformation step of the mean shape to each example shape and a very inexpensive step updating the mean shape.The algorithm is evaluated by comparing it to a state of the art registration algorithm [5]. Bone surfaces of wrists, segmented from CT data with a voxel size of 0.3 × 0.3 × 0.3 mm 3 , serve as an example test set.…”

“…The algorithm is evaluated by comparing it to a state of the art registration algorithm [5]. Bone surfaces of wrists, segmented from CT data with a voxel size of 0.3 × 0.3 × 0.3 mm 3 , serve as an example test set.…”

Group MRF for fMRI activation detection

“…The anatomical ROIs were rigidly aligned (Fig. 8) using a method that models each ROI point cloud as a Gaussian mixture and registers the ROIs by aligning the mixture distributions [3]. Enhanced robustness to noise and outliers was shown with this method over standard techniques [3].…”

“…If multiple images containing objects of the same class are available, one can exploit common features shared among the images to enhance the segmentation of each image. This general idea of incorporating group information is widely used in many areas including recognition [2], registration [3], and reconstruction [4]. A popular approach is to build a model or template from a set of training images that is then used to segment new images [2].…”