Geodesic-Based Bayesian Coherent Point Drift

Abstract

Coherent point drift is a well-known algorithm for non-rigid registration, i.e., a procedure for deforming a shape to match another shape. Despite its prevalence, the algorithm has a major drawback that remains unsolved: It unnaturally deforms the different parts of a shape, e.g., human legs, when they are neighboring each other. The inappropriate deformations originate from a proximity-based deformation constraint, called motion coherence. This study proposes a non-rigid registration method that addresses the drawback. The key to solving the problem is to redefine the motion coherence using a geodesic, i.e., the shortest route between points on a shape's surface. We also propose the accelerated variant of the registration method. In numerical studies, we demonstrate that the algorithms can circumvent the drawback of coherent point drift. We also show that the accelerated algorithm can be applied to shapes comprising several millions of points.

Dataset of Finite Element Models of Normal and Deformed Thoracolumbar Spine

“…The BCPD++ open-source codes could be accessed at the GitHub repository 36 , and the SOS relaxation algorithm to check and repair the hexahedral meshes were available at the GitHub repository 70 . The repository for the online platform 71 can be accessed at Github repository 72 .…”

“…This iterative process allows for the optimization of the transformation parameters based on the available data and the underlying statistical models. In this study, the BCPD++ open-source codes are downloaded from the GitHub repository 36 and used to perform the morphing of the template vertebra. The morphing process utilizes a multi-layer BCPD++ approach, where if the initial morphing yields a Euclidean distance greater than 0.04 mm, the prior output is considered as the template mesh, and the BCPD++ parameters are fine-tuned again.…”

“…The template mesh undergoes a 90° rotation about the y-axis for the initial rotation. Rigid registration is performed using the available BCPD++ code 36 with a sufficiently large lambda value, such as 1e9. Lambda is one of the tuned parameters in BCPD++, controlling the expected length of deformation vectors.…”

Combination of photogrammetry and non-rigid pinna registration for the calculation of personalised head- related transfer functions

“…As a target, we used three PR point clouds of the same listener containing the additional information of confidence levels. We applied the NRR algorithm geodesic-based Bayesian coherent point drift (GBCPD), because it protects the relationship between the points, i.e., takes the surface of the template pinna into account [10].…”

Data-Weighted Multivariate Generalized Gaussian Mixture Model: Application to Point Cloud Robust Registration

“…The purpose of point cloud registration is to extract the key points or features corresponding to the target point set and the point set to be registered as well as find the transformation mapping relationship between two point sets [ 1 , 2 , 3 , 4 , 5 ]. This task involving image processing, data analysis and computer vision has essential applications in many practical scenarios.…”