Nonrigid object motion and deformation estimation from three‐dimensional data

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Abstract
This article presents a model‐based approach for nonrigid object motion and deformation analysis from 3D data. The modeling primitives used in this research are the superquadrics, which have already been proven useful in describing a variety of natural and man‐made objects. This model‐based approach is not only in accordance with the human visual perception process but also able to decouple the large and unstructured nonrigid motion estimation system into simple and well structured subsystems. We develop a recursive algorithm for estimating global motion and object shape, which effectively incorporates aprioriknowledge of the object into the estimation procedure and obtains a good estimate of the global motion and object shape even if the given 3D points are distributed bias. After compensating for the global motion of the object a tensor model of local deformation is introduced and a spherical harmonic surface‐fitting algorithm is described such that the localized deformations of the object surface can be characterized. The local deformations of the object are then estimated using tensor‐description‐based analysis and parametrized by the directions and magnitudes of the extreme deformations in a localized surface element. To illustrate the potential of this model‐based approach for nonrigid motion analysis, a real data example is presented using the proposed approach. This example involves estimating the left ventricle motion and deformations from a time sequence of 3D coordinates of coronary artery bifurcation points. The estimation results show the success of the model‐based approach even when the given bifurcation points are distributed only on half of the left ventricle surface.

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