Graduation Year

2005

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Computer Science and Engineering

Major Professor

Dr. Dmitry B. Goldgof.

Co-Major Professor

Dr. Sudeep Sarkar

Keywords

Nonrigid deformation, Elasticity, Computer vision, Face recognition

Abstract

The past two decades has witnessed growing interest in physics based techniques in computer vision, computer graphics and medical imaging. The main advantage of a physical model is its mathematical rigor and physical soundness, which makes it an ideal tool to study complex nonrigid motion. However, since a model based on continuum mechanics is computationally demanding, an idealized framework is often adopted where physical motion parameters are significantly simplified, which inevitably affects the accuracy and reliability of modeling results. In this study, a new modeling approach is developed that features the reconstruction of actual material properties such as the Young's modulus and the Poisson's ratio. Justified by the constitutive law and mathematical considerations, the Young's modulus is identified as a unique physical motion parameter.

By imposing an adaptive smoothness constraint, the Young's modulus helps preserve the local characteristics (discontinuity) of an object's deformation, a role similar to the weighting coefficient in the study of edge-preserving visual surface reconstruction. The contribution of this work is fourfold: (1) two recovery algorithms are developed to solve the inverse elastic problem: A deterministic algorithm that is based on the Gauss-Newton method and the general cross validation, and a stochastic algorithm that is based on the constrained genetic evolution; (2) a new modeling approach is proposed that has the ability to recover nonrigid motion in terms of the physical parameters. The use of recovered parameters can be implemented within a boundary-driven motion synthesis scheme; (3) A sensitivity method is proposed to evaluate the impact of different parameters.

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