Weixin Chen

Date of Award


Degree Type


Degree Name

Master of Science


Computer Science


Dr. John Barron


This thesis presents the implementation and the qualitative and quantitative evalua­ tion of a 3D optical flow algorithm, whose derivation is based on the 2D optical flow method published in the European Conference on Computer Vision (ECCV 2004) by Thomas Brox, Andrés Bruhn, Nils Papenburg and Joachim Wieickert. The optical flow minimizes an energy function built with three assumptions: a brightness con­ stancy assumption, a gradient constancy assumption, and a smoothness assumption. They minimize this functional using a robust estimator, which make the functional convex and gaurantees convergence to a single solution. They propose a numerical scheme based on nested fixed points iterations and shows that this scheme imple­ ments a coarse-to-fine warping strategy within a 2D hierarchical image pyramid.. In our 3D extension, our solution requires the regularization of a 3D functional based on 3D extensions of their assumptions in a 3D hierarchical volume pyramid. We solve the corresponding Euler-Lagrange equations iteratively using nested iterations that uses Cramer’s rule, as suggested by Faisal and Barron (ICIAR 2007) rather than Brox et al.’s SOR calculation. We present 3D quantitative results on three sets of 3D sinusoidal data (with and without 3D intensity discontinuities). We also presented qualitative evaluation on a gated MRI cardiac dataset.



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