Technical Report PHD-2013-14

Title: On Natural Parametrizations of Motion and Structure Manifolds
Authors: Guy Rosman
Supervisors: Ron Kimmel
Abstract: One of the most important aspects of solving a problem is that of choosing an appropriate parameterization. This trivial observation can be seen in many forms in image processing and computer vision. Global parametrizations include the Hough and Fourier transforms, whereas local parameterizations include sparsity-based patch models and over-parameterized approaches. This research explores important cases in motion analysis and 3D reconstruction where a careful choice of the parameterization matters. It leads, in these cases, to simple and yet generic formulations that can be efficiently implemented.

The first part of the work related to 2D stereovision, where we suggest to use the plane equation and planar homographies as a basis for an over-parameterized optical flow estimation. The algorithm achieves state of the art results in term of accuracy in optical flow computation. The regularization term has a physically meaningful interpretation bridging the gap between optical flow computation and scene understanding.

The second part of the dissertation relates to 3D motion understanding, where we reformulate articulated motion as edge-preserving smoothing of Lie-group-valued images of two types. By choosing carefully the parameterization and regularization terms, the resulting algorithms obtain results comparable to those of domain specific tools, on 3D range data. One of these algorithms can be implemented at real-time speeds due to a novel formulation. Furthermore, it applies also to other inverse problems such as diffusion tensor imaging reconstruction, and direction diffusion.

In the third and final part of the dissertation, we show how structured light reconstruction can be formulated as probability maximization with respect to the scene geometry, given the camera and projector images. This allows us to incorporate sparse priors for the surface into the non-linear reconstruction process itself. These priors, resulting from the data, have a natural and intuitive interpretation, and in themselves parameterize epipolar motion between the camera and projector. Furthermore, they help us obtain 3D reconstruction that is robust to low sensor exposure and motion artifacts.

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