M.Sc Student | Devir Yohai |
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Subject | Intrinsic Regularization of Inverse Problems Involving Non-Rigid Shapes |

Department | Department of Computer Science |

Supervisor | Professor Yuval Rabani |

Full Thesis text |

In many visions problems, both human and computer, there is a
need to reconstruct an unknown three dimensional object from a partial data
that is derived from that object. This problem is ill-posed since in many
cases, one may find a different object from which similar data can be derived.
Therefore, it is common to solve a different problem in which except for the
derived data there is some other prior knowledge about the nature of the
unknown object.In this work we solve the problems where beside of the
derived data, we are also given that the unknown object is similar to (a
bending of) a known non-rigid object denoted as the prior.Many of the objects surrounding us are non-rigid in the sense
that they have infinite variety of deformations preserving their topology and
density. Among those, one may count the outer skin of living bodies, faces,
cloths and others. Two objects that can be obtained from each other by means of
non-rigid deformations are said to be intrinsically similar.Many intrinsic similarity measures are based on the
geodesic
distances between two points on the shape measuring the length of the
minimal path contained in the shape connecting those two points.In computer vision applications, shapes are approximated by a
set of samples forming a triangulated mesh. There are two common ways to
approximate geodesic distances on meshes, using the Dijkstra's well known
shortest paths algorithm and using the fast marching method (FMM), which
lacks some of the inherent disadvantages of Dijkstra's algorithm.In this work, we propose to solve such reconstruction
problems in the framework of optimization problems, where the optimization
variables are the spatial locations of the shapes' vertices. In order to do so
we enhance the FMM algorithm so that beside of approximating the geodetic
distances, it also calculate the derivatives of those distances with respect to
the spatial locations of the shape's vertices. Synthesis examples are given for
a few shape reconstruction applications.