Ph.D Thesis | |

Ph.D Student | Rozenfeld Stas |
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Subject | Improving Model Estimation via Statistical Tools in Computer Vision |

Department | Department of Industrial Engineering and Management |

Supervisors | PROF. Ilan Shimshoni |

PROF. Michael Lindenbaum | |

Full Thesis text |

Noise and outliers in the input to
computer vision applications tend to damage the results and can even render
them useless. In our work we suggest an approach to reduce the severity of
these phenomena. The improvement is achieved by applying appropriate
statistical tools. Two well known general computer vision tools are considered
for testing the approach, robust regression and epipolar geometry estimation. A
relatively new specific task of the three dimensional mirroring surface
recovery is considered for testing purpose as well. The approach includes the
following steps: 1) In each considered problem the results are obtained through
optimization; 2) the cost function of the optimization problem is modified into
a likelihood function form, causing it to reflect correctly the statistical
properties of the data corruption; 3) the corresponding (*maximum likelihood*)
problem is then solved. An additional improvement is achieved in the three
dimensional mirroring surface recovery process by utilizing robust regression
and a statistically valid heteroscedastic approach. In this process a dense
depth map is built based only on a sparse set of initial points and using one dimensional
*homographies*. For all the considered problems the performance
improvement is verified using experiments on real data. In the experiments the
three dimensional dense shape of real mirroring objects was recovered, the
epipolar geometry was estimated from noisy data and in the presence of outliers.