Ph.D Student | Goshen Liran |
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Subject | Accurate and Robust Epipolar Geometry Estimation |

Department | Department of Industrial Engineering and Management |

Supervisor | Professor Ilan Shimshoni |

Full Thesis text |

Epipolar geometry estimation is a fundamental problem in computer vision. The estimation of the epipolar geometry is especially difficult in three cases: (1) when the extent of the data and/or the motion is small, (2) when the putative correspondences include a low percentage of inliers, and (3) when a large subset of inliers is consistent with degenerate epipolar geometry. In these cases standard epipolar geometry estimation algorithms give poor results.

This work describes new approaches to these difficult cases.

In the first approach the recently introduced Integrated Maximum Likelihood (IML) method was developed. The IML method seeks the manifold which has the highest ``support'', in the sense that a large measure of its points are close to the data.

The second approach presents an accelerated algorithm for an identification of false matches. The algorithm generates a set of weak motion models (WMMs). The distribution of the median of the geometric distances of a correspondence to the WMMs is represented as a mixture model of outlier and inlier correspondences. It generates an outlier correspondence sample from the data. This sample is used to estimate the outlier pdf. These pdfs are used to guide the sampling in the RANSAC stage and accelerate the search process.

In the third approach a new robust matching algorithm is proposed to work specifically with methods that produce region-to-region putative correspondences, such as the Scale Invariant Feature Transform (SIFT) method. The Balanced Exploration and Exploitation Model Search (BEEM) algorithm is simple and very efficient for epipolar geometry estimation. It works very well for difficult scenes where the putative correspondences include a low percentage of inlier correspondences and/or a dominant subset of the inliers is consistent with a degenerate configuration.

The resulting algorithms when tested on real images give quality estimations and achieve significant speedups compared to the state of the art algorithms.

This work also describes new approaches to two additional important tasks: (1) the task of prediction that two images are unrelated. The proposed method exploits available prior information to define a simple decision rule to detect unrelated image pairs. (2) The task of place recognition in which a database of images and one query image are given. The task is to retrieve all and only all the images from the database that are related to the query image. The proposed methods were checked on a large database of images and achieve high quality results.