| Summary: | 碩士 === 華梵大學 === 資訊管理學系碩士班 === 93 === In the research of computer vision, reconstruction of a 3-D model can be obtained by a well estimated fundamental matrix. Both methods for estimating fundamental matrices and the efficiencies of random sampling may affect the accurate estimation of the fundamental matrix. In this thesis, some existing methods proposed in the literature for estimating the fundamental matrix were tested and analyzed. Also, a method of increasing the efficiencies of random sampling to achieve robust estimation the fundamental matrix is proposed.
According to our experiments, eight-point algorithm is chosen to estimating the fundamental matrix. The Hartley's normalization is used to estimate the fundamental matrix, In order to obtain accurate estimation of the fundamental matrix, some existing non-linear algorithms, such as gold standard algorithm, first-order geometric error and symmetric epipolar distance, proposed in the literature were tested and analyzed. According to experimental results, using the symmetric epipolar distance algorithm with least median of squares can decrease the influence of outliers and perform best.
For estimating the fundamental matrix, the method to select eight corresponding point pairs is important. If the exhaustive selection of all combination is considered, it is time-consuming. Therefore, random sampling should be used. In our implementation, we assume the percentage of outliers is 50% and require 99% probability that at least one of eight corresponding point pairs is good, then at least 1,177 subsamples should be processed. However, it still has 1% probability to select subsamples containing outliers and results in incorrect estimation of the fundamental matrix. In this thesis, a method was proposed to diagnose the efficiencies of random sampled points. According to experimental results, more than 70% (from 1% probability to select subsamples containing outliers) to diagnose the incorrect sampled points are detected. The proposed method can both effectively increase the efficiencies of random sampling and achieve robust estimation of the fundamental matrix.
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