Overviews of Optimization Techniques for Geometric Estimation [in Japanese]
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We summarize techniques for optimal geometric estimation from noisy observations for computervision applications. We first discuss the interpretation of optimality and point out that geometricestimation is different from the standard statistical estimation. We also describe our noisemodeling and a theoretical accuracy limit called the KCR lower bound. Then, we formulate estimationtechniques based on minimization of a given cost function: least squares (LS), maximumlikelihood (ML), which includes reprojection error minimization as a special case, and Sampsonerror minimization. We describe bundle adjustment and the FNS scheme for numerically solvingthem and the hyperaccurate correction that improves the accuracy of ML. Next, we formulateestimation techniques not based on minimization of any cost function: iterative reweight, renormalization,and hyper-renormalization. Finally, we show numerical examples to demonstrate thathyper-renormalization has higher accuracy than ML, which has widely been regarded as the mostaccurate method of all. We conclude that hyper-renormalization is robust to noise and currently isthe best method.
- Memoirs of the Faculty of Engineering, Okayama University
Memoirs of the Faculty of Engineering, Okayama University 47, 1-18, 2013-01
Faculty of Engineering, Okayama University