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Abstract : |
All computer vision algorithms applied to real data have to deal with input data corrupted by errors, which leads to the necessity to select an appropriate loss function and to minimize it. The fact that the errors in different components can be of individual size or even be correlated, makes a statistical analysis of an algorithm absolutely necessary. A statistically justified loss function can only be obtained by a statistical consideration of errors, or, in other words, optimization criteria that are not statistically justified (i.e. criteria that use a wrong error metric) may result in drastic failure of an algorithm in the presence of errors. In this paper, we will show that two different models of input data errors are possible in two-view algorithms. Additionally, we will focus on the estimation of the fundamental matrix and explain the role of the so-called ?algebraic ? and ?geometric ? distances from a statistical point of view. 1 Motivation for (re)considering error models All algorithms that try to extract quantitative 3D-information from a set of images start from establishing and exploiting correspondences between geometrical entities such as points, lines, regions etc. that are found and located in two or more images. When these tokens are represented in quantitative form, |
