The role of total least squares in motion analysis
The main goal of this paper is to put well-established techniques for two-view motion analysis in the context of the theory of Total Least Squares and to make clear that robust and reliable motion analysis algorithms cannot be designed without a thorough statistical consideration of the consequences of errors in the input data.
We focus on the non-iterative 8+n-point algorithm for estimating the fundamental matrix and present a comprehensive statistical derivation of the compelling necessity for one of the normalization transforms proposed by Hartley [1, 2]. It turns out that without these transformations the results of the well-known non-iterative methods for two-view motion analysis are biased and inconsistent. With some further improvements proposed in this paper, the quality of the algorithm can even be enhanced beyond what has been reported in the literature before.
KeywordsSingular Value Decomposition Coordinate Frame Motion Type Frobenius Norm Fundamental Matrix
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