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Accelerating Globally Optimal Consensus Maximization in Geometric Vision
Branch-and-bound-based consensus maximization stands out due to its important
ability of retrieving the globally optimal solution to outlier-affected
geometric problems. However, while the discovery of such solutions caries high
scientific value, its application in practical scenarios is often prohibited by
its computational complexity growing exponentially as a function of the
dimensionality of the problem at hand. In this work, we convey a novel, general
technique that allows us to branch over an dimensional space for an
n-dimensional problem. The remaining degree of freedom can be solved globally
optimally within each bound calculation by applying the efficient interval
stabbing technique. While each individual bound derivation is harder to compute
owing to the additional need for solving a sorting problem, the reduced number
of intervals and tighter bounds in practice lead to a significant reduction in
the overall number of required iterations. Besides an abstract introduction of
the approach, we present applications to three fundamental geometric computer
vision problems: camera resectioning, relative camera pose estimation, and
point set registration. Through our exhaustive tests, we demonstrate
significant speed-up factors at times exceeding two orders of magnitude,
thereby increasing the viability of globally optimal consensus maximizers in
online application scenarios
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