Robust Fitting for Multiple View Geometry

Abstract

Abstract. How hard are geometric vision problems with outliers? We show that for most fitting problems, a solution that minimizes the number of outliers can be found with an algorithm that has polynomial timecomplexity in the number of points (independent of the rate of outliers). Further, and perhaps more interestingly, other cost functions such as the truncated L2-norm can also be handled within the same framework with the same time complexity.We apply our framework to triangulation, relative pose problems and stitching, and give several other examples that fulfill the required conditions. Based on efficient polynomial equation solvers, it is experimentally demonstrated that these problems can be solved reliably, in particular for low-dimensional models. Comparisons to standard random sampling solvers are also given.

Tractable and Reliable Registration of 2D Point Sets

“…However, as they are based on branch-and-bound, the computational complexity of the algorithm is exponential. The most closely related work to ours is [10,1], where a truncated L 2 -norm algorithm is derived with complexity O(n 4 ). However, the runtime tends to be prohibitive (see experimental section), making it a less tractable alternative.…”

Optimal Geometric Fitting under the Truncated L2-Norm

“…Just as in [7], we introduce an dummy goal function f . In the end, f will be chosen to achieve simple equations, but now it is sufficient to say that it should be differentiable.…”

“…This result was recently generalized in [7] by improving the complexity bound and weaken-ing the conditions on the class of residual functions that can be handled. Our work is closely related at the conceptual level.…”

“…Our work is closely related at the conceptual level. Still, only the 0 − 1 loss function (or more precisely, a piece-wise constant function) can be handled in [7], and not the statistically motivated truncated L 2 -norm.…”

Fast and Reliable Two-View Translation Estimation

“…Thus, there is no guarantee of actually finding a good solution even if there exists one. A direct application of the general theory of optimal robust model fitting proposed in [3] would yield an O(n 3 )-algorithm for minimizing the number of outliers. Our approach is significantly faster.…”