Quasiconvex Optimization for Robust Geometric Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
Generalized Convexity in Multiple View Geometry
Journal of Mathematical Imaging and Vision
Fast multiple-view L2 triangulation with occlusion handling
Computer Vision and Image Understanding
EVP-based multiple-view triangulation
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part III
Robust Estimation for an Inverse Problem Arising in Multiview Geometry
Journal of Mathematical Imaging and Vision
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Geometric reconstruction problems in computer vision can be solved by minimizing the maximum of reprojection errors, i.e., the L\infty-norm. Unlike L2-norm (sum of squared reprojection errors), the global minimum of L\infty-norm can be efficiently achieved by quasiconvex optimization. However, the maximum of reprojection errors is the meaningful measure to minimize only when the measurement noises are independent and identically distributed at every 2D feature point and in both directions in the image. This is rarely the case in real data, where the positional noise not only varies at different features, but also has strong directionality. In this paper, we incorporate the directional uncertainty model into a quasiconvex optimization framework, in which global minimum of meaningful errors can be efficiently achieved, and accurate geometric reconstructions can be obtained from feature points that contain high directional uncertainty.