Global Optimization for Shape Fitting

We propose a global optimization framework for 3D shape reconstruction from sparse noisy 3D measurements frequently encountered in range scanning, sparse featurebased stereo, and shape-from-X. In contrast to earlier local or banded optimization methods for shape fitting, we compute global optimum in the whole volume removing dependence on initial guess and sensitivity to numerous local minima. Our global method is based on two main ideas. First, we suggest a new regularization functional with a data alignment term that maximizes the number of (weaklyoriented) data points contained by a surface while allowing for some measurement errors. Second, we propose a touchexpand algorithm for finding a minimum cut on a huge 3D grid using an automatically adjusted band. This overcomes prohibitively high memory cost of graph cuts when computing globally optimal surfaces at high-resolution. Our results for sparse or incomplete 3D data from laser scanning and passive multi-view stereo are robust to...

• Type: Conference
• Year: 2007
• Where: CVPR
• Authors: Victor S. Lempitsky, Yuri Boykov
• Keywords: Computer Vision, CVPR 2007, Global Optimization Framework, Incomplete 3d Data, Noisy 3d Measurements, Passive Multi-view Stereo, Sparse Featurebased Stereo