A Closed-Form Solution to Tensor Voting: Theory and Applications
This work addresses the problem of robust structure detection and parameter estimation in computer vision, particularly for multiview stereo matching, offering incremental improvements over existing tensor voting methods.
The authors introduced a closed-form solution to tensor voting (CFTV) that provides an exact and efficient algorithm for computing structure-aware tensors from point sets, and developed EMTV, an expectation maximization method that outperforms original tensor voting and state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching, with quantitative improvements in accuracy and robustness.
We prove a closed-form solution to tensor voting (CFTV): given a point set in any dimensions, our closed-form solution provides an exact, continuous and efficient algorithm for computing a structure-aware tensor that simultaneously achieves salient structure detection and outlier attenuation. Using CFTV, we prove the convergence of tensor voting on a Markov random field (MRF), thus termed as MRFTV, where the structure-aware tensor at each input site reaches a stationary state upon convergence in structure propagation. We then embed structure-aware tensor into expectation maximization (EM) for optimizing a single linear structure to achieve efficient and robust parameter estimation. Specifically, our EMTV algorithm optimizes both the tensor and fitting parameters and does not require random sampling consensus typically used in existing robust statistical techniques. We performed quantitative evaluation on its accuracy and robustness, showing that EMTV performs better than the original TV and other state-of-the-art techniques in fundamental matrix estimation for multiview stereo matching. The extensions of CFTV and EMTV for extracting multiple and nonlinear structures are underway. An addendum is included in this arXiv version.