A Closed-Form Solution to Tensor Voting: Theory and Applications

—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 origin...

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Tai-Pang Wu, Sai Kit Yeung, Jiaya Jia, Chi-Keung Tang, Gérard G. Medioni
• Keywords: CORR 2016, Education