  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.
