An Efficient Method for Tensor Voting Using Steerable Filters

Franken, Erik; Almsick, Markus van; Rongen, Peter; Florack, Luc; Romeny, Bart ter Haar

doi:10.1007/11744085_18

Cited by 43 publications

(60 citation statements)

References 7 publications

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“…While similar in effect to the decay function used in the original tensor voting, and also to the one used in [9] where a vote attenuation function is defined to decouple proximity and curvature terms, our modified function, which also differs from that in [21], enables a closed-form solution for tensor voting without resorting to precomputed discrete voting fields.…”

Section: Data Communicationmentioning

confidence: 99%

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

Yeung

Jia

et al. 2012

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-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-ofthe-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.

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Section: Data Communicationmentioning

confidence: 99%

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

Yeung

Jia

et al. 2012

IEEE Trans. Pattern Anal. Mach. Intell.

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“…To compute the TV-integral in reasonable time the initial measurements in TV are typically sparse. Recently, Franken et al [2] proposed an efficient way to compute a dense Tensor Voting in 2D. The idea makes use of a steerable expansion of the voting field.…”

Section: Related Workmentioning

confidence: 99%

“…Perona generalized this concept in [8] and introduced a methodology to decompose a given filter kernel optimally in a set of steerable basis filters. The idea of Franken et al [2] is to use the steerable decomposition of the voting field to compute the voting process by convolutions in an efficient way. Complex calculus and 2D harmonic analysis are the major mathematical tools that make this approach possible.…”

Section: Related Workmentioning

confidence: 99%

Spherical Tensor Calculus for Local Adaptive Filtering

Reisert¹,

Burkhardt²

2009

Tensors in Image Processing and Computer Vision

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“…As a last remark we like to point out that the stochastic completion kernel p(r, φ, α) and the tensor voting fields p T V (r, φ) and p S (r, φ) can be decomposed into m-modes to facilitate their rotation in φ [11]. In the case of the stochastic tensor voting field we obtain p S (r, φ) = …”

Section: Not All Voting Systems Are Created Equalmentioning

confidence: 99%

From Stochastic Completion Fields to Tensor Voting

Almsick

Duits

Franken

et al. 2005

Lecture Notes in Computer Science

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Abstract. Several image processing algorithms imitate the lateral interaction of neurons in the visual striate cortex V1 to account for the correlations along contours and lines. Here we focus on two methodologies: tensor voting by Guy and Medioni, and stochastic completion fields by Mumford, Williams and Jacobs. The objective of this article is to compare these two methods and to place them into a common mathematical framework. As a consequence we obtain a sound stochastic foundation of tensor voting, a new tensor voting field, and an analytic approximation of the stochastic completion kernel.

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An Efficient Method for Tensor Voting Using Steerable Filters

Cited by 43 publications

References 7 publications

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

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

Spherical Tensor Calculus for Local Adaptive Filtering

From Stochastic Completion Fields to Tensor Voting

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