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

Wu, Tong; Yeung, Sai-Kit; Jia, Jiaya; Tang, Chi-Keung; Medioni, Gérard

doi:10.1109/tpami.2011.250

Cited by 27 publications

(8 citation statements)

References 23 publications

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“…Although tensor voting is a robust technique for extracting perceptual information from point clouds, the complexity of its original formulation makes it difficult to use in robotics applications. We use the closed-form (CFTV) formulation proposed by Wu et al (2012) for efficiency. The generic second order symmetric tensor is then computed given…”

Section: K-nearest Neighbors Closed Form Tensor Votingmentioning

confidence: 99%

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Geometry Preserving Sampling Method Based on Spectral Decomposition for Large-Scale Environments

2020

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In the context of 3D mapping, larger and larger point clouds are acquired with lidar sensors. Although pleasing to the eye, dense maps are not necessarily tailored for practical applications. For instance, in a surface inspection scenario, keeping geometric information such as the edges of objects is essential to detect cracks, whereas very dense areas of very little information such as the ground could hinder the main goal of the application. Several strategies exist to address this problem by reducing the number of points. However, they tend to underperform with non-uniform density, large sensor noise, spurious measurements, and large-scale point clouds, which is the case in mobile robotics. This paper presents a novel sampling algorithm based on spectral decomposition analysis to derive local density measures for each geometric primitive. The proposed method, called Spectral Decomposition Filter (SpDF), identifies and preserves geometric information along the topology of point clouds and is able to scale to large environments with a non-uniform density. Finally, qualitative and quantitative experiments verify the feasibility of our method and present a large-scale evaluation of SpDF with other seven point cloud sampling algorithms, in the context of the 3D registration problem using the Iterative Closest Point (ICP) algorithm on real-world datasets. Results show that a compression ratio up to 97 % can be achieved when accepting a registration error within the range accuracy of the sensor, here for large scale environments of less than 2 cm.

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Section: K-nearest Neighbors Closed Form Tensor Votingmentioning

confidence: 99%

“…As the input is generally not oriented, we still have to do a first pass by encoding K j as a unit ball to derive a preferred direction. Then, we do a second pass by encoding points with the tensors previously obtained, but with the ball component disabled as suggested by Wu et al (2012), such as…”

Section: K-nearest Neighbors Closed Form Tensor Votingmentioning

confidence: 99%

Geometry Preserving Sampling Method Based on Spectral Decomposition for Large-Scale Environments

2020

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“…Tensor voting in its original formulation is clearly not expressed in a closed‐form, as has been pointed out in [21, 26]. This is because of the need for discrete sampling and integration steps in the computation of votes (other than the ones produced by a stick tensor), as explained in Section 2.4.…”

Section: Difficultiesmentioning

confidence: 99%

“…A closed‐form expression is often desired to achieve an efficient solution with less implementation efforts. In addition, it allows the application of a number of mathematical operations, including differential calculus, which otherwise would not be possible [26].…”

Section: Difficultiesmentioning

confidence: 99%

Perceptual grouping by tensor voting: a comparative survey of recent approaches

Maggiori¹,

Manterola

Fresno³

2015

IET Computer Vision

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Tensor voting is a computational framework that addresses the problem of perceptual organisation. It was designed to convey human perception principles into a unified framework that can be adapted to extract visually salient elements from possibly noisy or corrupted images. The original formulation featured some concerns that made it difficult or impractical to be applied directly. Therefore, several partial or total theoretical reformulations or augmentations have been proposed. These almost parallel publication were presented in different directions, with different priorities and even in a different notation. Thus, the authors observed the need for a coherent description and comparison of the different proposals. This work, after describing the original approach of tensor voting, reviews and explains a number of high impact theoretical modifications in a self‐contained manner and including possible future directions of work. The authors have selected and organised a number of formulations and unified the way the problem is addressed across the different proposals. The aim of this study is to contribute with a modern comprehensive source of information on the theoretical aspects of tensor voting.

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“…Moreno et al [3] proposed two alternative formulations of tensor voting based on numerical approximations of the votes, to reduce the high computational complexity while keeping the same perceptual meaning of the original tensor voting. [4] attempt to propose a closed-form solution to tensor voting (CFTV), which does not require numerical integration. But, as pointed in [3], [5], their methods yield very different values from those obtained through the original tensor voting.…”

Section: Introductionmentioning

confidence: 99%

Research on Analytical Solution Tensor Voting

Lin¹,

Wu²,

Lei³

et al. 2018

IEICE Trans. Inf. & Syst.

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This letter presents a novel tensor voting mechanismanalytic tensor voting (ATV), to get rid of the difficulties in original tensor voting, especially the efficiency. One of the main advantages is its explicit voting formulations, which benefit the completion of tensor voting theory and computational efficiency. Firstly, new decaying function was designed following the basic spirit of decaying function in original tensor voting (OTV). Secondly, analytic stick tensor voting (ASTV) was formulated using the new decaying function. Thirdly, analytic plate and ball tensor voting (APTV, ABTV) were formulated through controllable stick tensor construction and tensorial integration. These make the each voting of tensor can be computed by several non-iterative matrix operations, improving the efficiency of tensor voting remarkably. Experimental results validate the effectiveness of proposed method.

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

Cited by 27 publications

References 23 publications

Geometry Preserving Sampling Method Based on Spectral Decomposition for Large-Scale Environments

Geometry Preserving Sampling Method Based on Spectral Decomposition for Large-Scale Environments

Perceptual grouping by tensor voting: a comparative survey of recent approaches

Research on Analytical Solution Tensor Voting

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