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Primitive fitting based on the efficient multiBaySAC algorithm.

Kang Z, Li Z - PLoS ONE (2015)

Bottom Line: Moreover, the updated version of the initial probability was implemented based on a memorable form of Bayes' Theorem, which describes the relationship between prior and posterior probabilities of a data point by determining whether the hypothesis set to which a data point belongs is correct.The proposed approach was tested using real and synthetic point clouds.Future work will aim at further optimizing this strategy through its application to other problems such as multiple point cloud co-registration and multiple image matching.

View Article: PubMed Central - PubMed

Affiliation: School of Land Science and Technology, China University of Geosciences, No. 29 Xueyuan Road, Haidian District, Beijing, 100083, China.

ABSTRACT
Although RANSAC is proven to be robust, the original RANSAC algorithm selects hypothesis sets at random, generating numerous iterations and high computational costs because many hypothesis sets are contaminated with outliers. This paper presents a conditional sampling method, multiBaySAC (Bayes SAmple Consensus), that fuses the BaySAC algorithm with candidate model parameters statistical testing for unorganized 3D point clouds to fit multiple primitives. This paper first presents a statistical testing algorithm for a candidate model parameter histogram to detect potential primitives. As the detected initial primitives were optimized using a parallel strategy rather than a sequential one, every data point in the multiBaySAC algorithm was assigned to multiple prior inlier probabilities for initial multiple primitives. Each prior inlier probability determined the probability that a point belongs to the corresponding primitive. We then implemented in parallel a conditional sampling method: BaySAC. With each iteration of the hypothesis testing process, hypothesis sets with the highest inlier probabilities were selected and verified for the existence of multiple primitives, revealing the fitting for multiple primitives. Moreover, the updated version of the initial probability was implemented based on a memorable form of Bayes' Theorem, which describes the relationship between prior and posterior probabilities of a data point by determining whether the hypothesis set to which a data point belongs is correct. The proposed approach was tested using real and synthetic point clouds. The results show that the proposed multiBaySAC algorithm can achieve a high computational efficiency (averaging 34% higher than the efficiency of the sequential RANSAC method) and fitting accuracy (exhibiting good performance in the intersection of two primitives), whereas the sequential RANSAC framework clearly suffers from over- and under-segmentation problems. Future work will aim at further optimizing this strategy through its application to other problems such as multiple point cloud co-registration and multiple image matching.

No MeSH data available.


Related in: MedlinePlus

The 2D histogram of a plane.The horizontal and vertical axes denote the angle between the normal vector n of a plane and horizontal plane and the perpendicular distance from the origin respectively; the upright axis represents the convergence degree of each candidate parameter set. This degree of candidate parameter set convergence in the histogram is calculated as the number of parameter sets that converge to the candidate parameter set divided by the total number of parameter sets.
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pone.0117341.g005: The 2D histogram of a plane.The horizontal and vertical axes denote the angle between the normal vector n of a plane and horizontal plane and the perpendicular distance from the origin respectively; the upright axis represents the convergence degree of each candidate parameter set. This degree of candidate parameter set convergence in the histogram is calculated as the number of parameter sets that converge to the candidate parameter set divided by the total number of parameter sets.

Mentions: a) The 2D histogram of a plane. In this paper, we use the Hesse form of the plane; therefore, differences between hypothesis planar parameters are described in terms of the normal vector and perpendicular distance from origin ρ. In Fig. 5, the horizontal and vertical axes denote the angle between the normal plane vector and horizontal plane and ρ, respectively. The upright axis denotes the convergence degree of each candidate parameter set. The planar parameters statistical test compares the angle between hypothesis planar normal vectors to the deviation between hypothesis ρ s.


Primitive fitting based on the efficient multiBaySAC algorithm.

Kang Z, Li Z - PLoS ONE (2015)

The 2D histogram of a plane.The horizontal and vertical axes denote the angle between the normal vector n of a plane and horizontal plane and the perpendicular distance from the origin respectively; the upright axis represents the convergence degree of each candidate parameter set. This degree of candidate parameter set convergence in the histogram is calculated as the number of parameter sets that converge to the candidate parameter set divided by the total number of parameter sets.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4363901&req=5

pone.0117341.g005: The 2D histogram of a plane.The horizontal and vertical axes denote the angle between the normal vector n of a plane and horizontal plane and the perpendicular distance from the origin respectively; the upright axis represents the convergence degree of each candidate parameter set. This degree of candidate parameter set convergence in the histogram is calculated as the number of parameter sets that converge to the candidate parameter set divided by the total number of parameter sets.
Mentions: a) The 2D histogram of a plane. In this paper, we use the Hesse form of the plane; therefore, differences between hypothesis planar parameters are described in terms of the normal vector and perpendicular distance from origin ρ. In Fig. 5, the horizontal and vertical axes denote the angle between the normal plane vector and horizontal plane and ρ, respectively. The upright axis denotes the convergence degree of each candidate parameter set. The planar parameters statistical test compares the angle between hypothesis planar normal vectors to the deviation between hypothesis ρ s.

Bottom Line: Moreover, the updated version of the initial probability was implemented based on a memorable form of Bayes' Theorem, which describes the relationship between prior and posterior probabilities of a data point by determining whether the hypothesis set to which a data point belongs is correct.The proposed approach was tested using real and synthetic point clouds.Future work will aim at further optimizing this strategy through its application to other problems such as multiple point cloud co-registration and multiple image matching.

View Article: PubMed Central - PubMed

Affiliation: School of Land Science and Technology, China University of Geosciences, No. 29 Xueyuan Road, Haidian District, Beijing, 100083, China.

ABSTRACT
Although RANSAC is proven to be robust, the original RANSAC algorithm selects hypothesis sets at random, generating numerous iterations and high computational costs because many hypothesis sets are contaminated with outliers. This paper presents a conditional sampling method, multiBaySAC (Bayes SAmple Consensus), that fuses the BaySAC algorithm with candidate model parameters statistical testing for unorganized 3D point clouds to fit multiple primitives. This paper first presents a statistical testing algorithm for a candidate model parameter histogram to detect potential primitives. As the detected initial primitives were optimized using a parallel strategy rather than a sequential one, every data point in the multiBaySAC algorithm was assigned to multiple prior inlier probabilities for initial multiple primitives. Each prior inlier probability determined the probability that a point belongs to the corresponding primitive. We then implemented in parallel a conditional sampling method: BaySAC. With each iteration of the hypothesis testing process, hypothesis sets with the highest inlier probabilities were selected and verified for the existence of multiple primitives, revealing the fitting for multiple primitives. Moreover, the updated version of the initial probability was implemented based on a memorable form of Bayes' Theorem, which describes the relationship between prior and posterior probabilities of a data point by determining whether the hypothesis set to which a data point belongs is correct. The proposed approach was tested using real and synthetic point clouds. The results show that the proposed multiBaySAC algorithm can achieve a high computational efficiency (averaging 34% higher than the efficiency of the sequential RANSAC method) and fitting accuracy (exhibiting good performance in the intersection of two primitives), whereas the sequential RANSAC framework clearly suffers from over- and under-segmentation problems. Future work will aim at further optimizing this strategy through its application to other problems such as multiple point cloud co-registration and multiple image matching.

No MeSH data available.


Related in: MedlinePlus