Research Papers: D3 Methods

V4PCS: Volumetric 4PCS Algorithm for Global Registration

[+] Author and Article Information
Jida Huang

Department of Industrial
and Systems Engineering,
University at Buffalo,
The State University of New York,
Buffalo, NY 14260
e-mail: jidahuan@buffalo.edu

Tsz-Ho Kwok

Department of Mechanical,
Industrial and Aerospace Engineering,
Concordia University,
Montreal, QC H3G 1M8, Canada
e-mail: tszho.kwok@concordia.ca

Chi Zhou

Department of Industrial and Systems
University at Buffalo,
The State University of New York,
Buffalo, NY 14260
e-mail: chizhou@buffalo.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 17, 2017; final manuscript received June 12, 2017; published online October 2, 2017. Assoc. Editor: Yan Wang.

J. Mech. Des 139(11), 111403 (Oct 02, 2017) (9 pages) Paper No: MD-17-1140; doi: 10.1115/1.4037477 History: Received February 17, 2017; Revised June 12, 2017

With the advances in three-dimensional (3D) scanning and sensing technologies, massive human-related data are now available and create many applications in data-driven design. Similarity identification is one of the basic problems in data-driven design and can facilitate many engineering applications and product paradigm such as quality control and mass customization. Therefore, reusing information can create unprecedented opportunities in advancing the theory, method, and practice of product design. To enable information reuse, different models must be aligned so that their similarity can be identified. This alignment is commonly known as the global registration that finds an optimal rigid transformation to align two 3D shapes (scene and model) without any assumptions on their initial positions. The Super 4-Points Congruent Sets (S4PCS) is a popular algorithm used for this shape registration. While S4PCS performs the registration using a set of four coplanar points, we find that incorporating the volumetric information of the models can improve the robustness and the efficiency of the algorithm, which are particularly important for mass customization. In this paper, we propose a novel algorithm, Volumetric 4PCS (V4PCS), to extend the four coplanar points to noncoplanar ones for global registration, and theoretically demonstrate the computational complexity is significantly reduced. Experimental tests are conducted on several models such as tooth aligner and hearing aid to compare with S4PCS. The experimental results show that the proposed V4PCS can achieve a maximum of 20 times speedup and can successfully compute the valid transformation with very limited number of sample points. An application of the proposed method in mass customization is also investigated.

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Grahic Jump Location
Fig. 5

CSE process illustrated by a triangle

Grahic Jump Location
Fig. 4

Relation between base width and size of congruent sets

Grahic Jump Location
Fig. 3

The flowchart of 4PCS

Grahic Jump Location
Fig. 1

The idea of picking four points to align two models

Grahic Jump Location
Fig. 6

CSE by Mohamad et al. [29]. Given a segment of length d1 with endpoints p1p2 and an intermediate point e, the other segments of length d2 are found based on the sphere centered at e with radius h.

Grahic Jump Location
Fig. 10

Alignment results for other models by V4PCS

Grahic Jump Location
Fig. 8

Alignment results for hearing aid models with n = 24

Grahic Jump Location
Fig. 9

Alignment results for human models with L = 10

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Fig. 12

A preselected base for a hearing aid model

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Fig. 11

Computational time for V4PCS and S4PCS on two teeth models. Note that the number of extracted congruent sets and the timings for the subtotals of the PG, CSE, and CSV steps are in log-scale.

Grahic Jump Location
Fig. 7

Alignment results for teeth models with n = 32



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