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Research Papers

Constraints Based Nonrigid Registration for 2D Blade Profile Reconstruction in Reverse Engineering

[+] Author and Article Information
Yongqing Li, Jun Ni

S. M. Wu Manufacturing Research Center, University of Michigan, Ann Arbor, MI 48109

J. Comput. Inf. Sci. Eng 9(3), 031005 (Aug 19, 2009) (9 pages) doi:10.1115/1.3184602 History: Received January 01, 2008; Revised January 31, 2009; Published August 19, 2009

In reverse engineering, 2D profile curve reconstruction based on cross-sectional points is a very crucial step for surface reconstruction such as lofting surface, swept surface, translational surface, and rotational surface. Unlike the traditional constrained fitting method that assumes that the cross-sectional points have been segmented in advance, and that the initial fitted curves are very close to the points, we propose a nonrigid registration method, through which a template curve can be automatically transformed and deformed to best fit the cross-sectional points. Compared with constrained fitting, nonrigid registration does not need any data preprocessing such as sorting, segmentation, and parametrization. The simulated and real examples have demonstrated the effectiveness and superiority of nonrigid registration for 2D blade profile curve reconstruction.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) A failed sorting example of a blade sectional points and (b) magnified view of lead edge area

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Figure 2

(a) Correspondence search with ICP method and (b) the binary correspondence matrix

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Figure 3

The end points of a curve are stretching out by minimizing the one-way directed distance

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Figure 4

All the points have the same correspondence on the curve in constrained fitting

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Figure 5

(a) Illustration of mutual distance between the source data and the target data, (b) weighted correspondence matrix from the target data to the source data, and (c) weighted correspondence matrix from the source data to the target data

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Figure 6

The function of weighted factor with respect to the distance dj,i and registration error σ

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Figure 7

(a) Cross sectional points of a physical turbine blade and a template curve, (b) section curves reconstructed with nonrigid registration, and (c) lofted solid model based on the reconstructed curves

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Figure 8

Three different stages of 2D nonrigid registration: (a) before registration, (b) after 5 iterations, and (c) after 20 iterations

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Figure 11

(a) Template profile curve and data points and (b) reconstructed curve with nonrigid registration

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Figure 9

(a) Initial profile curve and data points, (b) reconstructed curve with nonrigid registration, and (c) reconstructed curve with constrained fitting method (13)

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Figure 10

(a) Template profile curve and measured points, (b) reconstructed curve with nonrigid registration, (c) lofted surface model, and (d) magnified view of the leading edges of the reconstructed curves

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