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Research Papers

Coarse-to-Fine Extraction of Free-Form Surface Features

[+] Author and Article Information
Bing Yi, Zhenyu Liu, Guifang Duan

State Key Laboratory of CAD&CG,
Zhejiang University,
Hangzhou 310027, China

Jianrong Tan

State Key Laboratory of CAD&CG,
Zhejiang University,
Hangzhou 310027, China
e-mail: liuzy@zju.edu.cn

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received March 24, 2014; final manuscript received December 3, 2014; published online February 2, 2015. Assoc. Editor: Charlie C.L. Wang.

J. Comput. Inf. Sci. Eng 15(1), 011011 (Mar 01, 2015) (9 pages) Paper No: JCISE-14-1091; doi: 10.1115/1.4029560 History: Received March 24, 2014; Revised December 03, 2014; Online February 02, 2015

Free-form surface features (FFSFs) extraction is one of the key issues for redesigning and reediting the surface models exported from commercial software or reconstructed by reverse engineering. In this paper, a coarse-to-fine method is proposed to robustly extract the FFSFs. First, by iterative Laplacian smoothing, a set of height functions are generated, and principal component analysis (PCA) is employed to obtain the appropriate iteration number for the feature field extraction that is then accomplished by the Gaussian mix model (GMM) with a high segmentation threshold. Second, based on the feature field, an adaptive smooth ratio for each vertex is proposed for Laplacian smoothing, which is implemented to generate a precise base surface. Thereby, with the base surface, the FFSFs can be easily extracted by using the GMM. The empirical results illustrate that the proposed method yields improved performance for extracting FFSFs compared with conventional methods.

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Figures

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Fig. 1

Height function extraction by Laplacian smoothing: (a) 50 iterations, (b) 250 iterations, (c) 500 iterations, (d) 750 iterations, (e) 1000 iterations, (f) 2000 iterations, (g) 3000 iterations, (h) 4000 iterations, (i) 5000 iterations, (j) 7500 iterations, (k) 10,000 iterations, and (l) 15,000 iterations

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Fig. 2

The base surface generated by the Laplacian smoothing method in the iterative smooth procedure (original model colored with grey, the generated base surface with 50, 250, 500, 1000, 2000, 3000, 4000, and 5000 iterations are colored with red, green, blue, maroon, yellow, green, purple, olive, and teal, respectively)

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Fig. 3

Flowchart of the proposed method

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Fig. 4

An example of learning a two dimensional subspace (colored in red) from a cosine sequence (blue dotted circle) in three dimensional space by PCA

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Fig. 5

An example of the fraction of total variation versus eigenvalues with the protrusion free-form surface model

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Fig. 6

Dimension reduced height functions in the subspace learned by PCA

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Fig. 7

Approximating the histogram of the height function using GMM to choose the segmentation threshold for feature field extraction

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Fig. 8

Comparing the generated base surface of the Laplacian smoothing method and the adaptive smooth ratio based Laplacian smoothing method: (a) the height functions of the Laplacian smoothing method, (b) the height functions of our method, and (c) a combination of the generated base surface, the original model is colored with grey, the base surface generated by the forward and backward method is colored with red and green, respectively

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Fig. 9

Approximating the histogram of the height function using GMM to choose the segmentation threshold for free-form feature extraction

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Fig. 10

Extraction of protrusion FFSFs: (a) and (b) the results of the relief extraction proposed by Ref. [6] with smoothness = 5, 25, respectively, (c) and (d) the results of feature extraction by our method with cut curve on the original model and base model, respectively

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Fig. 11

Extraction of saddle FFSFs: (a) and (b) the results of the relief extraction proposed by Ref. [6] with smoothness = 5, 25, respectively, (c) and (d) the results of feature extraction by our method with cut curve on the original model and base model, respectively

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Fig. 12

Extraction of combined FFSFs: (a) and (b) the results of the relief extraction proposed by Ref. [6] with smoothness = 5, 25, respectively, (c) and (d) the results of feature extraction by our method with cut curve on the original model and base model, respectively

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Fig. 13

Extraction of compound FFSFs: (a) and (b) the results of the relief extraction proposed by Ref. [6] with smoothness = 5, 25, respectively, (c) and (d) the results of feature extraction by our method with cut curve on the original model and base model, respectively

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Fig. 14

Extraction of mix FFSFs: (a) and (b) the results of the relief extraction proposed by Ref. [6] with smoothness = 5, 25, respectively, (c) and (d) the results of feature extraction by our method with cut curve on the original model and base model, respectively

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Fig. 15

Extraction free-form feature from deformable model: (a) the original surface, (b) the base surface, (c) the deformed surface, and (d) the deformed base surface

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Fig. 16

Extraction free-form feature from noise surface model (the noise models are generated with a Gaussian noise on the original model, and σ = β × the length of the model; left: our method, right: easy mesh cutting, red and green curves indicate the background and foreground, respectively). (a) The original surface, (b) β = 0.001, (c) β = 0.005, (d) β = 0.01, (e) β = 0.02, and (f) β = 0.05.

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Fig. 17

Extraction FFSFs from car sheet panels (left: our method, middle: easy mesh cutting, red and green curves indicate the background and foreground, respectively, right: ridges and valleys: blue and red curves indicate the ridges and valleys, respectively). (a) Extracted internal FFSFs of the front sheet panel, (b) extracted border FFSFs of the front sheet panel, (c) extracted channel FFSFs of the front sheet panel, and (d) extracted FFSFs of the door sheet panel.

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