一种改进的三维网格凸度衡量方法

doi:10.3969/j.issn.1000-5641.2017.06.006

华东师范大学学报(自然科学版) ›› 2017, Vol. 2017 ›› Issue (6): 63-75,113.doi: 10.3969/j.issn.1000-5641.2017.06.006

一种改进的三维网格凸度衡量方法

李瑞, 刘磊, 盛蕴, 张桂戌

华东师范大学计算机科学与软件工程学院, 上海 200062

收稿日期:2016-08-16 出版日期:2017-11-25 发布日期:2017-11-25
通讯作者: 盛蕴,男,副教授,硕士生导师,研究方向为计算机图形学、计算机视觉等.E-mail:ysheng@cs.ecnu.edu.cn E-mail:ysheng@cs.ecnu.edu.cn
作者简介:李瑞,男,硕士研究生,研究方向为计算机图形学.E-mail:15201802836@163.com.
基金资助:
国家自然科学基金（61202291）

An improved convexity measure for 3D meshes

LI Rui, LIU Lei, SHENG Yun, ZHANG Gui-xu

School of Computer Science and Software Engineering, East China Normal University, Shanghai 200062, China

Received:2016-08-16 Online:2017-11-25 Published:2017-11-25

摘要/Abstract

摘要： 针对现有方法需要不断地调整投影方向、时间消耗大的缺点，提出了一种改进的三维网格凸度衡量方法，该方法只需在物体主方向投影一次，减少了时间消耗.该方法首先采用主成分分析（Principal Component Analysis，PCA）计算网格模型的主方向，然后计算模型在主方向上的投影面积和网格模型中每个面片在主方向上的投影面积之和，将它们的比值作为凸度值的初始估计，最后在主方向上对模型进行切片处理，计算所有切片的二维凸度值的加权平均，并将其作为凸度值的修正.实验结果证明，这种改进的凸度衡量方法在计算速度上比现有方法更快，而且更加符合人类的视觉感知.

关键词: 形状分析, 凸度衡量, 主成分分析

Abstract: In this paper we proposed an improved 3D mesh convexity measure by projecting only once a given 3D mesh onto the orthogonal 2D planes along its principal directions. Unlike the previous work which was time-consuming and required constant adaptations of the projection direction, we used the calculated result along the principal directions as an initial estimate of mesh convexity, followed by a correction process. In the initial estimation, our measure computed only once the summed area ratio of mesh silhouette images to mesh faces, along the principal directions of the mesh. Then, the mesh was sliced into a number of 2D cross sections along its principal directions. Finally, a 2D convexity measure for the 2D sliced cross sections was employed to correct the convexity overestimated by the initial estimation. Experimental results had demonstrated the effectiveness and effciency of the improved convexity measure against the existing ones.

Key words: shape analysis, convexity measure, principal component analysis

中图分类号:

TP391.4

李瑞, 刘磊, 盛蕴, 张桂戌. 一种改进的三维网格凸度衡量方法[J]. 华东师范大学学报(自然科学版), 2017, 2017(6): 63-75,113.

LI Rui, LIU Lei, SHENG Yun, ZHANG Gui-xu. An improved convexity measure for 3D meshes[J]. Journal of East China Normal University(Natural Sc, 2017, 2017(6): 63-75,113.

参考文献

[1] ŽUNIĆ J, ROSIN P L. A new convexity measure for polygons[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(7):923-934.
[2] LIAN Z, GODIL A, ROSIN P L, et al. A new convexity measurement for 3D meshes[C]//Computer Vision and Pattern Recognition (CVPR), 2012 IEEE Conference on. IEEE, 2012:119-126.
[3] ŽUNIĆ J, ROSIN P L. A rectilinearity measurement for polygons[C]//European Conference on Computer Vision. Berlin:Springer, 2002:746-758.
[4] LIAN Z, ROSIN P L, SUN X. Rectilinearity of 3D meshes[J]. International Journal of Computer Vision, 2010, 89(2/3):130-151.
[5] ROSIN P L. A two-component rectilinearity measure[J]. Computer Vision and Image Understanding, 2008, 109(2):176-185.
[6] ŽUNIĆ J, HIROTA K, MARTINEZ-ORTIZ C. Compactness measure for 3D shapes[C]//Informatics, Electronics & Vision (ICIEV), 2012 International Conference on. IEEE, 2012:1180-1184.
[7] ROSIN P L. Measuring shape:Ellipticity, rectangularity, and triangularity[J]. Machine Vision and Applications, 2003, 14(3):172-184.
[8] LEOU J J, TSAI W H. Automatic rotational symmetry determination for shape analysis[J]. Pattern Recognition, 1987, 20(6):571-582.
[9] REN Z, YUAN J, LIU W. Minimum near-convex shape decomposition.[J]. IEEE Transactions on Pattern Analysis & Machine Intelligence, 2013, 35(10):2546-2552.
[10] ROSIN P L. Classification of pathological shapes using convexity measures[J]. Pattern Recognition Letters, 2009, 30(5):570-578.
[11] SARFRAZ M, RIDHA A. Content-based image retrieval using multiple shape descriptors[C]//Ieee/acs International Conference on Computer Systems and Applications. 2007:730-737.
[12] YANG Y B, LIN H, ZHU Q. Content-based 3D model retrieval:A survey[J]. Chinese Journal of Computers, 2004, 27(10):1297-1310.
[13] BIEDERMAN I. Recognition-by-components:A theory of human image understanding[J]. Psychological Review, 1987, 94(2):115.
[14] SIDDIQI K, KIMIA B B. Parts of visual form:Computational aspects[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17(3):239-251.
[15] SINGH M, HOFFMAN D D. 13-part-based representations of visual shape and implications for visual cognition[J]. Advances in Psychology, 2001, 130:401-459.
[16] LIU H, LIU W, LATECKI L J. Convex shape decomposition[C]//Computer Vision and Pattern Recognition (CVPR), 2010 IEEE Conference on. IEEE, 2010:97-104.
[17] GHOSH M, AMATO N M, LU Y, et al. Fast approximate convex decomposition using relative concavity[J]. Computer-Aided Design, 2013, 45(2):494-504.
[18] ASAFI S, GOREN A, COHEN-OR D. Weak convex decomposition by lines-of-sight[J]. Computer Graphics Forum, 2013, 32(5):23-31.
[19] 刘磊. 三维网格特征提取与分割[D]. 上海:华东师范大学, 2015.
[20] ROSIN P L, MUMFORD C L. A symmetric convexity measure[J]. Computer Vision & Image Understanding,2004, 103(2):101-111.
[21] KOLESNIKOV A, FRANTI P. Optimal algorithm for convexity measure calculation[C]//IEEE International Conference on Image Processing. 2005:353-356.
[22] RAHTU E, SALO M, HEIKKILA J. A new convexity measure based on a probabilistic interpretation of images[J]. IEEE Transactions on Pattern Analysis & Machine Intelligence, 2006, 28(9):1501-1512.
[23] CHEN X, GOLOVINSKIY A, FUNKHOUSER T. A benchmark for 3D mesh segmentation[J]. ACM Transactions on Graphics, 2009, 28(3):341-352.

一种改进的三维网格凸度衡量方法

An improved convexity measure for 3D meshes

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