An improved convexity measure for 3D meshes
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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.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.
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Key words:
- shape analysis /
- convexity measure /
- principal component analysis
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图 1 具有相同的体积与凸包体积的网格模型
Fig. 1 Different meshes with identical mesh and convex hull volumes
图 4 模型在主方向坐标系下的投影以及C2和Ce的值
Fig. 4 Mesh silhouettes along the principal axes with the mesh convexity values calculated by C2 and Ce
表 1 时间消耗对比
Tab. 1 Comparison of time consumptions
网格模型 顶点数 时间消耗 C3耗时 C2一次迭代 C2总耗时 
673 11.34 0.064 8 648 
4 463 45.11 0.090 5 905 
9 261 86.08 0.140 0 1 400 
14 872 148.4 0.170 0 1 700 
34 817 316.1 0.311 5 3 115 
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