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A New Convexity Measurement for 3D Meshes



Afzal A. Godil, Zhouhui Lian


This paper presents a novel convexity measurement for 3D meshes. The new convexity measure is calculated by minimizing the ratio of the summed area of valid regions in a mesh’s six views, which are projected on faces of the bounding box whose edges are parallel to the coordinate axes, to the sum of three orthogonal projected areas of the mesh. The complete definition, theoretical analysis, and a computing algorithm of our convexity measure are explicitly described. This paper also proposes a new 3D shape descriptor CD (i.e., Convexity Distribution) based on the distribution of above-mentioned ratios, which are computed by randomly rotating the mesh around its center, to better describe the object’s convexity-related properties compared to existing convexity measurements. Our experiments not only show that the proposed convexity measure corresponds well with human intuition, but also demonstrate the effectiveness of the new convexity measure and the new shape descriptor by significantly improving the performance of other methods in the application of 3D shape retrieval.
Conference Dates
June 16-21, 2012
Conference Location
Providence, RI
Conference Title
The 25th Conference on Computer Vision and Pattern Recognition (CVPR)


Shape measurement, shape metrology, Convexity, 3D models, 3D shape retrieval, non-rigid 3D shapes


Godil, A. and Lian, Z. (2012), A New Convexity Measurement for 3D Meshes, The 25th Conference on Computer Vision and Pattern Recognition (CVPR), Providence, RI, [online], (Accessed July 19, 2024)


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Created June 16, 2012, Updated February 19, 2017