Automatic rotational symmetry determination for shape analysis
Pattern Recognition
Machine Vision and Applications
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MULTIMEDIA '01 Proceedings of the ninth ACM international conference on Multimedia
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ACM Transactions on Graphics (TOG)
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Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology
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Proceedings of the sixth Eurographics workshop on Multimedia 2001
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SMI '03 Proceedings of the Shape Modeling International 2003
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SMI '03 Proceedings of the Shape Modeling International 2003
Rotation invariant spherical harmonic representation of 3D shape descriptors
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Rectilinearity Measurements for Polygons
IEEE Transactions on Pattern Analysis and Machine Intelligence
Measuring shape: ellipticity, rectangularity, and triangularity
Machine Vision and Applications
A Reflective Symmetry Descriptor for 3D Models
Algorithmica
A New Convexity Measure for Polygons
IEEE Transactions on Pattern Analysis and Machine Intelligence
SMI '04 Proceedings of the Shape Modeling International 2004
Partial matching of 3D shapes with priority-driven search
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
An easy measure of compactness for 2D and 3D shapes
Pattern Recognition
A survey of content based 3D shape retrieval methods
Multimedia Tools and Applications
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IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Coarse filters for shape matching
IEEE Computer Graphics and Applications
International Journal of Computer Vision
SHREC'09 track: generic shape retrieval
EG 3DOR'09 Proceedings of the 2nd Eurographics conference on 3D Object Retrieval
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In this paper, we propose and evaluate a novel shape measurement describing the extent to which a 3D mesh is rectilinear. Since the rectilinearity measure corresponds proportionally to the ratio of the sum of three orthogonal projected areas and the surface area of the mesh, it has the following desirable properties: 1) the estimated rectilinearity is always a number from (0,1]; 2) the estimated rectilinearity is 1 if and only if the measured 3D shape is rectilinear; 3) there are shapes whose estimated rectilinearity is arbitrarily close to 0; 4) the measurement is invariant under scale, rotation, and translation; 5) the 3D objects can be either open or closed meshes, and we can also deal with poor quality meshes; 6) the measurement is insensitive to noise and stable under small topology errors; and 7) a Genetic Algorithm (GA) can be applied to calculate the approximate rectilinearity efficiently. We have also implemented two experiments of its applications. The first experiment shows that, in some cases, the calculation of rectilinearity provides a better tool for registering the pose of 3D meshes compared to PCA. The second experiment demonstrates that the combination of this measurement and other shape descriptors can significantly improve 3D shape retrieval performance.