Context-free attentional operators: the generalized symmetry transform
International Journal of Computer Vision - Special issue on qualitative vision
Detecting Symmetry in Grey Level Images: The Global Optimization Approach
International Journal of Computer Vision
Robust Rotation Angle Estimator
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introductory Techniques for 3-D Computer Vision
Introductory Techniques for 3-D Computer Vision
A Reflective Symmetry Descriptor
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
The Angular Difference Function and Its Application to Image Registration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detecting Rotational Symmetries
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Accurate detection of symmetries in 3D shapes
ACM Transactions on Graphics (TOG)
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Discovering structural regularity in 3D geometry
ACM SIGGRAPH 2008 papers
Global intrinsic symmetries of shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
Efficient symmetry detection using local affine frames
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Full and Partial Symmetries of Non-rigid Shapes
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detecting symmetry and symmetric constellations of features
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Discovering texture regularity as a higher-order correspondence problem
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Volume Registration Using the 3-D Pseudopolar Fourier Transform
IEEE Transactions on Signal Processing
Finding axes of symmetry from potential fields
IEEE Transactions on Image Processing
Pseudopolar-based estimation of large translations, rotations, and scalings in images
IEEE Transactions on Image Processing
A signal processing approach to symmetry detection
IEEE Transactions on Image Processing
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Symmetry detection and analysis in 3D images is a fundamental task in a gamut of scientific fields such as computer vision, medical imaging and pattern recognition to name a few. In this work, we present a computational approach to 3D symmetry detection and analysis. Our analysis is conducted in the Fourier domain using the pseudo-polar Fourier transform. The pseudo-polar representation enables to efficiently and accurately analyze angular volumetric properties such as rotational symmetries. Our algorithm is based on the analysis of the angular correspondence rate of the given volume and its rotated and rotated-inverted replicas in their pseudo-polar representations. We also derive a novel rigorous analysis of the inherent constraints of 3D symmetries via groups-theory based analysis. Thus, our algorithm starts by detecting the rotational symmetry group of a given volume, and the rigorous analysis results pave the way to detect the rest of the symmetries. The complexity of the algorithm is O(N 3log驴(N)), where N脳N脳N is the volumetric size in each direction. This complexity is independent of the number of the detected symmetries. We experimentally verified our approach by applying it to synthetic as well as real 3D objects.