Determination of the orientation of 3D objects using spherical harmonics
Graphical Models and Image Processing
Extracting group transformations from image moments
Computer Vision and Image Understanding
International Journal of Computer Vision
Catadioptric Projective Geometry
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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Rotation invariant spherical harmonic representation of 3D shape descriptors
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
ACM SIGGRAPH 2004 Papers
Rotation Estimation from Spherical Images
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Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
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CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
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International Journal of Robotics Research
Cross-Correlation and Rotation Estimation of Local 3D Vector Field Patches
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Eigendecomposition of images correlated on S1, S2, and SO(3) using spectral theory
IEEE Transactions on Image Processing
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SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
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Proceedings of the 29th DAGM conference on Pattern recognition
Spherical Correlation of Visual Representations for 3D Model Retrieval
International Journal of Computer Vision
On azimuthally symmetric 2-sphere convolution
Digital Signal Processing
Rotation estimation and vanishing point extraction by omnidirectional vision in urban environment
International Journal of Robotics Research
Orientation and pose estimation for panoramic imagery
Machine Graphics & Vision International Journal - Special issue on Image Databases
Bubble space and place representation in topological maps
International Journal of Robotics Research
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This paper addresses the problem of rotation estimation directly from images defined on the sphere and without correspondence. The method is particularly useful for the alignment of large rotations and has potential impact on 3D shape alignment. The foundation of the method lies in the fact that the spherical harmonic coefficients undergo a unitary mapping when the original image is rotated. The correlation between two images is a function of rotations and we show that it has an SO(3)-Fourier transform equal to the pointwise product of spherical harmonic coefficients of the original images. The resolution of the rotation space depends on the bandwidth we choose for the harmonic expansion and the rotation estimate is found through a direct search in this 3D discretized space. A refinement of the rotation estimate can be obtained from the conservation of harmonic coefficients in the rotational shift theorem. A novel decoupling of the shift theorem with respect to the Euler angles is presented and exploited in an iterative scheme to refine the initial rotation estimates. Experiments show the suitability of the method for large rotations and the dependence of the method on bandwidth and the choice of the spherical harmonic coefficients.