FFTs for the 2-Sphere-Improvements and Variations
FFTs for the 2-Sphere-Improvements and Variations
Rotation invariant spherical harmonic representation of 3D shape descriptors
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
SMI '04 Proceedings of the Shape Modeling International 2004
Technical section: Second order 3D shape features: An exhaustive study
Computers and Graphics
3D invariants with high robustness to local deformations for automated pollen recognition
Proceedings of the 29th DAGM conference on Pattern recognition
3D object detection using a fast voxel-wise local spherical Fourier tensor transformation
Proceedings of the 32nd DAGM conference on Pattern recognition
Rotation-Invariant HOG Descriptors Using Fourier Analysis in Polar and Spherical Coordinates
International Journal of Computer Vision
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Spherical harmonics are widely used in 3D image processing due to their compactness and rotation properties. For example, it is quite easy to obtain rotation invariance by taking the magnitudes of the representation, similar to the power spectrum known from Fourier analysis. We propose a novel approach extending the spherical harmonic representation to tensors of higher order in a very efficient manner. Our approach utilises the so called tensorial harmonics [1] to overcome the restrictions to scalar fields. In this way it is possible to represent vector and tensor fields with all the gentle properties known from spherical harmonic theory. In our experiments we have tested our system by using the most commonly used tensors in three dimensional image analysis, namely the gradient vector, the Hessian matrix and finally the structure tensor. For comparable results we have used the Princeton Shape Benchmark [2] and a database of airborne pollen, leading to very promising results.