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Fast Rotation Invariant 3D Feature Computation Utilizing Efficient Local Neighborhood Operators
Aug. 2012 (vol. 34 no. 8)
pp. 1563-1575
O. Ronneberger, Dept. of Comput. Sci., Univ. of Freiburg, Freiburg, Germany
T. Brox, Dept. of Comput. Sci., Univ. of Freiburg, Freiburg, Germany
T. Schmidt, Dept. of Comput. Sci., Univ. of Freiburg, Freiburg, Germany
M. Reisert, Dept. of Radiol., Med. Phys., Univ. Med. Center Freiburg, Freiburg, Germany
H. Skibbe, Dept. of Radiol., Med. Phys., Univ. Med. Center Freiburg, Freiburg, Germany
H. Burkhardt, Dept. of Comput. Sci., Univ. of Freiburg, Freiburg, Germany
We present a method for densely computing local rotation invariant image descriptors in volumetric images. The descriptors are based on a transformation to the harmonic domain, which we compute very efficiently via differential operators. We show that this fast voxelwise computation is restricted to a family of basis functions that have certain differential relationships. Building upon this finding, we propose local descriptors based on the Gaussian Laguerre and spherical Gabor basis functions and show how the coefficients can be computed efficiently by recursive differentiation. We exemplarily demonstrate the effectiveness of such dense descriptors in a detection and classification task on biological 3D images. In a direct comparison to existing volumetric features, among them 3D SIFT, our descriptors reveal superior performance.

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Index Terms:
image classification,computer graphics,differential equations,3D SIFT,fast rotation invariant 3D feature computation,efficient local neighborhood operators,local rotation invariant image descriptors,volumetric image,harmonic domain,differential operators,fast voxelwise computation,differential relationship,Gaussian Laguerre,spherical Gabor basis function,recursive differentiation,classification task,biological 3D image,Harmonic analysis,Tensile stress,Three dimensional displays,Vectors,Polynomials,Solids,Couplings,Gauss-Laguerre functions.,Voxel classification,local 3D descriptors,rotation invariants,spherical harmonics
Citation:
O. Ronneberger, T. Brox, T. Schmidt, M. Reisert, H. Skibbe, H. Burkhardt, "Fast Rotation Invariant 3D Feature Computation Utilizing Efficient Local Neighborhood Operators," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 8, pp. 1563-1575, Aug. 2012, doi:10.1109/TPAMI.2011.263
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