This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Fast Rotation Invariant 3D Feature Computation Utilizing Efficient Local Neighborhood Operators
Aug. 2012 (vol. 34 no. 8)
pp. 1563-1575
ASCII Text
x 
 
H. Burkhardt, T. Brox, O. Ronneberger, T. Schmidt, M. Reisert, H. Skibbe, "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.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2011.263,
author = {H. Burkhardt and T. Brox and O. Ronneberger and T. Schmidt and M. Reisert and H. Skibbe},
title = {Fast Rotation Invariant 3D Feature Computation Utilizing Efficient Local Neighborhood Operators},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {34},
number = {8},
issn = {0162-8828},
year = {2012},
pages = {1563-1575},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2011.263},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Fast Rotation Invariant 3D Feature Computation Utilizing Efficient Local Neighborhood Operators
IS - 8
SN - 0162-8828
SP1563
EP1575
EPD - 1563-1575
A1 - H. Burkhardt,
A1 - T. Brox,
A1 - O. Ronneberger,
A1 - T. Schmidt,
A1 - M. Reisert,
A1 - H. Skibbe,
PY - 2012
KW - image classification
KW - computer graphics
KW - differential equations
KW - 3D SIFT
KW - fast rotation invariant 3D feature computation
KW - efficient local neighborhood operators
KW - local rotation invariant image descriptors
KW - volumetric image
KW - harmonic domain
KW - differential operators
KW - fast voxelwise computation
KW - differential relationship
KW - Gaussian Laguerre
KW - spherical Gabor basis function
KW - recursive differentiation
KW - classification task
KW - biological 3D image
KW - Harmonic analysis
KW - Tensile stress
KW - Three dimensional displays
KW - Vectors
KW - Polynomials
KW - Solids
KW - Couplings
KW - Gauss-Laguerre functions.
KW - Voxel classification
KW - local 3D descriptors
KW - rotation invariants
KW - spherical harmonics
VL - 34
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
H. Burkhardt, Dept. of Comput. Sci., Univ. of Freiburg, Freiburg, Germany
T. Brox, Dept. of Comput. Sci., Univ. of Freiburg, Freiburg, Germany
O. Ronneberger, 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
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.

[1] Q. Wang, O. Ronneberger, and H. Burkhardt, "Rotational Invariance Based on Fourier Analysis in Polar and Spherical Coordinates," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 31, no. 9, pp. 1715-1722, Sept. 2009.
[2] H. Skibbe, M. Reisert, Q. Wang, O. Ronneberger, and H. Burkhardt, "Fast Computation of 3D Spherical Fourier Harmonic Descriptors—A Complete Orthonormal basis for a Rotational Invariant Representation of Three-Dimensional Objects," Proc. IEEE Int'l Conf. Computer Vision Workshop, 2009.
[3] M. Kazhdan, T. Funkhouser, and S. Rusinkiewicz, "Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors," Proc. Eurographics/ACM Siggraph Symp. Geometry Processing, pp. 156-164, 2003.
[4] J. Fehr and H. Burkhardt, "Phase Based 3D Texture Features," Proc. 28th Conf. Pattern Recognition, pp. 263-272, 2006.
[5] J. Koenderink and A. van Doorn, "Generic Neighborhood Operators," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 6, pp. 597-605, June 1992.
[6] O. Ronneberger, J. Fehr, and H. Burkhardt, "Voxel-Wise Gray Scale Invariants for Simultaneous Segmentation and Classification," Proc. DAGM Conf. Pattern Recognition, pp. 85-92, 2005.
[7] M. Reisert and H. Burkhardt, "Harmonic Filters for Generic Feature Detection in 3D," Proc. DAGM Symp. Pattern Recognition, pp. 131-140, 2009.
[8] H. Skibbe, M. Reisert, T. Schmidt, K. Palme, O. Ronneberger, and H. Burkhardt, "3D Object Detection Using a Fast Voxel-Wise Local Spherical Fourier Tensor Transformation," Proc. DAGM Conf. Pattern Recognition, pp. 412-421, 2010.
[9] M. Reisert and H. Burkhardt, "Spherical Tensor Calculus for Local Adaptive Filtering," Tensors in Image Processing and Computer Vision, S. Aja-Fernández, R. de Luis García, D. Tao, and X. Li, eds., Springer, 2009.
[10] M. Rose, Elementary Theory of Angular Momentum. Dover Publications, 1995.
[11] R. Kondor, "Group Theoretical Methods in Machine Learning," PhD dissertation, Columbia Univ., 2008.
[12] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, 1964.
[13] D.M. Brink and G. Satchler, Angular Momentum. Oxford Science Publications, 1993.
[14] D. Gabor, "Theory of Communication," J. IEE, vol. 93, pp. 429-441, 1846.
[15] M. Reisert and H. Burkhardt, "Complex Derivative Filters," IEEE Trans. Image Processing, vol. 17, no. 12, pp. 2265-2274, Dec. 2008.
[16] O. Matsuoka, "Molecular Integrals over Real Solid Spherical Gaussian-Type Functions," J. Chemical Physics, vol. 108, pp. 1063-1067, 1998.
[17] M.M. Chow and L.-Y. Chiu, "The Addition Theorem of Spherical Laguerre Gaussian Functions and Its Application in Molecular Integrals," J. Molecular Structure: THEOCHEM, vol. 536, pp. 263-267, Feb. 2001.
[18] T. Lindeberg, "Scale-Space for Discrete Signals," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 3, pp. 234-254, Mar. 1990.
[19] M.M. Lue-YungChow Chiu, "Fourier Transform of Spherical Laguerre Gaussian Functions and Its Application in Molecular Integrals," Int'l J. Quantum Chemistry vol. 73, pp. 265-273, 1999.
[20] L. Sorgi, N. Cimminiello, and A. Neri, "Keypoints Selection in the Gauss Laguerre Transformed Domain," Proc. British Machine Vision Conf., pp. 539-547, 2006.
[21] J. Daugman, "Complete Discrete 2-D Gabor Transforms by Neural Networks for Image Analysis and Compression," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 36, no. 7, pp. 1169-1179, July 1988.
[22] J. Daugman, "Two-Dimensional Spectral Analysis of Cortical Receptive Field Profiles," Vision Research, vol. 20, no. 10, pp. 847-856, 1980.
[23] A.C. Bovik, M. Clark, and W.S. Geisler, "Multichannel Texture Analysis Using Localized Spatial Filters," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 55-73, Jan. 1990.
[24] A.K. Jain and F. Farrokhnia, "Unsupervised Texture Segmentation Using Gabor Filters," Proc. IEEE Int'l Conf. Systems, Man and Cybernetics, pp. 14-19, 1990.
[25] R. Sandler and M. Lindenbaum, "Optimizing Gabor Filter Design for Texture Edge Detection and Classification," Int'l J. Computer Vision, vol. 84, no. 3, pp. 308-324, 2009.
[26] Z. Qian, D. Metaxas, and L. Axel, "Extraction and Tracking of MRI Tagging Sheets Using a 3D Gabor Filter Bank," Proc. Int'l Conf. IEEE Eng. Medicine Biology Soc., vol. 1, 2006.
[27] J. Bigun, "Speed, Frequency, and Orientation Tuned 3-D Gabor Filter Banks and Their Design," Proc. Int'l Conf. Pattern Recognition, pp. C:184-187, 1994.
[28] J.J. Thomson, "On the Structure of the Atom: An Investigation of the Stability and Periods of Oscillation of a Number of Corpuscles Arranged at Equal Intervals around the Circumference of a Circle; with Application of the Results to the Theory of Atomic Structure," Philosophical Magazine Series 6, vol. 7, no. 39, pp. 237-265, Mar. 1904.
[29] H. Farid and E.P. Simoncelli, "Differentiation of Discrete Multidimensional Signals," IEEE Trans. Image Processing, vol. 13, no. 4, pp. 496-508, Apr. 2004.
[30] M. Frigo and S.G. Johnson, "The Design and Implementation of FFTW3," Proc. IEEE, special issue on program generation, optimization, and platform adaptation, vol. 93, no. 2, pp. 216-231, Feb. 2005.
[31] S. Allaire, J. Kim, S. Breen, D. Jaffray, and V. Pekar, "Full Orientation Invariance and Improved Feature Selectivity of 3D SIFT with Application to Medical Image Analysis," Proc. IEEE CS Workshop Math. Methods in Biomedical Image Analysis, pp. 1-8, 2008.
[32] L. Breiman, "Random Forests," Machine Learning, vol. 45, pp. 5-32, Oct. 2001.
[33] P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser, "The Princeton Shape Benchmark," Proc. Int'l Conf. Shape Modeling and Applications, pp. 167-178, 2004.

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:
H. Burkhardt, T. Brox, O. Ronneberger, T. Schmidt, M. Reisert, H. Skibbe, "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
Usage of this product signifies your acceptance of the Terms of Use.