3D Rotation-Invariant Description from Tensor Operation on Spherical HOG Field

Rotation-invariant descriptions are required in many 3D volumetric image analysis tasks. The histogram-of-oriented-gradient (HOG) is widely used in 2D images and proves to be a very robust local description. This paper concentrates on how to use the HOG feature in 3D volumetric images when rotation-invariance is concerned. This is challenging because of the complexity of 3D rotations. We present a decent solution based on the spherical harmonics theory which is an effective tool for analysing 3D rotations, together with the spherical tensor operations which explore high order tensor information in spherical coordinates. The design is quite general and could be used for different applications. It achieves high scores on Princeton Shape Benchmark and SHREC 2009 Generic Shape Benchmark, and also produces promising results when applying on biological microscopy images.

[1]  Hans Burkhardt,et al.  A Bag of Features Approach for 3D Shape Retrieval , 2009, ISVC.

[2]  Qing Wang,et al.  3D Invariants with High Robustness to Local Deformations for Automated Pollen Recognition , 2007, DAGM-Symposium.

[3]  Thomas A. Funkhouser,et al.  The Princeton Shape Benchmark , 2004, Proceedings Shape Modeling Applications, 2004..

[4]  Szymon Rusinkiewicz,et al.  Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors , 2003, Symposium on Geometry Processing.

[5]  Janis Fehr.  Local Rotation Invariant Patch Descriptors for 3D Vector Fields , 2010, 2010 20th International Conference on Pattern Recognition.

[6]  Vladimir Pekar,et al.  Full orientation invariance and improved feature selectivity of 3D SIFT with application to medical image analysis , 2008, 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops.

[7]  Qing Wang,et al.  Rotational Invariance Based on Fourier Analysis in Polar and Spherical Coordinates , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Petros Daras,et al.  SHREC 2009 - Generic Shape Retrieval Contest , 2009 .

[9]  M. E. Rose.  Elementary Theory of Angular Momentum , 1957 .

[10]  Hans Burkhardt,et al.  Increasing the Dimension of Creativity in Rotation Invariant Feature Design Using 3D Tensorial Harmonics , 2009, DAGM-Symposium.

[11]  Hans Burkhardt,et al.  Harmonic Filters for 3D Multichannel Data: Rotation Invariant Detection of Mitoses in Colorectal Cancer , 2010, IEEE Transactions on Medical Imaging.

[12]  Bill Triggs,et al.  Histograms of oriented gradients for human detection , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[13]  William T. Freeman,et al.  Latent hierarchical structural learning for object detection , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[14]  David A. McAllester,et al.  Object Detection with Discriminatively Trained Part Based Models , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Robin Green,et al.  Spherical Harmonic Lighting: The Gritty Details , 2003 .

[16]  Hans Burkhardt,et al.  Spherical Tensor Calculus for Local Adaptive Filtering , 2009, Tensors in Image Processing and Computer Vision.

[17]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[18]  Andrea J. van Doorn,et al.  Generic Neighborhood Operators , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Cordelia Schmid,et al.  A Spatio-Temporal Descriptor Based on 3D-Gradients , 2008, BMVC.

[20]  Najla Megherbi Bouallagu,et al.  Object Recognition using 3D SIFT in Complex CT Volumes , 2010, BMVC.

[21]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

[22]  Hans Burkhardt,et al.  Efficient Tensor Voting with 3D tensorial harmonics , 2008, 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops.

[23]  Hans Burkhardt,et al.  Voxel-Wise Gray Scale Invariants for Simultaneous Segmentation and Classification , 2005, DAGM-Symposium.

[24]  Thomas Bülow,et al.  Spherical Diffusion for 3D Surface Smoothing , 2004, 3DPVT.