The generalization of the R-transform for invariant pattern representation

The beneficial properties of the Radon transform make it a useful intermediate representation for the extraction of invariant features from pattern images for the purpose of indexing/matching. This paper revisits the problem of Radon image utilization with a generic view on a popular Radon transform-based transform and pattern descriptor, the R-transform and R-signature, bringing in a class of transforms and descriptors spatially describing patterns at all directions and at different levels, while maintaining the beneficial properties of the conventional R-transform and R-signature. The domain of this class, which is delimited due to the existence of singularities and the effect of sampling/quantization and additive noise, is examined. Moreover, the ability of the generic R-transform to encode the dominant directions of patterns is also discussed, adding to the robustness to additive noise of the generic R-signature. The stability of dominant direction encoding by the generic R-transform and the superiority of the generic R-signature over existing invariant pattern descriptors on grayscale and binary noisy datasets have been confirmed by experiments.

[1]  J. Joseph,et al.  Fourier transforms , 2012 .

[2]  Ehud Rivlin,et al.  Applying algebraic and differential invariants for logo recognition , 1996, Machine Vision and Applications.

[3]  Ernest Valveny,et al.  Optimal Classifier Fusion in a Non-Bayesian Probabilistic Framework , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Hamid Soltanian-Zadeh,et al.  Rotation-invariant multiresolution texture analysis using Radon and wavelet transforms , 2005, IEEE Transactions on Image Processing.

[5]  Sameer A. Nene,et al.  Columbia Object Image Library (COIL100) , 1996 .

[6]  P. Wintz,et al.  An efficient three-dimensional aircraft recognition algorithm using normalized fourier descriptors , 1980 .

[7]  Salvatore Tabbone,et al.  A Geometric Invariant Shape Descriptor Based on the Radon, Fourier, and Mellin Transforms , 2010, 2010 20th International Conference on Pattern Recognition.

[8]  James F. Boyce,et al.  The Radon transform and its application to shape parametrization in machine vision , 1987, Image Vis. Comput..

[9]  Laurent Wendling,et al.  A new shape descriptor defined on the Radon transform , 2006, Comput. Vis. Image Underst..

[10]  Bin Xiao,et al.  Scaling and rotation invariant analysis approach to object recognition based on Radon and Fourier-Mellin transforms , 2007, Pattern Recognit..

[11]  Gunilla Borgefors,et al.  Distance transformations in digital images , 1986, Comput. Vis. Graph. Image Process..

[12]  Ronald R. Coifman,et al.  Fast Slant Stack: a Notion of Radon Transform for Data in a Cartesian Grid Which Is Rapidly Computible, Algebraically Exact, Geometrically Faithful and Invertible , 2001 .

[13]  Salvatore Tabbone,et al.  Text extraction from graphical document images using sparse representation , 2010, DAS '10.

[14]  A. Poularikas.  The transforms and applications handbook , 2000 .

[15]  Hjouj Hjouj,et al.  Identification of Reflected, Scaled, Translated, and Rotated Objects From Their Radon Projections , 2008, IEEE Transactions on Image Processing.

[16]  Alexander Poularikas,et al.  The Mellin Transform , 1998 .

[17]  Violet F. Leavers.  Use of the Two-Dimensional Radon Transform to Generate a Taxonomy of Shape for the Characterization of Abrasive Powder Particles , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  M. Teague.  Image analysis via the general theory of moments , 1980 .

[19]  P. Mahalanobis.  On the generalized distance in statistics , 1936 .

[20]  Richard O. Duda,et al.  Use of the Hough transformation to detect lines and curves in pictures , 1972, CACM.

[21]  Violet F. Leavers,et al.  Use of the Radon transform as a method of extracting information about shape in two dimensions , 1992, Image Vis. Comput..

[22]  Guojun Lu,et al.  Shape-based image retrieval using generic Fourier descriptor , 2002, Signal Process. Image Commun..

[23]  Alexander Kadyrov,et al.  The Trace Transform and Its Applications , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Salvatore Tabbone,et al.  Generic R-transform for invariant pattern representation , 2011, 2011 9th International Workshop on Content-Based Multimedia Indexing (CBMI).

[25]  Mehmet Ali Aktas.  Shape descriptors , 2009, Encyclopedia of Database Systems.

[26]  Rama Chellappa,et al.  Appearance Modeling Using a Geometric Transform , 2009, IEEE Transactions on Image Processing.

[27]  Alireza Khotanzad,et al.  Invariant Image Recognition by Zernike Moments , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Salvatore Tabbone,et al.  Shape-Based Image Retrieval Using a New Descriptor Based on the Radon and Wavelet Transforms , 2010, 2010 20th International Conference on Pattern Recognition.

[29]  Ying Wang,et al.  Human Activity Recognition Based on R Transform , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[30]  Richard Souvenir,et al.  Viewpoint Manifolds for Action Recognition , 2009, EURASIP J. Image Video Process..

[31]  Martin L. Brady,et al.  A Fast Discrete Approximation Algorithm for the Radon Transform , 1998, SIAM J. Comput..

[32]  Salvatore Tabbone,et al.  Invariant pattern recognition using the RFM descriptor , 2012, Pattern Recognit..

[33]  Yan Qiu Chen,et al.  Invariant Description and Retrieval of Planar Shapes Using Radon Composite Features , 2008, IEEE Transactions on Signal Processing.

[34]  S. Deans.  The Radon Transform and Some of Its Applications , 1983 .

[35]  JEFFREY WOOD,et al.  Invariant pattern recognition: A review , 1996, Pattern Recognit..

[36]  Cc Grosjean.  The Mellin Transform , 2018, Handbook of Formulas and Tables for Signal Processing.

[37]  H H Arsenault,et al.  Rotation-invariant digital pattern recognition using circular harmonic expansion. , 1982, Applied optics.

[38]  Guojun Lu,et al.  Review of shape representation and description techniques , 2004, Pattern Recognit..

[39]  W. A. Götz,et al.  A fast digital Radon transform--An efficient means for evaluating the Hough transform , 1995, Pattern Recognit..

[40]  Zhuowen Tu,et al.  Learning Context-Sensitive Shape Similarity by Graph Transduction , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.