Rotation-invariant multiresolution texture analysis using ra

IEEE TRANSACTIONS ON IMAGE PROCESSING,VOL.14,NO.6,JUNE 2005783

Rotation-Invariant Multiresolution Texture Analysis

Using Radon and Wavelet Transforms

Kourosh Jafari-Khouzani and Hamid Soltanian-Zadeh ,Senior Member,IEEE

Abstract—A new rotation-invariant texture-analysis technique using Radon and wavelet transforms is proposed.This technique utilizes the Radon transform to convert the rotation to translation and then applies a translation-invariant wavelet transform to the result to extract texture features.

A -nearest neighbors classi?er is employed to classify texture patterns.A method to ?nd the op-timal number of projections for the Radon transform is proposed.It is shown that the extracted features generate an ef?cient orthog-onal feature space.It is also shown that the proposed features ex-tract both of the local and directional information of the texture patterns.The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step.To test and evaluate the method,we em-ployed several sets of textures along with different wavelet bases.Experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent texture-analysis methods.

Index Terms—Radon transform,rotation invariance,texture analysis,wavelet transform.

I.I NTRODUCTION

T

EXTURE analysis is an important issue in image processing with many applications including medical imaging,remote sensing,content-based image retrieval,and document segmentation.Over the last three decades,texture analysis has been widely studied and many texture classi?ca-tion techniques have been proposed in the literature.Ideally,texture analysis should be invariant to translation and rotation.However,most of the proposed techniques assume that texture has the same orientation,which is not always the case.

Recently,rotation-invariant approaches have been the focus of interest,and different groups have proposed various rota-tion-invariant texture-analysis methods [1].Davis [2]uses po-larogram,which is a statistical function,de?ned on the co-oc-currence matrix with a ?xed displacement vector and variable orientation.Pietikainen et al.[3]present a collection of features based on center-symmetric auto-correlation,local binary pat-tern,and gray-level difference to describe the texture,most of

Manuscript received December 10,2003;revised August 16,2004.This work was supported in part by NIH Grant R01EB002450.The associate editor co-ordinating the review of this manuscript and approving it for publication was Dr.Ivan W.Selesnick.

K.Jafari-Khouzani is with the Radiology Image Analysis Laboratory,Henry Ford Health System,Detroit,MI 48202USA,and also with the Department of Computer Science,Wayne State University,Detroit,MI 48202USA (e-mail:1-kjafari@f11dc3b8fd0a79563c1e72e4).

H.Soltanian-Zadeh is with the Radiology Image Analysis Laboratory,Henry Ford Health System,Detroit,MI 48202USA,and also with the Control and In-telligent Processing Center of Excellence,Electrical and Computer Engineering Department,University of Tehran,Tehran,Iran (e-mail:hamids@f11dc3b8fd0a79563c1e72e4;hszadeh@ut.ac.ir).

Digital Object Identi?er 10.1109/TIP.2005.847302

which locally invariant to rotation.Ojala et al.[4]use binary patterns de?ned for circularly symmetric neighborhood sets to describe the texture.Kashyap and Khotanzad [5]have devel-oped a circular symmetric autoregressive random ?eld (CSAR)model to solve the problem.In this method,for each pixel,the neighborhood points are de?ned on only one circle around the pixel.Mao and Jain [6]present rotation-invariant SAR (RISAR)model based on CSAR model,in which the neighborhood points of a pixel are de?ned on several circles around it.In all of these methods,a neighborhood is utilized,which captures only the local variation information of the texture and overlooks the global information of texture.

Markov random ?eld (MRF)has been used by researchers for texture analysis.Cohen et al.[7]model texture as Gaussian Markov random ?eld and use the maximum likelihood tech-nique to estimate the coef?cients and rotation angles.The problem of this method is that the likelihood function is highly nonlinear and local maxima may exist.Chen and Kundu [8]use multichannel subband decomposition and a hidden Markov model (HMM)to solve the problem.They use a quadrature mirror ?lter to decompose the image into subbands and model the features of subbands by an HMM.In their method,textures with different orientations are assumed to be in the same class.Since textures with different orientations create different signal components for each subband,this increases the variations in the feature space.Hence,as the number of classes increases,the performance may deteriorate.

Circular–Mellin features [9]are created by decomposing the image into a combination of harmonic components in its polar form and are shown to be rotation and scale invariant.Zernike moments [10]are used to create rotation,scale,and illumina-tion-invariant color texture characterization.Greenspan et al.[11]use the steerable pyramid model to get rotation invariance.They extract features from the outputs of oriented ?lters and de-?ne a

curve

across the orientation space.Since the rota-tion of the image corresponds to the translation

of

across ,DFT magnitude

of (which is translation invariant)pro-vides rotation-invariant features.

Recently,multiresolution approaches such as Gabor ?lters,wavelet transforms,and wavelet frames have been widely studied and used for texture characterization.Wavelets provide spatial/frequency information of textures,which are useful for classi?cation and segmentation.However,wavelet transform is not translation and rotation invariant.Several attempts have been made to use the wavelet transform for rotation-invariant texture analysis.The proposed methods may use a prepro-cessing step to make the analysis invariant to rotation or use rotated wavelets and exploit the steerability to calculate the

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