IEEE SIGNAL PROCESSING LETTERS, VOL. 21, NO. 3, MARCH 2014 321 Scale and Rotation Invariant Texture Classification Using Covariate Shift Methodology Ali Hassan, Farhan Riaz, and Arslan Shaukat Abstract—In this letter, we propose to tackle rotation and scale variance in texture classification at the machine learning level. This is achieved by using image descriptors that interpret these varia- tions as shifts in the feature vector. We model these variations as a covariate shift in the data. This shift is then reduced by minimising the Kullback–Leibler divergence between the true and estimated distributions using importance weights (IW). These IWs are used in support vector machines (SVMs) to formulate the IW-SVMs. The experimental results show that IW-SVMs exhibit good invari- ance characteristics and outperform other state-of-the-art classi- fication methods. The proposed methodology gives a generic solu- tion that can be applied to any texture descriptor that models the transformations as a shift in the feature vector. Index Terms—Covariate shift and support vector machines, ro- tation and scale invariance. I. INTRODUCTION T EXTURE is an important visual feature which plays a fundamental role in various computer vision and image processing related applications. It is generally regarded as a function of spatial variations in image intensities leading to image textures such as roughness, structuredness, dominant ori- entations etc. There are many different applications involving texture analysis such as medical imaging, remote sensing, document segmentation etc. [1]–[3]. Texture analysis has been studied thoroughly over the past decades and one of the issues that the researchers have encountered is rotation and scale invariant texture classification. Its need arises from the fact that in several applications such as medical imaging, aerial imaging etc., the imaging conditions are not controlled resulting in varying perspectives of viewing the same imaging site. With invariant texture analysis methods, the image classification would cater for these issues giving better classification results. The need of invariant texture classification has stimulated re- search on the design of several methods to this effect. Some au- thors such as [1]–[7], have proposed scale and rotation invariant classification methodologies, which mostly deal with this issue on the feature extraction layer and thus propose novel image Manuscript received February 27, 2013; revised November 06, 2013; ac- cepted December 18, 2013. Date of publication January 24, 2014; date of current version January 30, 2014. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Bo Hong The authors are with the Department of Computer Engineering, College of E&ME, National University of Sciences and Technology (NUST), Islamabad, Pakistan (e-mail: alihassan@ceme.nust.edu.pk; farhan.riaz@ceme.nust.edu.pk; arslanshaukat@ceme.nust.edu.pk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LSP.2014.2302576 features which are invariant to rotation and scale changes in the images. In this letter, we propose to tackle this issue of in- variant texture classification at the machine learning level by modelling the rotations and scaling of the images as the co- variate shift between the training and testing data. Our novel methodology would be applicable to all those feature extraction methods which interpret the image transformations as shifts in the resulting image features. The letter is organized as follows: the problem statement is given in Section II, the details of co- variate shift in Section III, the test bed and classification results in Section IV and Section V concludes this letter by giving the future directions of this research. II. PROBLEM STATEMENT We have extracted the texture features using state-of-the-art Gabor filter based homogeneous textures (HT). A Gabor filter is the product of a Gaussian function with a complex sinusoid. This forms a bandpass filter in the frequency domain, where the bandwidth and center frequency of the filter are controlled by the standard deviation of the Gaussian function and the fre- quency of complex sinusoid respectively. A Gabor filter bank having a number of bandpass filters, with varying center fre- quencies, bandwidths and orientations is controlled by the pa- rameters of Gabor wavelets. Assuming that the local texture of an image is spatially homogeneous, the HT descriptor can be obtained by concatenating the means and standard deviations of Gabor filter responses for each image [8]: (1) This HT descriptor has been used as one of the visual descriptors in MPEG-7 and is known to give good texture classification results. However, one of the major drawbacks of HT is that it is not rotation and scale invariant. It is shown in Fig. 1 that rotation and scaling in an image results in a shift in the corresponding HT features. Any machine learning algorithm will fail to give good classification results when an image is transformed with respect to its training image as the features would be shifted. In this letter, we propose to deal with this resultant shift in the HT feature vectors using covariate shift. This is a generic solution for those image descriptors, which perceive the image transformations as shifts in the feature vectors. III. INTRODUCTION TO COVARIATE SHIFT It is an implicit assumption in any system developed using machine learning that the input data is independently drawn from the distribution and the corresponding labels from the conditional distribution , in the training as well as the testing phase. A situation where the data is assumed to 1070-9908 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.