IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 9, NO. 10, OCTOBER 2000 1693 Texture Classification Using Logical Operators Vidya Manian, Ramón Vásquez, Senior Member, IEEE, and Praveen Katiyar Abstract—In this paper, a new algorithm for texture classifica- tion based on logical operators is presented. Operators constructed from logical building blocks are convolved with texture images. An optimal set of six operators are selected based on their texture dis- crimination ability. The responses are then converted to standard deviation matrices computed over a sliding window. Zonal sam- pling features are computed from these matrices. A feature selec- tion process is applied and the new set of features are used for tex- ture classification. Classification of several natural and synthetic texture images are presented demonstrating the excellent perfor- mance of the logical operator method. The computational superi- ority and classification accuracy of the algorithm is demonstrated by comparison with other popular methods. Experiments with dif- ferent classifiers and feature normalization are also presented. The Euclidean distance classifier is found to perform best with this algo- rithm. The algorithm involves only convolutions and simple arith- metic in the various stages which allows faster implementations. The algorithm is applicable to different types of classification prob- lems which is demonstrated by segmentation of remote sensing im- ages, compressed and reconstructed images and industrial images. Index Terms—Image classification, logical operators, texture analysis, zonal filtering. I. INTRODUCTION T EXTURE classification is an image processing technique by which different regions of an image are identified based on texture properties. This process plays an important role in many industrial, biomedical and remote sensing appli- cations. Early work utilized statistical and structural methods for texture feature extraction [1]–[4]. Gaussian Markov random field (GMRF) and Gibbs distribution texture models were developed and used for texture recognition [5], [6]. Power spectral methods [1] using the Fourier spectrum have also been used. DCT, Walsh–Hadamard, and DHT have been used for recognition of two-dimensional binary patterns [7]. One of the major developments recently in texture segmentation has been the use of multiresolution and multichannel descriptions [8] of the texture images. This description provides information about the image contained in ever smaller regions of the frequency domain, and thus provides a powerful tool for the discrimination of similar textures. The use of scale-space-fil- tering is equivalent to a decomposition of the image in terms of wavelets. Several wavelet transform algorithms such as the Manuscript received February 4, 1999; revised May 10, 2000. This work was supported in part by the National Science Foundation under Grant CDA 9417659, NASA under Grants NCCW-0088 and NCC5340, and the Department of Electrical and Computer Engineering, University of Puerto Rico, Mayagüez. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Josiane B. Zerubia. The authors are with the Department of Electrical and Computer Engi- neering, University of Puerto Rico, Mayagüez Campus, Puerto Rico (e-mail: reve@ece.uprm.edu). Publisher Item Identifier S 1057-7149(00)07592-8. pyramidal and tree structured wavelet transforms [9]–[12], Gabor filters [13], and the Haar [14] basis functions have been used for multiresolution and multichannel texture classifica- tion/segmentation. Laws [15] proposed a simple scheme which used local linear transformations and energy computation to extract texture features. This simple scheme often gives good results but is not consistent in performance. The statistical methods share one common weakness, of primarily focusing on the coupling between image pixels on a single scale and are also computationally intensive processes. Logical operators have been used for Boolean analysis, minimization, spectral layered network decomposition, spectral translation synthesis, image coding, cryptography and commu- nication. Logical systems considered in this work are logical Hadamard transform, adding and arithmetic transforms and logical operators such as equivalence, negation, and conjunc- tion. A family of all essential RADIX-2 addition/subtraction transforms [16] has been developed. One of it is the well known Hadamard transform, the other is called arithmetic trans- form when applied to binary vectors. The third is the adding transform. The arithmetic and adding transforms are based on addition/subtraction of real numbers and are counterparts of generalized Reed Muller canonical expressions based on modulo-2 algebra. Fast computer implementation of these two transforms for logic design is presented in [17], and ways of generation of forward and inverse fast transform for orthogonal arithmetic and adding transform have been developed [18]. In [19], a new algorithm for computing Hadamard transform is presented. For simplicity, all the above logical systems are called operators in this work. Logical operators have been used recently for image compression [20]. As pointed out, fast algorithms [21] are already available for implementation of these schemes. But, surprisingly their usefulness in image classification has not been exploited. This is the first paper in open literature that applies the logical systems for applications other than in logical synthesis. This work is a unique attempt in the following respects: 1) construction of a texture feature space using logical oper- ators; 2) the algorithm is computationally attractive with excellent performance over a wide variety of images. This paper is organized as follows. Logical operators are de- scribed in Section II. In Section III, texture analysis using the operators is explained and the algorithm for texture classifica- tion is presented. In Section IV experimental results of clas- sifying different types of images and comparison with other methods are presented. Section V presents application of the al- gorithm to segmentation problems. Finally, Section VI gives the conclusions and a few pointers on future directions. 1057–7149/00$10.00 © 2000 IEEE