Multiscale texture classification using dual-tree complex wavelet transform

Abstract

This paper presents a multiscale texture classifier that exploits the Gabor-like properties of the dual-tree complex wavelet transform, shift invariance and six directional subbands at each scale, and uses a feature vector comprising of a variance and an entropy at different scales of each of the directional subbands. Experimental results demonstrate its robustness against noise and a higher classification accuracy than a discrete wavelet transform based classifier.

Introduction

Numerous methods have been proposed for texture feature extraction and classification (Tuceryan and Jain, 1993). A comparative study (Randen and Husoy, 1999) suggests that for texture classification it is preferable to extract texture features by learning discriminative texture features from texture samples. Most approaches to texture analysis use a hybrid of different methodologies, making it difficult to categorize them. By considering the main methodology used in texture analysis, we can loosely classify them into three main categories (Kim and Kang, 2007).

Statistical approach to texture analysis is motivated from the findings that the human visual system recognizes textured objects based on the statistical distribution of their image grey-levels via first-order, second-order, or higher-order statistics (Julesz et al., 1973, Julesz, 1962). The most commonly used method is the grey-level co-occurrence matrix (Haralick et al., 1973), which estimates texture properties related to the second-order statistics. It is worth pointing out that although statistical textural features are usually used to classify texture regions, most of them are extracted explicitly or implicitly based on a statistical representation of texture.

Model based approach to texture analysis views textures as mathematical image perceptual models. The key problems with this approach is how to choose a suitable model for characterizing the selected textures and how to estimate the parameters of these models based on some criteria. Another concern is that an intensive computation is usually required to determine the model parameters. The derived parameters are used as the features to capture the perceived essential qualities of the texture. Commonly used texture models include the autoregressive model (AR) (Randen and Husoy, 1999, Cariou and Chehdi, 2008), Markov random field (MRF) (Cohen et al., 1991), and Wold decomposition model (Liu and Picard, 1996). AR model is a linear model derived from the training samples via a least-mean-squares fitting. Using cliques MRF attempts to describe the relationship of texture pixels within a region of interest. Its optimization is based on maximizing the posteriori probability. Wold decomposition model is a perceptual texture model that decomposes textures into deterministic and non-deterministic fields, that correspond to regular textural component and random textural component, respectively. Usually, these models can capture the local contextual information in a texture image. However, the model parameters are optimized based on an image representative features instead of its discriminative features.

Signal processing approach to texture analysis includes multichannel Gabor filter, wavelet transform, finite impulse response (FIR) filter, etc. Gabor filter is appealing because of its simplicity and support from neurophysiological experiments (Faugeras, 1978). Gabor filters have been used for texture segmentation despite being based on texture reconstruction (Jain and Farrokhnia, 1991, Arivazhagan et al., 2006). A general filter bank is often too large because it is designed to capture general texture properties. However, textures can be classified by only a small set of filters, which gives rise to the filter selection problem. For example, a neural network system has been used to select a minimum set of Gabor filters for texture discrimination while keeping the performance at an acceptable level compared to the case without filter selection (Jain and Karu, 1996). In these filtering methods, texture images are usually decomposed into several feature images through projection by using a set of selected filters. These filters are often based on representation such that textures are reconstructed with the minimum information loss. On the other hand, our proposed approach extracts features that maximizes the separation or discrimination among different textures. The wavelet based methods are similar to Gabor based methods with the Gabor filters replaced by Discrete Wavelet Transform (DWT) (Wang et al., 1998, Laine and Fan, 1993, Arivazhagan and Ganesan, 2003a, Arivazhagan and Ganesan, 2003b, Muneeswarana et al., 2005, Kim and Kang, 2007, Kokare et al., 2007, Hiremath and Shivashankar, 2008). Since the DWT is shift variance, a shift in the signal degrades the performance of DWT based classifiers.

For the purpose of pattern discrimination, linear Fisher discriminant (Duda et al., 2001) can incorporate feature extraction, dimensionality reduction and discrimination. However, its linear optimal solution heavily depends on the assumption that the input patterns have equal covariance matrix. This assumption is usually not true for real data. To overcome this limitation, a kernel version of the Fisher discriminant is recently developed for non-linear discriminative feature extraction. The optimal solution of the kernel Fisher discriminant corresponds to the optimal Bayesian classifier which accounts for the minimization of the classification (Bayesian) error rate (Schölkopf and Smola, 2002, Mika et al., 1999). But these methods are computationally expensive.

Since the dual-tree complex wavelet transform (DT-CWT) (Kingsbury, 2001) is a special case of the Gabor filters with complex coefficients it has the directional advantages of the Gabor filters but requiring less computation. Furthermore, it is better than DWT as it is approximately shift invariance and has good directional selectivity in two dimensions. Thus, we propose a computationally efficient multiscale texture classifier using DT-CWT which exploits these advantages. The proposed multiscale texture classifier utilises the benefits of the multiresolution structure of DT-CWT for multiscale feature extraction.

This paper is organized as follows. Section 2 presents DT-CWT. Section 3 presents the proposed multiscale texture classifier, and the learning and classification of texture features for different classes. The experimental results and discussions are presented in Section 4. Finally, Section 5 concludes the paper.