Texture classification using ridgelet transform

Abstract

Texture classification has long been an important research topic in image processing. Now a day’s classification based on wavelet transform is being very popular. Wavelets are very effective in representing objects with isolated point singularities, but failed to represent line singularities. Recently, ridgelet transform which deal effectively with line singularities in 2-D is introduced. It allows representing edges and other singularities along lines in a more efficient way compared to wavelet transform. In this paper, the issue of texture classification based on ridgelet transform has been analyzed. Features are derived from the sub-bands of the ridgelet decomposition and are used for classification for the four different datasets containing 20, 30, 112 and 129 texture images respectively. Experimental results show that this approach allows obtaining high degree of success rate in classification.

Introduction

The analysis of texture in images provides an important cue to the recognition of objects. It has been recently observed that different image objects are best characterized by different texture methods. Successful applications of texture analysis methods have been widely found in industrial, biomedical, remote sensing areas and target recognition (e.g., Kaplan, 1999). In addition, the recent emerging of multimedia and the availability of large image and video archives has made content-based information retrieval become a very popular research topic. Texture is also deemed as one of the most important features when performing content-based information retrieval (e.g., Chan et al., 1997). Various textural features have been adopted to fulfill these applications. Since there are a lot of variations among natural textures, to achieve the best performance for texture analysis or retrieval, different features should be chosen according to the characteristics of texture images. A number of texture analysis methods have been proposed over the years and it is well-recognized that they capture different texture properties of the image.

Texture analysis methods used can be categorized as statistical, geometrical, model-based and signal processing (e.g., Tuceyran and Jain, 1998). Early works were based on the analysis of statistical properties of the texture which deals with the spatial distribution of gray values. Some statistical methods used are co-occurrence matrix features (e.g., Haralick et al., 1973, Argenti et al., 1990) and autocorrelation function (e.g., Kaizer, 1955). In geometrical methods textures are considered to be composed of texture primitives and are extracted and analyzed (e.g., Tuceryan and Jain, 1990). Several stochastic models have been proposed for texture modeling and classification such as Gaussian Markov random fields (e.g., Cross and Jain, 1983, Rama and Shankar, 1985, Charles, 1995) and spatial autocorrelation function model (e.g., Patrizio et al., 2002). The signal processing techniques are mainly based on texture filtering for analyzing the frequency contents either in spatial domain (e.g., Laws, 1980, Unser, 1986) or in frequency domain (e.g., Bajcsy and Lieberman, 1976). Filter bank instead of a single filter has been proposed, giving rise to several multi-channel texture analysis systems such as Gabor filters and wavelet transforms (e.g., Unser and Eden, 1989). The major disadvantage of the Gabor transform is that its output are not mutually orthogonal, which may result in a significant correlation between texture features.

In the last decade, wavelet theory has been widely used for texture classification purposes. Here, image is decomposed using wavelet transform and statistics such as mean and standard deviation are derived from the decomposed sub-bands and is used as features for classification (e.g., Smith and Chang, 1994, Nicu and Michael, 2000, DeBrunner and Kadiyala, 2000). Apart from these statistical features, co-occurrence features are extracted from the wavelet decomposed sub-bands in order to increase the correct classification rate (e.g., Arivazhagan and Ganesan, 2003). In order to explore the middle-band characteristics, tree structured wavelet transform (e.g., Chang and Kuo, 1992), pyramid structured wavelet transform (e.g., Chang and Kuo, 1993), dual-tree complex wavelet transform (e.g., Serkan et al., 1999), wavelet packets (e.g., Moon-Chuen and Chi-Man, 2000, Rajpoot, 2002) were used for texture classification. A comparative study by Randen and Husoy (1999) shows that various filtering approaches yield different results for different images. No single approach did perform best or very close to the best for all images.

The success of wavelets is mainly due to the good performance for piecewise smooth functions in one dimension. Unfortunately, such is not the case in two dimensions. In essence, wavelets are good at catching zero-dimensional or point singularities, but two-dimensional piecewise smooth signals resembling images have one-dimensional singularities (e.g., Minh and Martin, 2003). Wavelets in two dimensions are obtained by a tensor-product of one dimensional wavelet and they are thus good at isolating the discontinuity across an edge, but will not see the smoothness along the edge. To overcome the weakness of wavelets in higher dimensions, Candes and Donoho pioneered a new system of representations named ridgelets which deal effectively with line singularities in two dimensions (e.g., Candes, 1998, Candes and Donoho, 1999). The idea is to map a line singularity into a point singularity using the Radon transform (e.g., Deans, 1983, Bolker, 1987). Then, the wavelet transform can be used to effectively handle the point singularity in the Radon domain. So, ridgelet transform allows representing edges and other singularities along lines in a more efficient way, in terms of compactness of the representation, than traditional transformations, such as the wavelet transform, for a given accuracy of reconstruction (e.g., Patrizio et al., 2002).

In this paper, the ridgelet transform is applied on a set of texture images and statistical features such as mean and standard deviation are extracted from each of the ridgelet sub-bands and used for classification. In order to improve the classification gain, the co-occurrence features are also extracted from each ridgelet sub-bands. The experimental result shows that the success rate is improved much when compared with traditional methods.

The paper is organized as follows: Section 2 describes the theory of continuous ridgelet transform (CRT). The digital implementation aspect of ridgelet transform is given in Section 3. The process of texture classification is explained in Section 4. Experimental results and discussion are given in Section 5. Finally, concluding remarks are given in Section 6.