Finite ridgelet



Keywords: finite ridgelet
Description: Copyright © 2016 Juan Wang et al. This is an open access article distributed under the Creative Commons Attribution License. which permits unrestricted use, distribution, and reproduction in any

Copyright © 2016 Juan Wang et al. This is an open access article distributed under the Creative Commons Attribution License. which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Texture classification is an important research topic in image processing. In 2012, scattering transform computed by iterating over successive wavelet transforms and modulus operators was introduced. This paper presents new approaches for texture features extraction using scattering transform. Scattering statistical features and scattering cooccurrence features are derived from subbands of the scattering decomposition and original images. And these features are used for classification for the four datasets containing 20, 30, 112, and 129 texture images, respectively. Experimental results show that our approaches have the promising results in classification.

The texture is one of the main contents of the image. Texture segmentation, texture classification, and shape recovery from texture are three primary issues in texture analysis [1 ]. Among them, texture classification plays an important role in many tasks, ranging from remote sensing and medical imaging to query by content in large image data bases, and so forth [2 ]. Texture analysis is one of the most important techniques when images which consist of repetition or quasi repetition of some fundamental image elements are analyzed and interpreted (e.g. [3 ]). Various feature extraction and classification techniques have been suggested for the purpose of texture analysis in the past. Since there are many variations among nature textures, to achieve the best performance for texture analysis or retrieval, different features should be chosen according to the characteristics of texture images. It is well recognized that these texture analysis methods capture different texture properties of the image.

There are four major stages in texture analysis, that is, feature extraction, texture discrimination, texture classification, and shape from texture [4 ]. The first stage of image texture analysis is feature extraction. Texture features obtained from this step are used to discriminate textures, classify image textures, or determine object shape. Feature extraction computes a characteristic that can describe texture properties of a digital image. The process that partitions a textured image into regions, each corresponding to a perceptually homogeneous texture, is texture discrimination. In the stage of texture classification, a rule, which classifies a given test image of unknown classes to one of the known classes, is designed. Shape from texture reconstructs 3D surface geometry from texture information. Feature extraction techniques mainly include first-order histogram based features, cooccurrence matrix based features, and multiscale features [4 ]. First-order histogram based features, according to the shape of the histogram of intensity levels, provides a number of clews as to the character of the image. The second-order histogram is considered as the cooccurrence matrix [5 ]. Cooccurrence matrix based features are the estimate of the joint probability distributions of pairs of pixels. In order to calculate multiscale features, many time-frequency methods are adopted [6 ]. The common methods are Wigner distributions, Gabor functions, wavelet transform, and ridgelet transform. Wigner distributions can produce inference terms which lead to wrong signal interpretation. Gabor filter results in redundant features at different scales or channels [7 ]. Wavelet transform is a linear operation and possesses a capability of time localisation of signal spectral features. For these reasons, it is interesting in application to texture analysis for wavelet transform. Ridgelet transform can deal effectively with line singularities in 2D. It is well known that texture classification based on ridgelet statistical features (RSFs) and ridgelet cooccurrence features (RCFs) has been done by Arivazhagan et al. [8 ].

In the last few decades, wavelet theory has been widely used for texture classification purposes [9 –11 ]. However, wavelet transform is not translation invariant. In 2012, Mallat advanced scattering transform which is invariant to translations and Lipschitz continuous relatively to deformations [12 ]. Scattering transform can overcome the weakness of wavelet transform, that is, not translation invariant. The idea is that scattering transform is computed by iterating over successive wavelet transforms and modulus operators. Scattering transform maps high frequency information of images to low frequency. Then, scattering transform can provide a stationary representation. Scattering transform has found applications in texture classification (e.g. [13. 14 ]). These classification tasks are based on original scattering vectors.

In this paper, the scattering transform is applied on a set of texture images. Statistical features and cooccurrence features are extracted from original images and each of scattering subbands. These features are used for classification. For the sake of comparative analysis, classification tasks are done using RSFs, RCFs, wavelet statistical features (WSFs), and wavelet cooccurrence features (WCFs), respectively. The experimental results show that the success rate of our feature extraction techniques is promising but unsatisfactory. But it is considered as a proof of concept for scattering statistical features (SSFs) and scattering cooccurrence features (SCFs).

The rest of this paper is organized as follows. In Section 2. the theory of scattering transform is briefly reviewed. The feature extraction and texture classification are explained in Section 3. In Section 4. texture classification experimental results are discussed in detail. Finally, concluding remarks are given in Section 5 .




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