Research Article
Colour Texture Image Analysis by Shearlets
PRIST University, Tanjore, Tamil Nadu, India
S. Audithan
Department of Computer Science and Engineering, PRIST University, Tanjore, Tamil Nadu, India
In computer vision and image processing, feature extraction is one of the important stages in gray and colour texture classification. Extensive researches have been proposed for the classification of texture images. A pair of quarter-size colour images directly from colour filter array images without any estimation is used to compute the Chromatic Co-occurrence Matrices (CCM) of these quarter-size images. This allows comparing textures by means of their CCM based similarity in texture classification or retrieval schemes, with the ability to use different colour spaces is presented in Losson and Macaire (2012). Chindaro et al. (2006) have explained a novel method that uses independent component analysis for systematically partitioning and combining textural features extracted from different colour spaces, in a multiple classifier based system, for colour texture classification.
Arivazhagan and Benitta (2013) have presented a new approach to extract the features of a color texture image for the purpose of texture classification. a four feature sets are involved to classify the texture features. Dominant neighbourhood structure is the new feature set that has been used for color texture image classification. Maia et al. (2010) have presented the contribution of the use of a texture-color combination in forest mapping. The spot image is transformed into different color spaces, then nine parameters using laws filter are extracted for color texture classification.
A new approach for color texture classification by use of Haralick features extracted from co-occurrence matrices computed from local binary pattern images is presented in Porebski et al. (2008). Features are extracted from color texture images which are coded in 28 different color spaces. The performances of two sequential feature selection schemes used for supervised color texture classification are compared in Porebski et al. (2010). They are sequential forward selection scheme and the more complex sequential forward floating selection scheme which avoids the nesting effect.
Akhloufi et al. (2007) gave an effective framework is proposed for color texture classification where statistical features are computed from a generalized isotropic co-occurrence matrix extracted from color bands and combined with image entropies. It is effectively tested in RGB, HSL and Lab color spaces. A new approach for color texture classification by use of Haralick features extracted from color co-occurrence matrices is explained by Porebski et al. (2007). This approach is to select the most discriminating color texture features in order to build a feature space with a low dimension.
An algorithm for classifying color textures using wavelet transform is described by Arivazhagan et al. (2005). Wavelet transform is useful for extracting texture features of images. A set of features are derived and color texture classification is done for different combination of the features and for different color models. The results obtained are found to be satisfactory. Sengur (2009) presented a composed of a wavelet domain feature extractor and ensembles of neural networks classifier. Entropy and energy features are integrated to the wavelet domain feature extractor of the proposed color texture classification.
An integrative approach towards color texture classification and recognition using a supervised learning frame work is described in Giotis et al. (2012). This approach is based on generalized learning vector quantization extended by an adaptive distance measure. The proposed technique is evaluated by two sets of color texture images and compares results with those other methods achieved. A novel approach to colour texture classification based on combinations of the information included in different colour spaces is presented in Chindaro et al. (2003). It is an empirical study of decision combination approaches using classifiers obtained through training in various colour spaces and sub-spaces based on the features extracted using Gaussian Markov random fields.
A color texture retrieval system using a multi-resolution mosaic for flexible image classification is described in Guan and Wada (2002). Texture can be characterized by features such as shape, structure, color and randomness. A novel approach to color texture characterization and classification is proposed by Vertan et al. (2000). The reduced dimensionality color spaces are used for color texture characterization and classification. This color spaces allow a good classification performance by the use of classical energy-distribution features, defined in a scalar spectral domain. The proposed scheme composed of a wavelet domain feature extractor and an ANFIS classifier in Sengur (2008). Both entropy and energy features are used on wavelet domain.
DISCRETE SHEARLET TRANSFORM
The proposed texture classification approach is based on new multi-scale directional representations called the shearlet transform introduced by Glenn Easley et al. (2008). An NxN image consists of a finite sequence of values:
where, . Identifying the domain with the finite group the inner product of image is defined as:
(1) |
Thus, the discrete analog of is . Given an image let denote 2D Discrete Fourier Transform (DFT) in Eq. 2:
(2) |
The brackets in the equations denote arrays of indices and parentheses denote function evaluations. Then, the interpretation of the numbers as samples is given by the following in Eq. 3 from the trigonometric polynomial:
(3) |
First, to compute:
(4) |
In the discrete domain, at the resolution level j, the Laplacian pyramid algorithm is implemented in the time domain. This will accomplish the multi scale partition by decomposing faj-1[n1, n2], 0≤n1, n2<Nj-1, into a low pass filtered image fja[n1, n2], a quarter of the size of fj-1a[n1, n2] and a high pass filtered image fjd[n1, n2]. Observe that the matrix f ja[n1, n2] has size NjxNj, where Nj = 2-2j and fa0[n1, n2] has size NxN. In particular:
(5) |
Thus, fdj[n1,n2] are the discrete samples of a function fdj[x1, x2], whose Fourier transform is . In order to obtain the directional localization the Discrete Fourier Transform (DFT) on the pseudo-polar grid is computed and then one-dimensional band-pass filter is applied to the components of the signal with respect to this grid. More precisely, the definition of the pseudo-polar co ordinates as follows:
(6) |
(7) |
After performing this change of co ordinates, is obtained and for l = 1-2j,..2j-1:
(8) |
This expression shows that the different directional components are obtained by simply translating the window function W. The discrete samples gj[n1, n2] = gj(n1, n2) are the values of the DFT of fjd[n1, n2] on a pseudo-polar grid. That is, the samples in the frequency domain are taken not on a Cartesian grid, but along lines across the origin at various slopes. This has been recently referred to as the pseudo-polar grid. One may obtain the discrete Frequency values of fjd on the pseudo-polar grid by direct extraction using the Fast Fourier Trans-form with complexity ON2logN or by using the Pseudo-polar DFT.
PROPOSED METHOD
The proposed approach for colour texture classification based on shearlet transform is shown in Fig. 1.
Feature extraction is an important step for any classification system. In the proposed approach, the shearlet band signatures; energy and entropy are used as features for colour texture classification. The feature extraction process is as follows.
The input texture image is first decomposed by using the DST at different level of decomposition and directions. At first, the shearlet band signature, energy is computed for all sub-images by Eq. 9. The number of sub-images depends on the level and direction of DST:
(9) |
where, xk (i, j) is the coefficient value of the kth sub-image and R, C is width and height of the sub-image, respectively. Then, the entropy signature is computed by Eq. 10:
(10) |
where, pi is the non-zero histogram value. These features are used for the analysis separately. In order to train the classifier, predefined number of images per class is used. From the training images, the proposed features are extracted and they are used as an input to the classifier. The class of an unknown texture image is predicted by using nearest neighbour classifier. The distance parameters used in the classifier are Euclidean, city block, correlation and cosine matrices. Initially, the distance between the proposed features and features in the database are computed. Among the distances, the target class is assigned to the class of texture that has minimum distance. The parameter, classification accuracy is used to test the performance of the proposed approach.
EXPERIMENTAL RESULTS
The evaluation of the proposed approach is carried on the VisTex database (http://vismod.media.mit.edu/ vismod/imagery/VisionTexture/vistex.html) texture images that consist of 30 colour textures of size 512x512. As the classifier needs training samples, each image in the database is subdivided into sub-images to create more samples of same texture image. The original image is divided into 128x128 non overlapping sub-images that produce 16 samples per class. Hence, there are 480 samples are available in total. Figure 2 shows the VisTex images used in this experiment.
Fig. 1: | Proposed texture classification system using discreat shearlet transform |
Fig. 2: | VisTex colour texture image used in this experiment |
In this experiment, KNN classifier is used to classify the unknown textures into known textures in the training database. The one nearest neighbor classifier is used i.e., k in the KNN classifier is set as 1. To train the classifier, 50% of images per class is used and the remaining 50% image per class is used for testing the classifier. To extract the features, 2 and 3-level shearlet transform with all possible direction is used. Table 1 and 2 shows the classification accuracy of the proposed approach using energy and entropy signatures based on 2 and 3-level decomposition, respectively. L represents the level of decomposition and D represents the number of directions used for the particular decomposition level.
The bold numerals in the tables show the maximum classification accuracy obtained by the proposed approach. Table 1 and 2 clearly show the dominance of entropy features over energy features as entropy signatures produces no misclassification irrespective of the levels and directions used. The number of features used in the classification task is chosen as one of the criteria as the speed of the classifier depends on this parameter. Table 3 shows the number of parameters in various combinations.
As the proposed approach achieves maximum classification accuracy at L2D2 which has the minimum number of features compared to other combinations. Hence, the proposed approach selects the L2D2 based shearlet entropy signatures and Euclidean distance/city block difference measure based KNN classifier for colour texture classification.
Table 1: | Classification accuracy using 2-level discrete shearlet transform |
Table 2: | Classification accuracy using 3-level discrete shearlet transform |
Table 3: | No. of features extracted by various combinations of shearlet parameters |
Table 4: | Comparative analysis of the proposed system with state-of-art techniques |
To demonstrate the performance of the proposed system, the classification accuracy of the proposed approach is compared with four state-of-art techniques. They are based on different techniques such as contourlet transform (Dong and Ma, 2013), Local Binary Pattern (Ojala et al., 2002), bit-plane probability (Choy and Tong, 2008) and singular value decomposition (Selvan and Ramakrishnan, 2007). Table 4 shows the comparative analysis of the proposed system with the aforementioned techniques in terms of classification accuracy.
It is observed from the comparative analysis; the proposed shearlet based approach achieves 100% classification accuracy for 30 colour textures due to the texture representation capability of shearlet transform. Also, the above table shows the superiority of shearlet over contourlet (Dong and Ma, 2013) Local Binary Pattern (Ojala et al., 2002), bit-plane probability (Choy and Tong, 2008) and singular value decomposition (Selvan and Ramakrishnan, 2007). The proposed approach performs better than these methods by at least 0.75% on 30 VisTex colour images.
In this study, shearlet band signatures such as energy and entropy are analyzed for colour texture classification. These signatures are extracted from the colour texture images after decomposing it by using DST. The textural properties of images are taken at various decomposition level and directions. VisTex colour texture images are used for the analysis. Experimental results demonstrate the texture representation properties of DST which produces better accuracy for entropy features than the energy features. The maximum classification accuracy achieved by the energy is 99.58% where as the entropy features produce no misclassification. Also, the proposed approach is compared with other state-of-art techniques.