Comparing Texture Analysis Methods through Classification

The development and testing of two techniques of texture analysis based on different mathematical tools—the semivariogram and the Fourier spectra—are presented. These are also compared against a benchmark approach: the Gray-Level Co-occurrence Matrix. The three methods and their implementation are briefly described. Three series of experiments have been prepared to test the performance of these methods in various classification contexts. These contexts are simulated by varying the number, type and visual likeness of the texture patches used in classification tests. More specifically, their ability to correctly classify, separate, and associate texture patches is assessed. Results suggest that the classification context has an important impact on performance rates of all methods. The variogram-based and the Gray-Tone Dependency Matrix methods were generally superior, each one in particular contexts. Introduction As scientists and researchers of the remote sensing community began to use high spatial resolution data, it soon became clear that spectral-based methods of computer classification and segmentation were doomed to yield unsatisfactory results. At high resolution, conceptual objects like forests or pasture usually show significant variations in their pixel values (Strahler et al., 1986). Stationary in nature, these variations can give rise to an apparently regular spatial pattern referred to as texture (Kittler, 1983). One of the key elements that the interpreters use to identify and analyze images is clearly the spatial arrangement of color and tone that form natural visual entities: visual texture (Haralick et al., 1973; Pratt et al., 1978). Because there is no universally accepted definition of visual texture, one has to choose a definition that best reflects the objective or the results being sought. The definition adopted here was given by Pratt (1991, p. 505): natural scenes containing semi-repetitive arrangements of pixels. The problem of analyzing and classifying texture has generated a wealth of studies and techniques that are seldom compared in a sys tematic way. This study is an experimental analysis of the problem of classifying texture using different mathematical tools. In particular, the specific classification context is analyzed in terms of the effect of between-class variation and number of classes on classification accuracy. To achieve the latter, a special experimental framework has been prepared and experimental results are presented and discussed. The paper is organized in six sections. A short background review of feature extraction methods for texture analysis follows the introduction. Then the three approaches are described individually and compared through sample data. The fourth section describes the experimental framework and the data used for the experiments. Next comes the results and their analysis followed by the main conclusions. Background Reed and du Buf (1993) claim that most development in texture has been concentrated on feature extraction methods (sometimes called channel-based methods) which seek to extract relevant textural information and map it onto a special dedicated channel called a feature. The authors classified the various fea ture extraction methods as belonging to one of three possible classes: feature-based, model-based, or structural. Cocquerez and Philipp (1995) have used a similar classification of image segmentation methods which they compare in varioussituations (including textured images). In feature-based methods, characteristics of texture (such as orientation, spatial frequency, or contrast) are used to classify homogeneous regions in an image. Model-based methods rely on the hypothesis that an underlying process governs the arrange ment of pixels (such as Markov chains or Fractals) and try to extract the parameters of such processes. Structural methods assume that a texture can be expressed by the arrangement of some primitive element using a placement rule. Feature-based, model-based, and hybrid methods have overwhelmingly dominated the scene in the last 20 years or so. One of their findings was that, although so many different methods have been devel oped, no rigorous quantitative comparison of their results had ever been done, which is a major theme of the present work. Because Bela Julesz (1965) has shown evidence that human perception of texture could be modeled using second-order statistics (although he would later change his theory for the “texton” approach; see Julesz (1981)) many researchers have explored second-order statistics as possible features for texture analysis. Among the most common second-order statistics that have been used are the co-occurrence matrix, the spatial-autocorrelation, the covariogram, and the semi-variogram. The frequency domain approach, also referred to as the Fourier Spectra approach, has been a long time favorite for texture analysis. From the early attempts at using it as a texture analysis tool by Rosenfeld (1962) to the recent use of Gabor functions as filters in the frequency domain to create frequencyand orientation-specific texture features (e.g., Fogel and Sagi, 1989; Jain and Farrokhinia, 1991; Manjunath and Ma, 1996), the Fourier transform offers infinite possibilities not only for texture analysis but for applications requiring the analysis of spatial frequencies and their orientation. In order to evaluate a technique, it is necessary to have some base for comparison. In this research, the comparison will take PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING Apr i l 2003 357 Photogrammetric Engineering & Remote Sensing Vol. 69, No. 4, April 2003, pp. 357–367. 0099-1112/03/6904–357$3.00/0 © 2003 American Society for Photogrammetry and Remote Sensing Universidad Federal de Minas Gerais, Departamento de Carto grafiá, Av. Antônio Carlos, 6627, Belo Horizonte MG 31270091, Brazil ([email protected]). the form of another technique that has already been widely accepted by the scientific community and obviously performs well. This method was proposed by Haralick et al. (1973) who have named it Gray-Tone Spatial-Dependence Matrices, also known as Gray-Level Co-occurrence Matrices (GLCM). Not only do almost all the authors in visual texture analysis quote the GLCM, but many have already used it as a comparison technique. Among them, Davis et al. (1979), Conners and Harlow (1980), Pratt (1991), Bonn and Rochon (1992), Wu and Chen (1992), Reed and du Buf (1993), Dikshit (1996), Franklin et al. (2001) and Zhang (2001) have either used the GLCM method as a comparison or have described it in their review. It was decided that all three methods be rotation-invariant so that the particular orientation of texture would not be considered even though it was observed that considering particular orientations can increase classification accuracy (Franklin and Peddle, 1989; Maillard, 2001). This was important especially for the crops and waves classes for which the factors controlling their orientation are difficult to predict. Description of the Three Texture Feature Extraction Methods The Variogram Approach Many authors have already shown the potential of the variogram as a texture analysis approach (Serra, 1982; Woodcock et al., 1988; Ramstein and Raffy, 1989; Miranda et al., 1992; Atkinson, 1995; St-Onge and Cavayas, 1995; Lark, 1996). On the one hand, the variogram is related to other statistical approaches like the autocorrelation function and the fractal Brownian motion (Xia and Clarke, 1997). On the other hand, it is computationally simple and easy to interpret as a graph. One point in which the variogram appears more appropriate is that only weak stationarity is assumed, in other words, the expectation only has to be constant locally (Woodcock et al., 1988). It appears, however, that most techniques using the variogram do so in the geostatistical manner, i.e., a model is usually applied whose parameters are taken as a way of describing the semi-variogram curve. In Remote Sensing images some texturebased variograms might be best modeled using the spherical model while others are best represented with an exponential or even sinusoidal model. This poses a problem in terms of creating a systematic approach. One solution would be to use the “best” model type, selected as a texture feature. But using a nominal scale feature would cause problems further down the classification process. This would also imply that a battery of models would have to be fitted for all pixels of all texture samples, and the cost in terms of computing would be high. For these reasons and because others have already pursued that line of research, the “traditional” function representation of sill and range has not been considered here. Another point that has received attention is the alternate use of the mean square-root pair difference (SRPD(h)) function proposed by Cressie and Hawkins (1980) as a semi-variance estimator which is resistant to outliers. Lark (1996) has also shown that for four different classes of texture (urban, farmland, woodland, and meadow), when tested for normality, the SRPD(h) function scored much better than the g(h) function, a fact confirmed by an earlier study by the author (Maillard, 2001). Considering these findings, a number of considerations were taken to implement the texture feature extraction based on the variogram: • a rather large window had to be used in order to cover larger distance lags (up to 32 pixels), • the texture feature set had to be rotation-invariant but had to preserve anisotropy, and • the behavior of the SRPD graph near the origin had to receive special attention because it bears a special significance in terms of micro-texture (Serra, 1982; Jupp et al., 1989; Xia and Clarke, 1997). After numerous tests using different ways to transform the variogram into texture features, the most promising approach was found to be the averaging of selected distance lag intervals. The SRPD texture feature extraction routine can be summarized in the following steps: • For every pixel in the image, a neighboring window (32 by 32 pixels) is considered and four directional variograms (0°, 45°, 90°, and 135°) are computed for all possible combinations in