Texture classification using Gabor filters
Introduction
In satellite image interpretation, classification is the operation by which an operator would like to detect different kinds of region like forest, urban zone, waterways, etc. As the scene is a set of points (pixels) with intensity in grey scale values in several bands, most methods use these grey scale values to determine the kind of terrain. However, a single ground cover usually occupies a number of pixels with some variability in their grey scale values. A more satisfactory interpretation of the scene should thus include textural aspects of regions.
In general, texture is characterized by invariance of certain local attributes that are periodically or quasi-periodically distributed over a region. There are many approaches for analyzing image texture. Haralick (1979) proposed a set of features (energy, entropy, maximum probability, correlation, etc.) based on grey level cooccurrence matrices. Some statistical techniques use Markov Random Field models to characterize textures (Cross and Jain, 1983). The spectral approach (Bovik et al., 1990; Randen and Husoy, 1999) to texture analysis is referred to as the multi-channel filtering approach. Textures are characterized by their responses to filters, each one being selective in spatial frequency and orientation.
In this paper, we present a spectral approach to extract texture features. The textured input image is decomposed into feature images using a bank of Gabor filters. These feature images are used to form feature vectors and each of them corresponds to one dimension of the feature space. Then, we present the Fuzzy c-means clustering algorithm used for unsupervised classification of the input pixels based on their associated feature vector. This method considers clusters as fuzzy sets, while membership function measures the possibility that each feature vector belongs to a cluster. At last, we present methods for evaluating how well different textures are separated in feature space, as well as measuring classification performance. In most applications, the number of classes is unknown. Here we propose a method for choosing the best number of classes and we apply it to a synthetic and a real texture representation problem.
Section snippets
Gabor filters and feature extraction
Gabor filters perform a local Fourier analysis and are essentially sine and cosine functions modulated by a Gaussian window. In the complex space these filters are defined aswhere x, y represent the spatial coordinates while kx, ky represent the frequency coordinates. X and Y are the spatial localizations of the Gaussian window. The filter's selectivity in spatial frequency and orientation is given by
Since the signals to
Classification
Many algorithms have been developed for supervised and unsupervised classification. In supervised classification, training sets are needed whereas unsupervised classification classifies images automatically by finding clusters in the feature space. One of the unsupervised data clustering methods is the hard k-means clustering algorithm. It assigns each sample (feature vector) to one and only one of the clusters. This method assumes that boundaries between clusters are well defined. The model
Classification validity
Classification of data should be of high quality, i.e., all samples should have a large membership degree for at least one cluster. This problem is related to how many classes there are in the data. In fuzzy c-means algorithm, the number of clusters is required though in many applications this information is unknown. A method for measuring performance is needed to compare the goodness of different classification results. Gath and Geva (1989) have defined an `optimal partition' of the data into
Synthetic images
For experimental results, we present first a visual evaluation of Gabor filters in texture characterization and classification. To do this, we use two synthetic 256×256 textured images, one containing three Gaussian Markov Random Field (GMRF) textures (Fig. 5) and the other containing five textures from the Brodatz album (Brodatz, 1966) (Fig. 7). As the number of texture categories is known for these images, we also present the efficiency of the method proposed for classification validity
Conclusions
A fuzzy clustering approach to textured image classification has been presented. The texture features are extracted using a set of Gabor filters with different frequencies and orientations.
The fuzzy c-means algorithm has been successfully used for discriminating different types of textured image but the drawback is that one has to specify the number of clusters. We thus discussed the use of cluster validity parameters. A modification of compactness and separation validity function is proposed
Acknowledgements
The authors are grateful to colleagues: Dr. V. Lacroix for the helpful and encouraging discussions during the preparation of this paper and X. Neyt who develops the Gabor filter tools. They also would like to thank the International Institute for Aerospace Survey and Earth Sciences (ITC, The Netherlands) for providing the minefield aerial image in the frame of European Pilot Project entitled: Airborne Minefield Detection.
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The first author's research is funded by the HUDEM project: HUDEM (HUmanitarian DEMining) is a technology exploration project on humanitarian demining launched by the Belgian Minister of Defense with funding provided by his Department, the Ministry of Foreign Affairs and the State Secretariat for Development Aid.