ADAPTIVE WAVELETS FOR IMAGE REPRESENTATION AND CLASSIFICATION Gemma Piella, Marine Campedel and B´ eatrice Pesquet-Popescu GET-ENST, Signal and Image Processing Department, 46 rue Barrault, 75634 Paris Cedex 13, France ABSTRACT In this paper we propose a feature-based wavelet representa- tion for image classification and visualization. The work is primarily motivated by the need to classify quickly and ef- ficiently large multispectral satellite images, and possibly to perform the classification task directly on compressed data. We propose a multiresolution approach based on a special class of adaptive wavelets which allows the extraction of salient features without loosing accuracy. 1. INTRODUCTION Typically, classification involves feature extraction and rep- resentation, class modeling and parameter estimation. These steps are highly interdependent, since the choice of features influences the conditions under which a classifier operates and vice versa. In fact, feature extraction is generally applicable to a wide range of imagery and tasks. It allows the identifica- tion of relevant features. Hence, the effective use of feature extraction can improve general analysis and interpretation of data. For classification, the goal of feature extraction is to produce a condensed information able to discriminate be- tween different classes. The extracted attributes generally correspond to models produced by human experts; automatic selection procedures can also be added to reduce features re- dundancy or irrelevance. Some of the most common feature extraction methods are principal component analysis, discriminant analysis feature extraction, and decision boundary feature extraction. These methods are usually referred to as statistic-based feature ex- traction [1]. In the context of image classification, typically extracted features correspond to textural and geometrical in- formation. The textural part can be represented using clas- sical wavelets based features (Gabor, QMF), statistics from co-occurrence matrices (Haralick coefficients [12]) or pa- rameters estimated from Gaussian Markov Random Fields (GMRF [15]) models. The geometrical one traditionnaly comes from shape or contour analysis. In the meantime, in the past two decades, the wavelet transform has been successfully applied in several applica- tions, among which, feature extraction and classification. Due to their scale-space localization properties, wavelet transforms (and their variants such as wavelet packets) have proven to be an appropriate starting point for classification, specially for texture images, since classical wavelet trans- forms present some limitations when dealing with geomet- rical structures such as edges. Moreover, in [2, 3] it is sug- The work of Piella is supported by a Marie-Curie Intra-European Fel- lowships within the 6th European Community Framework Programme. The work of Pesquet-Popescu was partially supported by the MUSCLE NoE un- der the contract no. IST-507752. gested that the choice of filters in the wavelet transform can be an important issue even for texture images. In this paper, an adaptive wavelet transform [4] is applied to extract the physical features of remote sensing images. An algorithm based on non-linear approximation of this adaptive representation is used to identify significant features directly in the transformed domain. An important characteristic of our approach is that the transform preserves salient features so that the image can be analyzed and visualized at low reso- lutions while providing a compact representation. Moreover, the resulting decomposition can be directly used for nearly lossless compression of remore sensing images, thus allow- ing to jointly achieve efficient storing and browsing capabil- ities. This paper is organized as follows. In the next section, we briefly describe the adaptive wavelet scheme used to rep- resent the input images. In Section 3, we propose a feature extraction algorithm based on selecting the largest amplitude wavelet coefficients along the different scales and orienta- tions as the important features for classification. In Section 4, we describe the classification method used in the simulations results, which are presented in Section 5. Concluding re- marks are given in Section 6. 2. ADAPTIVE WAVELET REPRESENTATION Our wavelet decomposition uses an adaptive update lifting step, followed by a fixed prediction step, such as illustrated in Fig. 1. U d D P 1 P 2 P 3 x y s 1 y s 2 y s 3 y ′ s 3 y ′ s 2 y ′ s 1 x ′ Figure 1: 2D adaptive wavelet decomposition. The input image bands x, y s 1 , y s 2 and y s 3 are the polyphase components of an original image x 0 : x(m, n)= x 0 (2m, 2n), y s 1 (m, n)= x 0 (2m, 2n + 1), y s 2 (m, n)= x 0 (2m + 1, 2n), y s 3 (m, n)= x 0 (2m + 1, 2n + 1). The output x ′ corre- sponds to the approximation band, whereas y ′ s 1 , y ′ s 2 , y ′ s 3 are the detail bands corresponding to different orientations (hor- izontal, vertical and diagonal, respectively). In the update step, D is the so-called decision map which uses inputs from all four bands, and whose output is a binary