Non-linear Invertible Representation for Joint Statistical and Perceptual Feature Decorrelation J. Malo 1 , R. Navarro 3 , I. Epifanio 2 , F. Ferri 2 , and J.M. Artigas 1 1 Dpt. d’ ` Optica, Universitat de Val` encia 2 Dpt. d’Inform`atica, Universitat de Val` encia Av. Vicent Andr´ es Estell´ es S/N, 46100 Burjassot, Val` encia, Spain 3 Instituto de ´ Optica (CSIC) C/ Serrano 122, 28006 Madrid, Spain Abstract. The aim of many image mappings is representing the sig- nal in a basis of decorrelated features. Two fundamental aspects must be taken into account in the basis selection problem: data distribution and the qualitative meaning of the underlying space. The classical PCA techniques reduce the statistical correlation using the data distribution. However, in applications where human vision has to be taken into ac- count, there are perceptual factors that make the feature space uneven, and additional interaction among the dimensions may arise. In this work a common framework is presented to analyse the perceptual and statistical interactions among the coefficients of any representation. Using a recent non-linear perception model a set of input-dependent fea- tures is obtained which simultaneously remove the statistical and per- ceptual correlations between coefficients. A fast method to invert this representation is also presented, so no input-dependent transform has to be stored. The decorrelating power of the proposed representation sug- gests that it is a promising alternative to the linear transforms used in image coding, fusion or retrieval applications 1 . 1 Introduction Independence among the features is recognized as an intrinsic advantage of a given signal representation because it allows simple scalar data processing and a better qualitative interpretation of the feature vector [1,2]. This is why the aim of most feature extraction transforms is to find out a complete set (a basis) of independent features. Two main factors should determine the basis selection problem: the data distribution and the qualitative (geometric) properties of the underlying space. The basis functions should not only reflect the principal axis of the training set but also the eventual anisotropies of the space. This is particularly important in applications involving natural imagery or texture description, such as indexing and retrieval, fusion, or transform coding. 1 The authors wish to thank A.B. Watson and E.P. Simoncelli for their fruitful com- ments. This work has been partially supported by the CICYT-FEDER (TIC) pro- jects 1FD97-0279 and 1FD97-1910 and CICYT (TIC) 98-677-C02 F.J. Ferri et al. (Eds.): SSPR&SPR 2000, LNCS 1876, pp. 658–667, 2000. c  Springer-Verlag Berlin Heidelberg 2000