Embedding Quality Measures in PIFS Fractal Coding Andrea Abate, Michele Nappi, and Daniel Riccio Universit´a Degli Studi di Salerno, via Ponte Don Melillo, 84084, Fisciano, Salerno, Italy {abate, mnappi, driccio}@unisa.it Abstract. Fractal image coding is a relatively recent technique based on the representation of an image by a map of self-similarities. In last years, most researchers focused their attention on the problem of speeding up the fractal coding process, while paying little attention to possible im- provements of the objective and subjective image quality. In this paper, we investigate image quality measures, which could represent a reason- able alternative to the RMSE when finding a suitable map of similarities. Subjective assessments have been performed in order to compare perfor- mances of the selected quality metrics. Experimental results bear witness to the superiority of such a quality metric based on Fourier coefficients. 1 Introduction Many objective quality measures [1], have been defined to replace subjective evaluations by retaining, as much as possible, the fidelity with the human per- ception of image distortions introduced by the coding schemes. The most com- mon measures undoubtedly are the RMSE (Root Mean Square Error) and the PSNR (Peak Signal to Noise Ratio). They owe their wide spread to that they work well on the average by showing a very low computational cost. However, there are cases in which the quality estimates given by the PSNR are very far from the human perception and this led many researchers to define new quality metrics providing better performances in terms of distortion measurement even if at a higher computational cost. Some examples are given by the Human Visual System [7] or the FFT Magnitude Phase Norm [1]. All these measures have been largely used to assess the global quality of the decoded image after a coding process has been applied on; in other words the original image is compressed/decompressed by means of an encoder and then the overall amount of distortion introduced by the coding scheme is measured. Thus, objective measures represent an effective way to compare different coding schemes in terms of percentage of distortion introduced for a fixed compression ratio. The key idea of this paper is to embed quality measures into the coding process, not curbing them to be a sheer analysis tool. The compression scheme we adopted for this study is the quad-tree based PIFS (Partitioned Iterated Function System), whose scheme is represented in Fig. 1. It lays itself open to a direct replacement of the RMSE by other quality measures. M. Kamel and A. Campilho (Eds.): ICIAR 2007, LNCS 4633, pp. 784–793, 2007. c  Springer-Verlag Berlin Heidelberg 2007