Using Fractal Coding for Progressive Image Transmission

1. ABSTRACT Fractal coding is gaining in popularity as an efficient still-image coder. One drawback of conventional block-based fractal coders, however, is that they do not offer progressive image transmission. This paper proposes two new methods by which fractal image coders can progressively transmit the image data. The first method, the transmission-sequence-based fractal coder (TSFC), progressively transmits the image blocks depending on their perceptual importance. The second method is the pyramidal fractal coder, (PFC) and it operates by progressively transmitting the pyramid levels of the coded image. Simulation results with PFC showed that existing quadtree fractal coders can readily be extended to provide progressive transmission, and that high quality images can be obtained with a compression ratio of 16:1. Transmission of digital images is becoming an increasingly challenging task with the growing number of images to be handled and the enormous amount of data needed to represent each image. This problem can be partially countered by using higher-bandwidth communication systems. However, a more effective solution should consider also how the digital images are represented and the transmission method employed. Seeking for a better method to represent a digital image has led to a myriad of image compression techniques. This has been proven to be an effective approach to tackle the problem. However, a better solution is to also improve the transmission method. Progressive image transmission (PIT) is an elegant method for making effective use of communication bandwidth. Instead of transferring an image at full resolution in a sequential manner, PIT will transmit an approximate image first. The quality of this image is then progressively improved over a number of transmission passes. The advantage behind this is that it allows the user to quickly recognise an image and make an accept or reject decision. 2 Current state-of-the-art compression techniques, such as those that involve wavelet transform and vector quantisation, can deliver grayscale images of acceptable quality with compression ratios greater than 30:1. More recently, fractal coding has been proposed as a promising new method for image coding (Jacquin, 1992). Indeed, fractal coding can outperform many of the other methods for applications that require very high compression ratios (Fisher et al., 1994). However, quadtree fractal coders do not have the capability for progressive transmission. This shortcoming limits the types of applications fractal coding can be used for, considering that other high-compression methods such as wavelet coding do offer progressive transmission. This paper …