| Wohlberg, B & Jager, Gd 1999, 'A Review of the Fractal Image Coding Literature', IEEE Transaction on Image Processing, vol. Vol. 8, viewed 1999. |
.... contexts, such as the compression of sub band coefficients in wavelet decomposition and coding of the sub blocks data in EBCOT algorithm [5] 6] The quad tree decomposition is an important tool for fractal image compression where many suitable smart variants of quad trees are used and applied (see [7] for a detailed survey) Function tree representation, introduced in [1] is another possible improvement of the original scheme proposed by Samet [3] The main innovation of function trees concerns the introduction into the node decomposition of classical quad trees of suitable new nodes ....
....a suitable data structure, i.e. a record storing all the relevant information. The structure of a typical node, together with a rough estimate of its content in bit is schematically reported in Figure 2. Graph of a discrete function Region Below Trapezoidal region Direction: South Boundary: [6,7,6,5,4,5,5,6] Figure 2. Scheme of the record relative to a node in a function tree. Function trees may be computed in the very same fashion than quad trees. In short a typical algorithm recursively reads the input, creates a new node in the tree and checks if the corresponding sub region is entirely black, ....
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B. Wohlberg, G. de Jager, "A Review of Fractal Image Coding Literature", IEEE Trans. on Image Processing, vol. 8, n. 12, December 1999.
....University Faculty Research Grant Nos. FRG 99 00 II 16. Corresponding author: Email: cstong(hkbu.edu. hk, Tel: 852) 23397023, Fax: 852) 23395811. I. INTRODUCTION A number of papers on fractal image encoding have been published since the pioneering idea of Barnsley and Sloan in 1988 (see [1] for the latest survey) It has since been used for special image archive applications such as MR, ECG, and space images [2 4] feature extractions [5] image signatures [6] image retrievals [7 10] texture segmentation [11] and many other image processing applications. Although it suffers from ....
.... from O(N o ) to O(log N o ) The idea of tree structured search to speed up encoding has long been used in the related technique of Vector Quantization (see e.g. 13] And many formulations of tree search for fractal encoding have been proposed, e.g. by Caso et al. 14] and Bani Eqbal [15] see [1] for recent survey) But perhaps the most elegant and general formulation is that proposed by Saupe [16] which also has the advantage of incorporating a small set of fixed basis blocks (a real codebook) to improve compression quality. In this paper, we shall discuss some of the drawbacks of ....
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B. Wohlberg and Jager G, A Review of the Fractal Image Coding Literature, IEEE Trans. on Image Processing, Vol. 8, No.12, pp. 1716-1729, 1999.
....of many fixed points, is computationally expensive. In this paper, we provide techniques that drastically reduce the time complexity of the algorithm. 1. INTRODUCTION The rate distortion results of the best fractal coders are inferior to those of the state of the art in image compression [14]. However, the potential of fractal image compression has not been fully exploited because current fractal schemes do not find optimal codes. In fractal image compression, the code is a representation of a contractive affine mapping in a complete metric space of digital images [5] The encoder ....
Wohlberg, B. E., de Jager G., A review of the fractal image coding literature, IEEE Transactions on Image Processing 8(12) (1999) 1716--1729.
....purely self a ne models would provide a signi cantly improved match with image statistics. This suspicion is supported by the tendency for the most effective fractal coding algorithms not to rely on a purely self a ne representation, but to incorporate aspects of alternative coding strategies [13]. Acknowledgement The authors wish to thank G. Cox and the anonymous reviewers for valuable comments on the manuscript. ....
B. Wohlberg and G. de Jager, \A review of the fractal image coding literature," To appear in IEEE Transactions on Image
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Wohlberg, B & Jager, Gd 1999, 'A Review of the Fractal Image Coding Literature', IEEE Transaction on Image Processing, vol. Vol. 8, viewed 1999.
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B. Wohlberg and G. de Jager, "A review of fractal image coding literature," IEEE Trans. Image Process. 8#12#, 1716 --1729 #1999#.
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