Hybrid 3D Fractal Coding with Neighbourhood Vector Quantisation
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Hybrid 3D Fractal Coding with Neighbourhood Vector Quantisation Zhen Yao Computer Science Department, University of Warwick, Coventry CV4 7AL, UK Email: [email protected]
Roland Wilson Computer Science Department, University of Warwick, Coventry CV4 7AL, UK Email: [email protected] Received 31 August 2003; Revised 12 September 2004 A hybrid 3D compression scheme which combines fractal coding with neighbourhood vector quantisation for video and volume data is reported. While fractal coding exploits the redundancy present in different scales, neighbourhood vector quantisation, as a generalisation of translational motion compensation, is a useful method for removing both intra- and interframe coherences. The hybrid coder outperforms most of the fractal coders published to date while the algorithm complexity is kept relatively low. Keywords and phrases: fractal, compression, video coding, neighbourhood vector quantisation, convergence.
1.
INTRODUCTION
Fractal image compression techniques, introduced by Barnsley and Jacquin [1, 2], are the product of the study of iterated function systems (IFS). These techniques involve an approach to compression quite different from standard transform coder-based methods. Transform coders model images in a simple fashion, as vectors drawn from a wide-sense stationary random process and store images as quantized transform coefficients. Fractal block coders, assume that image redundancy can be efficiently exploited through self-similarity on a blockwise basis. They represent images by contraction maps, of which the images are approximate fixed points. Images are decoded by iterating these maps to their fixed points. The fundamental principle of fractal coding is to represent the image by a set of contractive mappings. First, the image I is partitioned into a set of blocks R = {r1 , r2 , . . . , rn } that covers I, referred to as the range blocks. For each ri ∈ R, a domain block d j ∈ D, usually twice as large as the range block, is sought which most resembles ri after a contractive transform involving operations like rotation, and contrast and brightness adjustments. At its simplest, the affine mapping can be expressed as φ(x) = sx + o,
|s| ≤ 1,
(1)
where s is the scaling coefficient and o is the offset coefficient. Hence a representation of the range block can be expressed
by the domain block index and s and o coefficients. The best-matching domain block can be found by a systematic search, while the latter two can be directly optimised in a least squares sense. The transform from the domain block to range block forms the contractive mapping φi for ri and the collection
Φ = φ1 , φ2 , . . . , φn
(2)
is the fractal coded representation of the image, also referred to as partitioned iterative function system (PIFS). While fractal image compression has been studied in a large body of published literature, fractal-based techniques have also been explored for coding image sequences. They are usually divided into two categories: single-frame-based schemes and volume-based schemes. In sin
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