The resolution independence of a fractal-encoded image can be used to increase the display resolution of an image. This indefinite scaling property of a fractal is known as "fractal scaling". This is because the iterated function systems in the compressed file scale indefinitely. Resolution independence and fractal scaling Īn inherent feature of fractal compression is that images become resolution independent after being converted to fractal code. Ĭompression efficiency increases with higher image complexity and color depth, compared to simple grayscale images. Fractal video compression ratios of 25:1–244:1 have been achieved in reasonable compression times (2.4 to 66 sec/frame). For satellite imagery, ratios of over 170:1 have been achieved with acceptable results. At high compression ratios fractal compression may offer superior quality. Īt common compression ratios, up to about 50:1, fractal compression provides similar results to DCT-based algorithms such as JPEG. While this asymmetry has so far made it impractical for real time applications, when video is archived for distribution from disk storage or file downloads fractal compression becomes more competitive. With fractal compression, encoding is extremely computationally expensive because of the search used to find the self-similarities. įractal image compression has many similarities to vector quantization image compression. Other researchers attempt to find algorithms to automatically encode an arbitrary image as RIFS (recurrent iterated function systems) or global IFS, rather than PIFS and algorithms for fractal video compression including motion compensation and three dimensional iterated function systems. The initial square partitioning and brute-force search algorithm presented by Jacquin provides a starting point for further research and extensions in many possible directions - different ways of partitioning the image into range blocks of various sizes and shapes fast techniques for quickly finding a close-enough matching domain block for each range block rather than brute-force searching, such as fast motion estimation algorithms different ways of encoding the mapping from the domain block to the range block etc. This bottleneck of searching for similar blocks is why PIFS fractal encoding is much slower than for example DCT and wavelet based image representation. On the other hand, a large search considering many blocks is computationally costly. In the second step, it is important to find a similar block so that the IFS accurately represents the input image, so a sufficient number of candidate blocks for D i need to be considered.
For each R i, search the image to find a block D i of size 2 s×2 s that is very similar to R i.Partition the image domain into range blocks R i of size s× s.We begin with the representation of a binary image, where the image may be thought of as a subset of R 2 Encoding Ī challenging problem of ongoing research in fractal image representation is how to choose the ƒ 1., ƒ N such that its fixed point approximates the input image, and how to do this efficiently.Ī simple approach for doing so is the following partitioned iterated function system (PIFS):
Fractal image representation may be described mathematically as an iterated function system (IFS).
0 kommentar(er)
