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FRACTAL IMAGE COMPRESSION, Thesis on fractal image compression

Thesis on fractal image compression

Almost all fractals are at least partially self-similar. This means that a part of the fractal is identical to the entire fractal itself except smaller.

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The coarse scale approximation sub-image is quantized using scalar quantization and then using DCT-base quantization to show the benefit of this new optional method in term of CPU computationa1 cost vs restitution quality.

Here we demonstrate that such self-similarity is also exhibited by subblocks of Fourier data. The underlying explanation for this block-based self-similarity is that a connection can be made between the well-known result of autoregressive (AR) correlation coefficients and block-based fractal coding. This justifies block-based fractal coding in the complex Fourier domain, which we then employ for the purpose of frequency extrapolation or magnetic resonance imaging (MRI) data.

The same rule applies to fractal geometry but less intuitively. To elaborate, a fractal line measured at first to be one length, when remeasured using a new stick scaled by 1/3 of the old may not be the expected 3 but instead 4 times as many scaled sticks long. In this case, N {\displaystyle N} =4 when ϵ {\displaystyle \epsilon } =1/3, and the value of D {\displaystyle D} can be found by rearranging Equation 1:

A fractal image compressor, done to satisfy a my project and bachelor's thesis. Quite dead since the defense in August 2009, but contributors are welcome. Sources aren't annotated yet, but the license is GPL2+.

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Thesis on fractal image compression

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FRACTAL IMAGE PYRAMIDS - Library and Archives Canada

Fractal Geometry, Graph and Tree Constructions - DiVA portal

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thesis on fractal image compression
thesis on fractal image compression

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