Image compression with linear regression and image segmentation to flat sectors

Gašper Primožič (2017) Image compression with linear regression and image segmentation to flat sectors. EngD thesis.

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Abstract

We propose a new approach for lossless and lossy image compression. Images are stored in computer in its primary form, as two dimensional fields of intensities of three color channels. We change the color model of an image to one which minimizes the covariance between the intensities of all channels, and maximizes the variance on a single one. With the help of sectorization, we split each of the color channels to sectors, whose intensities are self similar. We approximate the intensities of all sectors, by applying first degree regression functions, to all rows and columns of a sector. Compression is achieved by storing only the coefficients of the regressed functions and discarding the original intensities. The procedure of finding the regression function coefficients can be speeded up since the positions of the intensities in a sector are known beforehand. This method is also expandable for paralellisation of crucial steps in the algorithm, because the majority of the time consuming calculations are matrix-based. Modern day processors and graphics cards are made for these kinds of applications, which can drastically drop the compression and decompression times. Our proposed compression method is thoroughly analyzed. Numerical approaches and statistical analysis are utilized to show that the advantage of this method is with highly compressed flat images.

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