Dirichlet Tessellation’s technique to compress a true color image using a Lossy compression

Abstract

In this paper, we show how to use the concept of Dirichlet Tessellations to compress, store and reconstruct an image without affecting on its dimensions and represent it with an acceptable quality, where a true color image has compressed by 60.05% with mean square error (MSE) = 9.6081 which represents the error between the restored image and the original image, and peak signal-to-noise ratio (PSNR) =38.3044 dB which represents the similarity between the restored image and the original image, using MATLAB R2017a. Dirichlet Tessellation has simply defined as dividing the space into geometric shapes by generating finite set of distinct points, each shape contains one of the distinct points and comprising that part of the space nearer to that distinct point than to any of the other points. We have used two algorithms for image compression, First algorithm selects set of distinct points distributed uniformly in an image and store their locations along with pixel values. In the second algorithm random selection of distinct points, which distributed in regions containing more details, using the edges detector algorithm to detect these details. In order to reconstruct the image, Saved distinct points placed at their corresponding locations in a new image that is formed, where two algorithms used, the first algorithm based on the concept of a growing region. It’s Region -Based image segmentation method, by checking the pixels adjacent to the saved distinct points and delimiting whether the pixels should add to the regions of saved distinct points depending on the region’s membership criteria such as pixel intensity. The second algorithm uses one of the Dirichlet Tessellations characteristics, Which divides an image into polygonal regions based on the distinct points that saved, Each pixel in the confined plane of saved distinct points will have the same characteristics of this point, This is done by taking each pixel in an image and calculating the minimum distance between pixel location and saved sites using the distance equation, This process repeated until each pixel assigned its value and specifying all color regions in the image.