abstract In this paper, we show how to use the concept of Dirichlet Tessellations to compress , store and reconstruct an image without effecting on its quality or size, using Matlab R2017a .

Dirichlet Tessellation is simply defined as the division of the space into geometric shapes by generating a 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 used two algorithms for image compression , The first algorithm is selecting a set of distinct points that are distributed uniformly on an image and store their locations along with pixel values . And in the second algorithm , a random selection of distinct points , which are distributed in regions containing more details , using the edges detector algorithm to detect these details . In order to reconstruct the image , saved distinct points are placed at their corresponding locations in a new image that is formed , where two algorithms are also used , The first algorithm is based on the concept of a growing region . it’s region -based image segmentation method , by examining the pixels adjacent to the saved distinct points and determines whether pixels should be added 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 characteristics of Dirichlet Tessellations , which is dividing an image into polygonal regions based on the distinct points that were saved , each pixel in the confined plane of saved distinct points will have the same characteristics of that points , 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 is repeated until each pixel assigned its values and all color regions are specified in the image .compress the image To compress the image , we need to reduce the image by eliminating some information , especially unnecessary information without effecting on the general structure of the image , this type of compression is called lossy compression .

the first step reduces an image by using Dirichlet Tessellations technique , This technique is used to generate image map by choosing a distinct points in an image and store their locations along with pixels value (RGB) of that points , using two algorithms of Dirichlet Tessellations . ? first algorithm choose pixels uniformly . ? second algorithm choose pixels randomly depending on edges detection algorithm .edge detection It is just a process of locating the edges of objects in an image , It is a very important step to comprehend image features .

Edges usually indicate to items in the image where the gray value changes considerably from one pixel to another . It symbolizes region in the image with sharp intensity variation representing object boundaries . The reason behind detecting sharp edges in the image is for capturing important events . An edge detector reduces the amount of data to be processed and remove useless information , while conserving the important structural properties of an image , It is a good way to solve the problem of the large space occupied by the image in computer memory and transmission over the Internet . Different methods are being used to detect edges in image processing among these is Sobel operator . The Sobel operator applies a 2-D spatial gradient metering on images , It uses a couple of horizontal and vertical gradient masks , which are 3×3 for edges detection function .

The Sobel detector is incredibly delicate to noise in an image , it effectively highlights them as edges , image smoothing .decompression of image The concept of decompression the image is simple , We only need to define some features that are distinguishing regions in the image , usually depends on the original image to know the important information for segmentation and the result that we want . In order to reconstruct the image , saved distinct points are placed in their corresponding locations in a new image that is formed, where two algorithms are also used for decompression .