Image Processing using Voronoi diagrams 1 Alondra Martínez Dept. of Mathematics University of Oriente Santiago de Cuba, Cuba Jennifer Martínez 2 Department of Telecommunications University of Oriente Santiago de Cuba, Cuba Hebert Pérez Center for Neuroscience, Image and Signal Proc. University of Oriente Santiago de Cuba, Cuba Ricardo Quirós Dept. of Information Systems and Languages University Jaume I Castellón, Spain 1 This work has been partially supported by grant TIN2005-08863-C03 of the Spanish Ministry of Science and Education 2 Corresponding address: jennifer@fie.uo.edu.cu Abstract – In this paper we present some techniques for obtaining non-photorealistc images with the aid of Voronoi diagrams, such as stained-glass images. We also show examples of their potential applications, including lossy image compression, and progressive and adaptive visualization of bitmap format images. Keywords: Image compression, Voronoi diagram, Mosaicing. 1 Introduction Several commercial applications dedicated to image processing offer choices for obtaining a non-photorealistic artistic effect known as stained-glass or mosaicing. You get, as a result, a mosaic-type image with the appearance of a stained-glass window. The artistic value of the mosaic depends of the thoroughness on which the tiny tiles or crystals are disposed, and the ability of absorbing the particularities of the original image which directly affects the beauty of the final piece. These aspects are usually omitted by commercial software. We propose obtaining the stained-glass effect by selecting a set of pixels from the image as Voronoi sites or generators, and constructing the Voronoi diagram associated to them; then each Voronoi cell is refilled with the color of the corresponding site, thus becoming a tile or crystal. The resulting image is designated as “Voronoi mosaic” or “Voronoi image”. You obtain a “good” Voronoi mosaic if the selection of the pixels that will operate as Voronoi generators is also “good”. It is easy to verify that if the generators are chosen with a uniform distribution inside the image the mosaic loses much of the desirable characteristics from the original image. Finding new ways to improve the results of the mosaicing operation, now with the assistance of Voronoi diagrams, is one of the fundamental purposes of this work. The proposed methods are classified into two groups: Contour- directed approaches and Homogenuos-color-region- directed approaches. The first ones result in a non-uniform collocation of Voronoi generators in a way that both the site density as well as the effort for the effective collocation is greater in the areas with finer details. The other approach consists of decomposing the image according to color in homogeneous polygonal regions, and then a set of sites is chosen inside each region, for the purpose of approximating this by one or several Voronoi cells. 1.1 Image compression A Voronoi mosaic can be used as a compressed representation of certain bitmap image: taking advantage of the property that a Voronoi cell is completely determined by the corresponding site, the information that describes an entire tile in the mosaic is contained in one single pixel (the Voronoi site). As the Voronoi mosaic is completely determined by the set of generators and their corresponding colors, this information could be stored in a single file and then we could reconstruct the image in an approximate way; we get this way a lossy compression method. For the Voronoi mosaic to be a “good” compressed representation a compromise between the amount of necessary information to characterize it and the adjustment level to the image that it approximates is established. The larger the number of generators of the Voronoi mosaic, the better it will show the distinguishing features of the original image. If every pixel is chosen as a generator, then the image will be exactly described; nevertheless an excessive amount of sites is not desirable, for it would make the file too large. 1.2 Other applications Mosaic construction techniques using Voronoi diagrams can be also useful for adaptive visualization: a way of representing images that does not require showing all the information, but only a certain amount, determined beforehand in a dynamic context. It is eventually unnecessary to show high resolution images, perhaps Conf. on Image Proc., Comp. Vision, and P. R. | IPCV'07 | 485