Image representation using Voronoi tessellation

The major approaches to image representation [l] in terms of its constituent regions may be divided into two broad categories: (1) those which specify the borders of the regions and (2) those which describe their interiors. Most of the approaches and the more interesting ones, belong to the latter category. This may be attributed to the increased dimensionality of information (regions, rather than curves) to be represented. An important subclass of these methods, called medial axis transforms (MAT) [l], involves representation of the regions by a set of maximal 2dimensional blocks, of a fixed shape. Each maximal block lies completely within a single region, and is not contained in any other such block. The blocks may have any size and may be placed anywhere in the image as determined by the locations of the regions. The simplest choice for the block shape is the circle as originally proposed by Blum [2]. Squares, or, equivalently, diamonds, may be more appropriate for grid images [3]. If the purpose of the image representation is data compression only, the choice of the block shape is not critical for an arbitrary image with unknown region geometry. However, if the image MAT must be transmitted and security is a concern along with compression, the choice of a fixed shape for blocks may not be ideal. A collection of randomly shaped blocks may provide an MAT coding for the image regions that is less likely to be broken. This paper describes an MAT that uses irregular polygonal blocks whose shapes and sizes are determined by a planar random process. Section 2 defines the Voronoi tessellation of the plane generated by a planar random point process; the cells of the tessellation are used as the blocks of the MAT. Section 3 discussed the derivation of the MAT and a scheme for secure transmission of a given piecewise uniform image. Experimental results on two images are also given. Section 4 describes an adaptive Voronoi partitioning scheme that uses variable spatial resolution to improve the