Information Processing Letters 25 (1987) 199-206 29 May 1987 North-Holland AN ENCODING SCHEME FOR THE EFFICIENT REPRESENTATION OF HIERARCHICAL IMAGE STRUCTURES N.A. ALEXANDRIDIS Department of Electrical Engineering and Computer Science, George Washington University, Washington, D.C. 20052, U.S.A. P.D. TSANAKAS Computer Science Dioision, Department of Electrical Engineerin~ National Technical Unioersity, Athens 15773, Greece Communicated by H.R. Wiehle Received 26 June 1985 Revised 28 April 1986 and 10 September 1986 Keywords: Image processing, hierarchical data structure, image encoding 1. Introduction This paper deals with a new scheme for encod- ing structured images. This method aims at mini- mizing the storage requirements while it ensures a rather short access time. For each picture to be represented in various resolution levels, the infor- mation for the finest resolution available is stored in a suitably constructed array as a reference object for the calculation of coarser image repre- sentations via function calls. In Section 2 we pre- sent the problems associated with storing and accessing the picture's contents and we give some of the most efficient solutions proposed in the literature. In Section 3 we give a detailed descrip- tion of the virtual pyramid structure and in Sec- tion 4 we present some algorithms for identifying the picture's quadrants. Finally, in Section 5, a discussion about the performance of the proposed scheme is presented. 2. Problem description and literature survey Pyramids and quadtrees have been proposed as efficient methods for the representation of two-di- mensional images [4,6,21,22]. The hierarchical rep- resentation of the image contents and the better utilization of the available memory space are two of the most attractive properties of these hierar- chical image structures. The availability of coarser versions of an image helps in designing more efficient algorithms because some functions may be applied on reduced data-spaces. Additionally, the hierarchical data structures allow many processing tasks tO be expressed in a form for which 'divide-and-conquer' schemes are directly applicable. As far as the storage is concerned, it can be shown that the reduced form of a quadtree structure may lead to certain improvements over the conventional nonhierarchical data structures [3,6,9]. This is because certain homogeneous re- gions can be stored as single quadtree nodes. A lot of algorithms based on the hierarchical image structures have been developed for applica- tions in areas such as image processing, computer graphics, and pattern recognition [2,3,7,14,22]. Al- gorithms for the conversion of rasters to quadtrees and vice versa have been presented in [13,15]. The full quadtree structure, where all the nodes are refined up to the single pixel level, is equiv- alent to the pyramid data-structure [1]. This struc- ture can be implemented by a linear array, without the use of any pointers. An efficient indexing 0020-0190/87/$3.50 © 1987, Elsevier Science Publishers B.V. (North-Holland) 199