3. Multiprocessor Pyramid Architectures for Bottom-Up Image Analysis * N. Ahuja and S. Swamy Coordinated Science Laboratory, University of Illinois at Urbana-Champaign Urbana, IL 61801, USA This paper describes three hierarchical organizations of small processors for bottom-up image analysis: pyramids, interleaved pyramids, and pyramid trees. Progressively lower levels in the hierarchies process image windows of de- creasing size. Bottom-up analysis is made feasible by transmitting up the levels quadrant borders and border-related information that captures quadrant interaction of interest for a given computation. The operation of the pyramid is illustrated by examples of standard algorithms for interior-based computa- tions (e.g., area) and border-based computations of local properties (e.g., perimeter). A connected component-counting algorithm is described that illus- trates the role of border-related information in representing quadrant inter- action. Interleaved pyramids are obtained by sharing processors among sev- eral pyramids. They increase processor utilization and throughput rate at the cost of increased hardware. Trees of shallow interleaved pyramids, called pyramid trees, are introduced to reduce the hardware requirements of large interleaved pyramids at the expense of increased processing time, without sacrificing processor utilization. The three org'anizations are compared with respect to several performance measures. 3.1 Introduction This paper explores the use of hierarchical organization of processors to perform strictly bottom-up computations. Three architectures are described: pyramids, interleaved pyramids, and pyramid trees. These architectures per- form computations that result in a small number of output bits (small compared to the number of bits necessary to represent the entire image). The architec- tures are thus intended to compute image properties or to perform image ana- lysis. They are not suitable for performing image transformations, such as segmentation or enhancement, which provide a whole image as output. The central feature of the architectures described is a hierarchy imposed on the image by a recursive square decomposition of the image. This hierarchy has formed the basis of various pyramid approaches (to be reviewed later in this section) and of the quadtree representation of images. To obtain its quadtree, the image is overlaid with a sequence of increasingly fine tessella- tions that defines a recursive embedding of quadrants and thus a hierarchy over image windows. The hierarchy is described by a tree whose root node is associated with the entire image. Each node in the tree represents a square window. A node has four children unless it corresponds to a window that is of the smallest allowed size. Each child node is associated with a quadrant *This research was supported by the Joint Services Electronics Program (U.S. Army, Navy and Air Force) under Contract N00014-79-C-0424. 38 A. Rosenfeld (ed.), Multiresolution Image Processing and Analysis © Springer-Verlag Berlin Heidelberg 1984