Linear time constant-working space algorithm for computing the genus of a digital object

Abstract

In recent years the design of space-efficient algorithms that work within a limited amount of memory is becoming a hot topic of research. This is particularly crucial for intelligent peripherals used in image analysis and processing, such as digital cameras, scanners, or printers, that are equipped with considerably lower memory than the usual computers. In the present paper we propose a constant-working space algorithm for determining the genus of a binary digital object. More precisely, given an m x n binary array representing the image, we show how one can count the number of holes of the array with an optimal number of O(mn) integer arithmetic operations and optimal O(1) working space. Our consideration covers the two basic possibilities for object and hole types determined by the adjacency relation adopted for the object and for the background. The algorithm is particularly based on certain combinatorial relation between some characteristics of a digital picture © Springer-Verlag Berlin Heidelberg 2008.