Abstract: This paper proposes a new algebraic algorithm for computing the Euler number of 3-D images. It is based on mathematical principles in differential geometry and algebraic topology. The basic idea can be easily generalized to images defined by other data structures such as a hierarchical data structure. We find that this kind of mathematical description of the basic structures of the objects which are invariant under rigid transformations such as rotation and translation of the ambient Euler space is a useful approach to analyse and understand 3-D images.

Key words: rigid transformation, algebraic topology, Euler number, hierarchical data structure