Abstract
New algorithms for computing the Euler number of a 3D digital image S are given, based on smoothing the image to a differentiable object and applying theorems of differential geometry and algebraic topology. They run in O( n) time, where n is the number of object elements of S with neighbors not in S. The basic idea is general and easily extended to images defined by other means, such as a hierarchical data structure or a union of isothetic (hyper) rectangles.
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