The rise of three-dimensional imaging technology has sharpened the need for quantitative geometric and topological analysis of 3D images. Increasingly popular tools for the topological analysis of data are Morse complexes and persistent homology. We present a homotopic algorithm for determining the Morse complex of a grayscale digital image. For two- or three-dimensional images we prove that

this algorithm constructs a discrete Morse function which has exactly the number and type of critical cells necessary to characterize the topological changes in the level sets of the image. The resulting

Morse complex is considerably simpler than the cubical complex originally used to represent the image and may be used to compute persistent homology.