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History Tree Descriptors of Grayscale Images

We are interested in translating three-dimensional arrays of real numbers (images) into simpler structures that nevertheless capture the topological/geometrical essence of the objects in the images. These structures are to be used as descriptors of images in databases. A foreground history tree structure (FHTS) contains all the information on the relationships between connected components when the image is thresholded at various levels. Unsimplified FHTSs are too sensitive to errors in the image to be good descriptors. We present a method of simplifying FHTSs, which can be shown to be robust in the sense of producing essentially the same simplifications in the presence of small perturbations. We demonstrate the potential applicability of our methodology to macromolecular databases by showing that the simplified FHTSs can be used to distinguish between two slightly different versions of an adenovirus.