Provably robust simplification of component trees of multidimensional images

Abstract

We are interested in translating n-dimensional arrays of real numbers (images) into simpler structures that nevertheless capture the topological/geometrical essence of the objects in the images. In the case n=3 these structures may be used as descriptors of images in macromolecular databases. A foreground component tree structure (FCTS) contains all the information on the relationships between connected components when the image is thresholded at various levels. But unsimplified FCTSs are too sensitive to errors in the image to be good descriptors. This chapter presents a method of simplifying FCTSs which can be proved 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 FCTSs can be used to distinguish between two slightly different versions of an adenovirus.