  The morphometric approach is a powerful ansatz for decomposing the chemical
potential for a complex solute into purely geometrical terms. This method has
proven accuracy in hard spheres, presenting an alternative to comparatively
expensive (classical) density functional theory approaches. Despite this,
fundamental questions remain over why it is accurate and how one might include
higher-order terms to improve accuracy. We derive the morphometric approach as
the exact resummation of terms in the virial series, providing further
justification of the approach. The resulting theory is less accurate than
previous morphometric theories, but provides fundamental insights into the
inclusion of higher-order terms and to extensions to mixtures of convex bodies
of arbitrary shape.
