Reconstructing discontinuous surfaces from a given gradient field using partial integrability

This paper describes an adaptive surface reconstruction method from a given gradient field that allows discontinuities in the solution. We first formalize a vector space projection technique to reconstruct a surface with a uniformly integrable gradient field that corresponds to the minimum norm solution in the gradient space over discrete imaging settings. Next, we generalize this technique to reconstruct minimum norm solution surfaces with partially integrable gradient fields, where partial integrability is characterized adaptively from the given gradient field using multi-scale gradient space expansions. The simulations on synthesized and real data using block processing techniques indicate that the proposed method provides fast and reliable surface reconstruction through accurate characterization of embedded partial integrability in a given gradient field.