A Robust and Universal Gradient Domain Imaging Solver Using Gradient Variables and Locally Varying Metrics

Abstract

Gradient Domain Imaging (GDI) has gained a high importance and provoked numerous powerful applications over the last decade. It employs a workflow of creating an inconsistent gradient field (GF) from one or more images using different non-linear operations and finally it determines an image with a consistent, integrable GF that falls near to the prescribed inconsistent one. However, the result is not really predictable, often suffers from halo-effects and other local distortions at higher frequencies as well as from uncontrollable far-effects arising from local gradient-contradictions. The unfolding of these artifacts culminates in an undesired overall image appearance. None of the common GDI solvers can overcome these side-effects as they utilize the same local isotropic 'coefficient-pattern' in a sparse matrix description and they differ only in the numerical solution techniques. We present a powerful GDI method solving the problem completely in the gradient domain with gradient-variables and using spatially varying metrics that depends only on the starting inconsistent gradient field. After obtaining the nearest consistent gradient field with the pre-defined metrics we return into the image space by double integration that yields the wanted pixel intensity values. Our method delivers a great aesthetic enhancement by eliminating halo effects and saving small details, furthermore providing a realistic and pleasant overall light distribution at lower frequencies. By significantly extending the range of allowed inconsistency in the prescribed gradient field, it also allows for solving a large class of problems that proved hopeless beforehand.