Detecting edges of reflections from a single image via convex optimization

We propose to detect edges of reflections, which we call the REF-edges, from a single image via convex optimization. Our method is designed based on two observations on reflections: (i) reflections have almost monotone color and (ii) color around REF-edges varies smoothly. The first one can be translated into the property that gradients around REF-edges distribute linearly in the RGB color space, which we call the REF-linearity. The second one can be interpreted as follows: color differences around REF-edges are small; for an entry of REF-edges, gradients among its surrounding entries have small variance. Using the above properties, we characterize REF-edges as a solution of a constrained convex optimization problem. The optimization problem is solved by the Alternating Direction Method of Multipliers (ADMM). Experiments using real-world images with reflections show the utility of our proposed method.