Extracting smooth and transparent layers from a single image

Layer decomposition from a single image is an under-constrained problem, because there are more unknowns than equations. This paper studies a slightly easier but very useful alternative where only the background layer has substantial image gradients and structures. We propose to solve this useful alternative by an expectation-maximization (EM) algorithm that employs the hidden Markov model (HMM), which maintains spatial coherency of smooth and overlapping layers, and helps to preserve image details of the textured background layer. We demonstrate that, using a small amount of user input, various seemingly unrelated problems in computational photography can be effectively addressed by solving this alternative using our EM-HMM algorithm.