Estimation of Alpha Mattes for Multiple Image Layers

Image matting deals with the estimation of the alpha matte at each pixel, i.e., the contribution of the foreground and background objects to the composition of the image at that pixel. Existing methods for image matting are typically limited to estimating the alpha mattes for two image layers only. However, in several applications one is interested in editing images with multiple objects. In this work, we consider the problem of estimating the alpha mattes of multiple (n ≥ 2) image layers. We show that this problem can be decomposed into n simpler subproblems of alpha matte estimation for two image layers. Moreover, we show that, by construction, the estimated alpha mattes at each pixel are constrained to sum up to 1 across the multiple image layers. A key feature of our framework is that the alpha mattes can be estimated in closed form. We further show that, due to the nature of spatial regularization used in the estimation, the final estimated alpha mattes are not constrained to take values in [0, 1]. Hence, we study the optimization problem of estimating the alpha mattes for multiple image layers subject to the fact that the alpha mattes are nonnegative and sum up to 1 at each pixel. We present experiments to show that our proposed method can be used to extract mattes of multiple image layers.