Image matting is the task of estimating a fore- and background layer from a single image. To solve this ill posed problem, an accurate modeling of the scene’s appearance is necessary. Existing methods that provide a closed form solution to this problem, assume that the colors of the foreground and background layers are locally linear. In this paper, we show that such models can be an overfit when the colors of the two layers are locally constant. We derive new closed form expressions in such cases, and show that our models are more compact than existing ones. In particular, the null space of our cost function is a subset of the null space constructed by existing approaches.  We discuss the bias towards specific solutions for each formulation. Experiments on synthetic and real data confirm that our compact models estimate alpha mattes more accurately than existing techniques, without the need of additional user interaction.