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.