Learning to Perceive Transparency from the Statistics of Natural Scenes
Certain simple images are known to trigger a percept of transparency: the input image I is perceived as the sum of two images I(x,y) = I1(x,y) + I2(x,y). This percept is puzzling. First, why do we choose the "more complicated" description with two images rather than the "simpler" explanation I(x,y) = I1(x,y) + 0 ? Second, given the infinite number of ways to express I as a sum of two images, how do we compute the "best" decomposition? 
 
Here we suggest that transparency is the rational percept of a system that is adapted to the statistics of natural scenes. We present a probabilistic model of images based on the qualitative statistics of derivative filters and "corner detectors" in natural scenes and use this model to find the most probable decomposition of a novel image. The optimization is performed using loopy belief propagation. We show that our model computes perceptually "correct" decompositions on synthetic images and discuss its application to real images.