Learning to perceive transparency from the statistics of natural scenes

Anat Levin, Assaf Zomet and Yair Weiss

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)=I_1(x,y)+I_2(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)=I_1(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.