Anat Levin, Assaf Zomet, Yair Weiss
Certain simple images are known to trigger a percept of trans- parency: 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 ? Sec- ond, given the inﬂnite 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 sys- tem that is adapted to the statistics of natural scenes. We present a probabilistic model of images based on the qualitative statistics of derivative ﬂlters and \corner detectors" in natural scenes and use this model to ﬂnd the most probable decomposition of a novel image. The optimization is performed using loopy belief propa- gation. We show that our model computes perceptually \correct" decompositions on synthetic images and discuss its application to real images.