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.