The pair of images along the top row are of Renoir's On the Terrace framed behind glass with a reflection of a mannequin. These images were photographed through a linear polarizer oriented to maximize and minimize the reflection. Note that even at the minimal orientation the reflection is quite salient.

From this pair of images we are able to digitally remove the reflection leaving the image of the objects behind the glass intact (bottom row).

This technique works by first noticing that each image is formed from a distinct linear combination of the light that is reflected by the painting and the light that is directly reflected by the glass. With a modest assumption of statistical independence, we employ an analytic version of independent components analysis (ICA) based on higher-order statistical moments to separate the reflection from the painting.

Matlab routines