Unveiling the secrets of Escher's lithographs

An impossible structure gives us the impression of looking at a three-dimensional object, even though this object cannot exist, since it possesses parts that are spatially non-connectable, and are characterized by misleading geometrical properties not instantly evident. Therefore, impossible artworks appeal to our intellect and challenge our perceptive capacities. We analyzed lithographs containing impossible structures (e.g., the Necker cube), created by the famous Dutch painter Maurits Cornelis Escher (1898-1972), and used one of them (The Belvedere, 1958) to unveil the artist's hidden secrets by means of a discrete model of the human retina based on a non-uniform distribution of receptive fields. We demonstrated that the ability of Escher in composing his lithographs by connecting spatial coherent details into an impossible whole lies in drawing these incoherent fragments just outside the zone in which 3D coherence can be perceived during a single fixation pause. The main aspects of our paper from the point of view of image processing and image understanding are the following: (1) the peculiar and original digital filter to process the image, which simulates the human vision process, by producing a space-variant sampling of the image; (2) the software for the filter, which is homemade and created for our purposes. The filtered images resulting from the processing are used to understand impossible figures. As an example, we demonstrate how the impossible figures hidden in Escher's paintings can be understood.