Unveiling the Secrets of Escher's Lithographs.

Primo Coltelli,Paolo Gualtieri,Laura Barsanti

doi:10.3390/jimaging6020005

Abstract

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.

Highlights

According to the dictionary definition, illusions are perceptions that represent what is perceived in a way different from the way it is in reality; i.e., they are instances of a wrong or misinterpreted perception of a sensory experience
The procedure gradually reduced the spatial resolution of the pre-attentive retina image (PRI) produced by the model by reducing the number of the receptive fields (RFs) in each peripheral ring one at a time, until the participants recognized a difference with the first stimulus, reaching their threshold, i.e., the resolution limit set by the number (N) of RFs in each ring of the peripheral zone of the last PRI matching the Belvedere original lithograph
We demonstrated that, when we look at one of Escher’s lithographs containing

Summary

Introduction

According to the dictionary definition, illusions are perceptions that represent what is perceived in a way different from the way it is in reality; i.e., they are instances of a wrong or misinterpreted perception of a sensory experience. The famous Dutch graphic artist Maurits Cornelis Escher (1898–1972) is especially well-known for the impossible structures he inserted in his lithographs, such as the Penrose triangle present in Waterfall (1961), the Penrose infinite staircase present in Ascending and Descending (1960), and the Necker cube present in Belvedere (1958) (Figure 1) Through these impossible structures, Escher challenged the concept of the real world everyone possesses by tweaking our perception. Escher was aware of the structure and functioning of the human visual system; he challenged the onlooker with images characterized by components whose 3D inconsistency is unperceivable pre-attentively because they were drawn by the artist just outside the zone surrounding the fixation point. This skillful creativity is very probably the reason of his success. We demonstrate how the impossible figures hidden in Escher’s paintings can be understood

Anatomy of Retina

The Model

Method, Procedure, and Results

Discussion