An image processing of a Raphael's portrait of Leonardo

In one of his paintings, the School of Athens, Raphael is depicting Leonardo da Vinci as the philosopher Plato. Some image processing tools can help us in comparing this portrait with two Leonardo's portraits, considered as self-portraits. The "Scuola di Atene" is one of the most famous paintings by Raphael, the Italian Renaissance artist. Painted between 1510 and 1511, this fresco decorates the wall of one of the rooms, the "Stanza della Segnatura", in the Apostolic Palaces of Vatican. The great Greek philosophers are represented inside a classic architecture. At the central position of this masterpiece, we see two philosophers, Plato on the left and Aristotle, his student, on the right. Plato is shown as a wise-looking man (see Fig.1). It is believed that Raphael based the Plato's face on the features of Leonardo da Vinci [1]. The two artists probably had established a direct interaction when Raphael spent a period of his life in Florence, perhaps from about 1504 to 1508 [2-4]. Leonardo da Vinci returned to Florence from 1500 to 1506: therefore, if the image of Plato is a portrait of Leonardo, this means that Raphael depicted him when Leonardo was 52 or 54 year old. There is a portrait in red chalk, dated approximately 1510 and held at the Biblioteca Reale of Turin, which is widely accepted as a self-portrait of Leonardo da Vinci. It is thought that Leonardo drew this self-portrait at the age of 58 or 60 (see Fig.2). Ref.5 tells that this well-known drawing is not universally accepted as a self-portrait, because the depicted face appears to be quite old, suggesting that Leonardo represented his father or grandfather. Another possibility is that Leonardo altered himself, in order that Raphael might use it for his Plato. However, Plato does not look so old in the painting by Raphael. In any case, let us try to find some matching points between the portraits, that of the man in red chalk (Fig.2)-let us call it, from now on, the self-portrait in red chalk – and the image of Plato (Fig.1) that Raphael had depicted in his fresco. To match the two faces, the image processing is fundamental: in particular, we will use another Leonardo's portrait merged with the self-portrait in red chalk. This portrait is a drawing of the Codex on the Flight of Birds, which Leonardo had partially hidden by his writing, as shown in Fig3, …