Art authentication from an inverse problems perspective

Abstract

In art authentication and attribution, the overall goal is to confirm whether a particular piece of art P is what it is claimed or thought to be. The claim O is likely to be an original work by a particular artist A. Consequently, the essential modus operandi in art authentication is the collection of information IP about P to compare with the known (and, possibly, yet to be determined) information IO and IA about O and A. The art P is often a painting, which is the current assumption, however, it can be a sculpture or pottery, in fact any artwork or antiquity, and, occasionally, a tapestry or a tablecloth. The connection to inverse problems comes via (a) the collection of the information IP and IO, (i.e. the collection of information about the work in question, and about securely provenanced works by the artist in question),and (b) the optimization of the comparison of IP with IO and A in order to have a strategy that maximizes the confirmation that P is a forgery when that is the situation. In one way or another, (a) will mostly involve the recovery of information from indirect measurements, such as spectroscopic analysis or chemical analysis. It can be quite qualitative, like a visual assessment of how the paint has been applied in terms of brush stroke geometry (stylometry), or quite complex quantitatively, like the non-destructive spectroscopic determination of the composition of the white paint in the painting. From an inverse problems perspective, (b) can be viewed as an identification protocol: What items, listed in IO and IA, would be the most difficult for a forger to reproduce and easy for the authentication to detect. This is a special type of inverse problem in that one does not aim to recover all the possible information hidden in P, but just some key features which allow P to be quickly identified as a forgery or to increase the probability that P is in fact O. From an image analysis and inverse problem perspective, P is an indirect measurement (a cumulative chronological summary) of all the things that the artist (actual or forger) did in making the painting under investigation - choice of the canvas and paints, the order in which the paints were applied, the techniques and geometry of how the paints were applied. Consequently, IP is not only a compendium of specific features, such as canvass type, paint application (geometry) and composition, paint application, but also key features in the chronology of its execution, such as the order in which things were performed and the effect of the passage of time on components, in that white paints or canvases, made with more or less identical components, will have deteriorated to different states after different time intervals. Consequently, focussed subsets of features FP, FO and FA of IP, IO and IA, respectively, are all that are required to support the decision making. Now, for the identification of the order in which the features are utilized, specific details about the artist A and O become crucial prior information. From this perspective, the stylometry of digital images of paintings is proving to be useful and rapid in performing the initial comparison. For forgeries, the decision making is finalized the moment a falsification occurs. Consequently, in authenticiation, the goal is to order the FP so that, when anticipated, falsification occurs sooner rather than later. Because of the inverse problem nature of the recovery, some form of stabilization must be utilized. It is often performed by using key features (signatures, fingerprints). The aim and goal of this paper is a discussion of the mentioned connection between art authentication and inverse problems concentrating on stylometry. A rapid initial test, based on the singular value decomposition of an image of a painting, is proposed for deciding whether P is in fact O.