When Van Gogh meets Mandelbrot: Multifractal classification of painting's texture

Recently, a growing interest has emerged for examining the potential of Image Processing tools to assist Art Investigation. Simultaneously, several research works showed the interest of using multifractal analysis for the description of homogeneous textures in images. In this context, the goal of the present contribution is to study the benefits of using the wavelet leader based multifractal formalism to characterize paintings. After a brief review of the underlying key theoretical concepts, methods and tools, two sets of digitized paintings are analyzed. The first one, the Princeton Experiment, consists of a set of seven paintings and their replicas, made by the same artist. It enables examination of the potential of multifractal analysis in forgery detection. The second one is composed of paintings by Van Gogh and contemporaries, made available by the Van Gogh and Kröller-Müller Museums (Netherlands) in the framework of the Image processing for Art Investigation research program. It enables us to show various differences in the regularity of textures of Van Gogh's paintings from different periods, or between Van Gogh's and contemporaries' paintings. These preliminary results plead for the constitution of interdisciplinary research teams consisting of experts in art, image processing, mathematics and computer sciences. ► We characterize image texture in painting using wavelet leader multifractal analysis. ► The analysis is conducted on two sets of digitized paintings (Casper, Van Gogh). ► The multifractal features characterize painting and are used for classification. ► We conclude that the method can assist and supplement in art investigation.