In a recent past, there has been a growing interest for examining the po- tential 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. To that end, after a brief review of the key theoretical concepts, methods and tools underlying the wavelet leader based formulation of multifractal analysis, two sets of digitized painting are analyzed. The first one, the Princeton Experiment, consists of a set of 7 paintings and of their 7 copies, made by the same artist. It enables to examine the potential of multifractal analysis in forgery detection. The second one is composed of several partially digitized paintings by Van Gogh and contemporaries, made available by the Van Gogh and Kr ̈oller-Mu ̈ller Museums (The Netherlands), in the framework of the Image processing for Art Investigation research program. It enables to show various differences in the regularity of the textures of Van Gogh's paintings from different periods or between Van Gogh's and contemporaries's paintings. These preliminary results plead for the constitution of interdisciplinary research teams gathering experts in art, image processing, mathematics and computer sciences.