Methods and Applications of Analysis

Volume 26 (2019)

Number 3

Special Issue in Honor of Roland Glowinski (Part 2 of 2)

Guest Editors: Xiaoping Wang (Hong Kong University of Science and Technology) and Xiaoming Yuan (The University of Hong Kong)

Curvature-based authentication of van Gogh paintings

Pages: 269 – 280



Haixia Liu (School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China; and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, China)

Xue-Cheng Tai (Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong)


Art authentication is the identification of genuine paintings by famous artists from the forgeries. In this paper, we introduce a novel curvature-based method to authenticate van Gogh paintings. We use curvature images to capture the shape information in the paintings. For each painting, we convert it from RGB to HSI color space. The features we propose are two simple statistics of the three parts: including (i) the H, S, I color information, (ii) their corresponding first order derivatives in $x, y$ directions, and (iii) the corresponding 2D curvature images. In order to select the appropriate features for art authentication, we use a forward stage-wise feature selection method such that van Gogh paintings are highly concentrated and forgeries are spread around as outliers. Numerical results show that our method gives the 88.61% classification accuracy, which outperforms the state-of-the-art methods for art authentication so far.


art authentication, curvature, HSI color space, van Gogh, moment statistics

2010 Mathematics Subject Classification


The authors would like to thank Profs. Haixiang Lin, Eric Postma and Raymond H. Chan for providing the 79 van Gogh paintings for use. The authors also would like to thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme ‘variational methods and effective algorithms for imaging and vision’ which was support by EPSRC Grant Number EP/K032208/1. Haixia Liu would like to thank Norwegian Research Council project through ISP-Matematikk (Project no. 239033/F20) to support her stay.

Received 21 December 2017

Accepted 30 July 2019

Published 2 April 2020