Artistic painting: A fractional calculus perspective

• Type: Article in International Scientific Journal
• Date: 2019

Authors

J. Tenreiro Machado (Author) Other; António Mendes Lopes (Author) FEUP

Journal

Title: Applied Mathematical Modelling

Vol. 65

Pages: 614-626

ISSN: 0307-904X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 4 Citations

ISI Web of Science

Scopus - 13 Citations

Other information

Authenticus ID: P-00P-PRE

DOI: 10.1016/j.apm.2018.09.009

Abstract (EN): This paper studies artistic paintings by means of information theory and fractional calculus. A set of artworks created by 100 artists in a time scale covering the last seven centuries of the human kind, is characterized through different entropy indices. First, the paintings are converted into digital format and discretized. Afterwards, the data for color and grayscale images are processed by means of the Shannon and the fractional entropies, both for 1- and 2-dim histograms. The results are correlated with artistic movements that took place throughout the history of painting. In a second phase, the similarities between artists are analyzed for various periods of time. A sample of 10 artworks per artist is considered and their 2-dim fractional entropy is calculated for time scales of 700 and 130 years. The data are processed by a hierarchical clustering algorithm and the results interpreted under the light of the emerging clusters. Finally, the works of a single artist are compared during a short time scale of 47 years.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13