Conceptualizing Birkhoff's Aesthetic Measure Using Shannon Entropy and Kolmogorov Complexity

Rigau, Jaume; Feixas, Miquel; Sbert, Mateu

Conceptualizing Birkhoff's Aesthetic Measure Using Shannon Entropy and Kolmogorov Complexity

Files

105-112.pdf (430.54 KB)

Date

2007

Authors

Rigau, Jaume
Feixas, Miquel
Sbert, Mateu

Publisher

The Eurographics Association

Abstract

In 1928, George D. Birkhoff introduced the Aesthetic Measure, defined as the ratio between order and complexity, and, in 1965, Max Bense analyzed Birkhoff s measure from an information theory point of view. In this paper, the concepts of order and complexity in an image (in our case, a painting) are analyzed in the light of Shannon entropy and Kolmogorov complexity. We also present a new vision of the creative process: the initial uncertainty, obtained from the Shannon entropy of the repertoire (palette), is transformed into algorithmic information content, defined by the Kolmogorov complexity of the image. From this perspective, the Birkhoff s Aesthetic Measure is presented as the ratio between the algorithmic reduction of uncertainty (order) and the initial uncertainty (complexity). The measures proposed are applied to several works of Mondrian, Pollock, and van Gogh.

        @inproceedings{:10.2312/COMPAESTH/COMPAESTH07/105-112
,
booktitle = {Computational Aesthetics in Graphics, Visualization, and Imaging
},
editor = {Douglas W. Cunningham and Gary Meyer and Laszlo Neumann
},
title = {{Conceptualizing Birkhoff's Aesthetic Measure Using Shannon Entropy and Kolmogorov Complexity
}},
author = {Rigau, Jaume and 
Feixas, Miquel and 
Sbert, Mateu
},
year = {2007
},
publisher = {The Eurographics Association
},
ISSN = {1816-0859
},
ISBN = {978-3-905673-43-2
},
DOI = {/10.2312/COMPAESTH/COMPAESTH07/105-112
}
}