Image: Martini cup
Credit: Jaume Rigau, Miquel Feixas, and Mateu Sbert
Date: June 2005

“Integral geometry and information theory tools are applied to quantify the shape complexity from two different perspectives: from the inside of the object, we evaluate its degree of structure or correlation between its surfaces (inner complexity), and from the outside, we compute its degree of interaction with the environment (outer complexity). Our shape complexity proposals are based on the following: a distribution of global lines crossing an object defines a continuous information channel and the continuous mutual information of this channel is independent of the discretization and invariant to a change of scale.”
Shape Complexity Based on Mutual Information (abstract)
Jaume Rigau, Miquel Feixas, and Mateu Sbert
IEEE International Conference on Shape Modeling and Applications (SMI '05)