Symmetry of similarity

Symmetry of Shapes Via Self-similarity

We describe a simple and novel approach to identify main similarity axes by maximizing self-similarity of object contour parts divided by the axes. For a symmetric or approximately symmetric shape, the main self-similarity axis coincides with the main axis of symmetry. However, the concept of the main self-similarity axis is more general, and significantly easier to compute. By identifying crit...

Correlation of Entropy with Similarity and Symmetry

Informational entropy is quantitatively related to similarity and symmetry. Some tacit assumptions regarding their correlation have been shown to be wrong. The Gibbs paradox statement (indistinguishability corresponds to minimum entropy, which is zero) has been rejected. All their correlations are based on the relation that less information content corresponds to more entropy. Higher value of e...

Similarity Beyond Correlation: Symmetry-Based Approach

When practitioners analyze the similarity between time series, they often use correlation to gauge this similarity. Sometimes this works, but sometimes, this leads to counter-intuitive results. In this paper, we use natural symmetries – scaling and shift – to explain this discrepancy between correlation and common sense, and then use the same symmetries to come up with more adequate measures of...

Symmetry of Fullerene C_60

A measure of symmetry based on shape similarity