Invariant histograms

Daniel Brinkman, Peter J. Olver

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We introduce and study a Euclidean-invariant distance histogram function for curves. For a sufficiently regular plane curve, we prove that the cumulative distance histograms based on discretizing the curve by either uniformly spaced or randomly chosen sample points converge to our histogram function. We argue that the histogram function serves as a simple, noise-resistant shape classifier for regular curves under the Euclidean group of rigid motions. Extensions of the underlying ideas to higher-dimensional submanifolds, as well as to area histogram functions invariant under the group of planar area-preserving affine transformations, are discussed.

Original languageEnglish (US)
Pages (from-to)4-24
Number of pages21
JournalAmerican Mathematical Monthly
Issue number1
StatePublished - Jan 2012


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