TY - JOUR
T1 - Invariant histograms
AU - Brinkman, Daniel
AU - Olver, Peter J.
PY - 2012/1
Y1 - 2012/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84055199834&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84055199834&partnerID=8YFLogxK
U2 - 10.4169/amer.math.monthly.119.01.004
DO - 10.4169/amer.math.monthly.119.01.004
M3 - Article
AN - SCOPUS:84055199834
SN - 0002-9890
VL - 119
SP - 4
EP - 24
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 1
ER -