Seminars

Euclidean Signature Curves

by

Mark Hickman (University of Canterbury, NZ)

In 1998, Calabi et al. suggested the use of signature curves in object
recognition problems. In that paper it was claimed that two curves were
congruent under a group G if and only if their G-signature curves were
identical. For the next decade the research was mainly focused on finding a
numerically stable method to compute the signature curve. However in 2009
Musso and Nicolodi produced examples of non-congruent curves that
nonetheless had identical Euclidean signature curves. In this talk, I will
simplify the Musso and Nicolodi construction to produce two simple closed
curves of the same length that are not congruent which have identical
signature curves. I will then give a corrected version of the fundamental
"theorem" of the 1998 paper.