## Günter Rote:

# Partial least-squares point matching under translations

*In: 26th European Workshop on Computational Geometry (EuroCG'10), Dortmund,
March 2010, pp. 249–251, Editor: Jan Vahrenhold.
*
### Abstract

We consider the problem of translating a given *pattern set*
` B` of size `m`, and matching every point of `B` to
some point of a larger *ground set* `A` of size `n`
in an injective way, minimizing the sum of the squared distances between
matched points. We show that when `B`
can only be translated along a
line, there can be at most `m`(`n` - `m`) + 1 different matchings as
`B` moves along the line, and hence the optimal translation can be
found in polynomial time.
Last update: April 12, 2010.