Point Pattern Matching

Years and Authors of Summarized Original Work

• 2003; Ukkonen, Lemström, Mäkinen

Problem Definition

Let ℝ denote the set of reals and ℝ^d the d-dimensional real space. A finite subset of $\mathbb{R}^d$ is called a point set. The set of all point sets (subsets of $\mathbb{R}^d$) is denoted $\mathcal{P}(\mathbb{R}^d)$.

Point pattern matching problems ask for finding similarities between point sets under some transformations. In the basic set–up a target point set ${T \subset \mathbb{R}^d}$ and a pattern point set (point pattern) ${P \subset \mathbb{R}^d}$ are given, and the problem is to locate a subset I of T (if it exists) such that Pmatches I. Matching here means that P becomes exactly or approximately equal to I when a transformation from a given set $\mathcal{F}$ of transformations is applied on P.

Set $\mathcal{F}$ can be, for example, the set of all translations (a constant vector added to each point in P), or all compositions of translations and rotations...