Three Dimensional Data Acquisition and The Registration Problem

Abstract

The use of 3D scanners for capturing three dimensional data give rise to many interesting mathematical problems. The main problem we consider is known as the registration problem. When we have two images, i.e. visualizations of some sort, of the same object taken at different viewpoints, or at different times, these will in general not be in the same coordinate system. The problem is in essence, how to bring the images together in a common coordinate system.

We will consider the problem in the context of scans of rigid body objects, captured by 3D scanners. This means that we will study registration where the objects are not allowed to undergo deformations, i.e. we focus on non-elastic registration.