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3.2.3 Algorithms to compare 3D models
In this section we are going to present different algorithms that we have planned to use
in order to fulfil the requirements of our project.
The first we have to do in order to compare two 3D models that represent the same
physical object is to align them. The process of finding a transformation to align two
meshes or point clouds is also called registration.
In order to perform the registration process, we present an algorithm called Iterative
Closest Point (ICP). The ICP algorithm has become the dominant method for aligning
three dimensional models based purely on the geometry, and sometimes colour, of the
meshes. ICP starts with two meshes and an initial guess for their relative rigid-body
transform, and iteratively refines the transform by repeatedly generating pairs of corresponding points on the meshes and minimising an error metric [8]. In our case, a rigid
body transform is not going to match all points, since the 3D models used are not going
to have exactly the same shape, but it should be working doing slight modifications to
the algorithm if needed.
Once we have the different meshes aligned we have to use a way to measure its differences.
Basic ideas include measuring areas or volumes, having algorithms that we consider too
basic to be included in this document. A more complex idea consists on using a structure
called Reeb graph. A Reeb graph is an interesting graph to describe topology structure
that encodes the connectivity of its level sets based on the critical points of a scalar
function [9]. We can think about the Reeb graph as a graph that represents a “skeleton”
of the mesh, thus containing information about its shape. Figure 3.2 shows an example
of Reeb graph.
Figure 3.2: Reeb graph of a 3D model of a camel.
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