128 Prakt. Met. Sonderband 38 (2006) 
certain areas can be masked out so that they are not used during the computation. Such 
areas may be plastically deformed areas, or areas where parts are broken out. After the 
registration, a profile can be marked within the digital image of one fracture surface and 
the corresponding profile in the second fracture surface will be found automatically. The 
registration algorithm does not only speed up the procedure for measuring local toughness 
parameters but also compensates for rotations that may be inherent in the 3D models of 
the reconstructed fracture surfaces. Such rotations usually occur when the specimen 
halves are not very carefully mounted in the SEM stage, especially then when no common 
reference plane of the broken parts is available. 
The registration of surfaces already plays an important role in computer vision [10] and 
computer graphics and has become increasingly popular in the field of archaeology [3] in 
the last few years. Special algorithms that are dedicated to the registration of fractured : 
surfaces with plastic deformations for the use in fracture research are not known in the 
literature. So far, the alignment of corresponding surface models has been performed by 
manually selecting several corresponding points in the two 3D models [14]. 
In the following, after a description of the generation of the 3D models (Section 2), we 
describe in Section 3 the algorithm for the registration of corresponding fracture surfaces. 
After a short chapter about the measurement of COD; (Section 4), examples from two 
different objects are presented (Section 5). 
2. 3D SURFACE RECONSTRUCTION 
In order to obtain 3D models of the two corresponding fracture surfaces, stereoscopic 
images are obtained from each specimen half using a SEM. The stereoscopic images are 
obtained by tilting each specimen at constant working distance (tilt angle about 5-15°). The 
reconstruction of the 3D models is done using the software package MeX by Alicona 
Imaging [9] which solves the reconstruction task in two steps. In the first step 
corresponding points are extracted from the stereoscopic images. In the second step, 
metrically correct 3D points are calculated using the geometric relationships from the SEM 
and the corresponding points identified in the first step. 
The 3D models can be either reconstructed using two or three input images with different 
tilt angles. If only two input images are used, the accuracy of the results depends mainly 
on the accuracy of the tilt angle [8]. Since the exact value of the tilt angle may be difficult to 
achieve, especially with manual tilt stages, the software package MeX provides a new 
module that is able to perform an automatic calibration of the tilt angles from 3 input 
images and thus produces more accurate 3D models [12] 
3. REGISTRATION OF CORRESPONDING FRACTURE SURFACES 
The registration of surfaces is a long-researched problem in the field of computer vision. 
The task is to find an Euclidean transformation that transforms one 3D model to another 
3D model so that the distance between the two models becomes a minimum. The 
transformation consists of three rotation and three translation parameters, thus having six 
degrees of freedom. 
Early approaches mainly used pre-computed features for alignment [2], but this approach 
has inherent problems with fine registration, since features are often rather sparse. The 
proposal of the Iterative Closest Point Algorithm (ICP) developed by Besl and McKay [1]