# A Novel 3D Topography Stitching Algorithm Based on Reflectance and Multimap
## 2 Materials and Methods  
### Topographical Measurements  
To evaluate the relevancy of the three variants of the new stitching algorithm, stitching tests are performed on four different surfaces. For each test, elementary maps are measured with a 3D optical profilometer, interferometer or focus variation microscope.  
Table 2 details the measurement configuration for each stitching test. The four stitching tests are designed to test each stitching algorithm in various situations that can be encountered by surface metrologists and roughness researchers:  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Descriptor** & **Descriptor Full Name** & **References** \\ \hline SIFT & \begin{tabular}{c} Scale-Invariant Feature \\ Transform \\ \end{tabular} & [38; 39; 40; 41; 42] \\ \hline SURF & Speeded-Up Robust Features & [43; 44] \\ \hline U-SURF & \begin{tabular}{c} U-Speeded-Up Robust \\ Features \\ \end{tabular} & [45] \\ \hline Harris Corner & Harris Corner & [46] \\ \hline BRISK & \begin{tabular}{c} Binary Robust Invariant \\ Scalable Keypoints \\ \end{tabular} & [47] \\ \hline FAST & FAST & [48] \\ \hline MSER & \begin{tabular}{c} Maximally Stable Extremal \\ Regions \\ \end{tabular} & [49; 50] \\ \hline Min Eigen & Minimum Eigenvalue & [51] \\ \hline ORB & \
\begin{tabular}{c} Oriented FAST and Rotated \\ BRIEF \\ \end{tabular} & [52] \\ \hline KAZE &
\begin{tabular}{c} KAZE \\ (Reference to the word “Wind” \\ in Japanese) \\ \end{tabular} & [53] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of feature descriptors.  
* Polymer rod abraded with FEPA grade 80 SiC abrasive paper: the aim is to verify that each tested algorithm can perform good quality stitching on a simple configuration. Succeeding in this test means that the test stitching algorithm has no major flaw, can handle non-measured points and can process elementary topographic maps with measurement uncertainties.
* Mirror-polished copper rod with indentations, dust and hair: a mirror-polished copper rod with indentations, dust and hair. As the surface is an Independent Multi-Physics (IMP) surface because of the presence of polishing, indentation, hair adhesion and dust adhesion, this is suitable to evaluate the flexibility of a stitching algorithm and its ability to perform a correct registration with various conditions within the same stitching. Moreover, two roughness scales (macroscopic and microscopic) are present and stitching algorithms should be able to register both at the same time.
* Arm skin replica: this test case evaluates the ability of a stitch algorithm to perform registration on macroscopic morphological structures. Moreover, as the polymer used for replication is more sensitive to thermal drift, this increases the difficulty of stitching as uncertainties might be amplified.
* Titanium alloy TA6V rod abraded with FEPA grade 80 SiC abrasive paper: as this surface contains a fractal pattern, the test evaluates the stitching algorithm ability to stitch a fractal pattern for many elementary maps, and to register microscopic morphological structures.  
The tested stitching algorithms should be able to perform correctly with maps containing non-measured points and measurement uncertainties (i.e., overlapping regions are almost identical but not identical). These two points are what makes stitching difficult, though they are present in each measured topography.