# A Novel 3D Topography Stitching Algorithm Based on Reflectance and Multimap
## 4 Discussion  
The first test case (A) is important to verify that each stitching algorithm has no major flaws and can stitch simple cases, including non-measured points and height measurement uncertainties. All tested stitching algorithms succeeded in this test case. Other test cases (B, C and D) are increasingly difficult, either due to larger stitching size, various roughness scales, measurement conditions (measurement apparatus, technologies, objective lens, replication) or a combination of the previous points. In this regard, the CC stitching algorithm failed on test cases B, C and D. This is due to its high sensitivity for measurement height uncertainties and noise. In a test case with only simulated surface with no measurement height uncertainties and noise, it is likely that the CC algorithm would perform successfully, but this situation is never found in practice with genuine measurements. Figure 16: Standardized mean repositioning error (**a**) and stitching error estimator (**b**) for each test case. The GOD stitching algorithm provides satisfactory stitched topographies in visual inspection. Only small defects can be observed, and roughness parameters from ISO standards 25178-2 [6] would not be significantly influenced by these defects. However, from a metrological point-of-view, surface fidelity is poor as local deformations, hidden by the blending step, are present with the GOD algorithm. This is confirmed by the mean repositioning error and the stitching error estimator, even though local deformations are difficult to observe by visual inspection. Only GEO and the proposed reflectance-based multimap stitching algorithms performed the stitching of all test cases successfully. If only visual inspection, run time and memory usage are considered (other quantitative criteria cannot be calculated for geometric algorithm as explained in the Materials and Methods section), stitching users would a priori prefer geometric stitching algorithm. In fact, most 3D profilometers use geometric stitching algorithm as it can produce an acceptable stitching result in most cases, although it is not the optimal stitching result. However, geometric stitching is dependent on the accuracy, the precision and the robustness of the measurement apparatus, contrary to other stitching algorithms, which compare overlapping regions to perform a finer (and more optimal) registration. All topography measurements in this article were performed with high-end 3D profilometers, which are more accurate, precise and robust than most 3D profilometers. That is why geometric stitching performed so well in all test cases. However, it is likely that geometric stitching would fail for lower-end 3D profilometers. Choosing geometric stitching is then largely based on the quality of the 3D profilometers available to the user. If overall qualitative and quantitative criteria are considered, reflectance-based multimap algorithms (NR, EER and TSR) should be selected. The mean repositioning error and stitching quality are similar for all the rising sun stitching algorithm variants. EER and TSR provide the same stitched topography, as the TSR algorithm should find the same lighting angle \(\phi\) just as the EER algorithm would but faster, as per its design. TSR should then be preferred over EER. Finally, the question is whether to use the NR algorithm or the TSR algorithm. The TSR stitching algorithm optimizes the reflectance of the elementary map to stitch; however, in some cases, optimization cannot converge into a unique solution. These pathologic cases are either isotropic surfaces or periodic surfaces without measurement uncertainties. In these pathologic cases, which happen mostly with simulated surfaces, it is better to arbitrary select a lighting angle \(\phi\), such as in the NR algorithm.