# A Novel 3D Topography Stitching Algorithm Based on Reflectance and Multimap
## 1 Introduction
Many descriptors (algorithms to find features) exist. The first major one, developed by [PERSON] [38], is the SIFT (Scale-Invariant Feature Transform) descriptor [39; 40; 41]. This descriptor was originally used for object recognition, but its usefulness for automatic image stitching came soon after [42]. Many other feature descriptors were developed with either increased precision or robustness, or shorter run time for the extraction, such as SURF [43; 44], U-SURF [45], Harris Corner [46], BRISK [47], FAST [48], MSER [49; 50], Min Eigen [51], ORB [52] or KAZE [53]. Table 1 provides more details about each descriptor. [PERSON] and [PERSON] [54] compare feature descriptors (SIFT, SURF, KAZE, AKAZE (a variant of KAZE), ORB and BRISK) and their performance for image registration, such as scale invariability, feature extraction run time and registration accuracy. A RANSAC (RANDOMSAmple Consensus) algorithm [41; 55] is used in feature detection to extract the most relevant features before performing the registration. Computer vision-based stitching algorithms can be very precise but also costly in time. While feature detection method aims at reducing run time by selecting a subset of interesting features for the registration, the use of these is viable with sufficiently large maps to observe a shorter run time compared to direct methods if features can be extracted, such as for surface defects or large structures. However, computer vision-based algorithms, and especially feature detection algorithms, cannot find features of high quality, i.e., of high gradient, or might find too many features of low quality, which behave in the same way as noise for the registration algorithm. The most common data classes are metadata and raw topographies, but a more promising data class is multimap data, i.e., a set of multiple layers with their own information about a surface sample (topography, image, quality map, etc.). A multimap stitching algorithm can then use multiple layers during the registration to improve the alignment precision and to reduce the vertical drift. This kind of stitching algorithm is notably used in the focus variation microscopes developed by [PERSON](tm) (Raaba, Austria). [PERSON]'s stitching strategy is then used to compute in-plane registration with high quality images and to calculate the out-of-plane registration with topographies, as images do not contain out-of-plane information (Z-translation and XY-rotations). A new stitching algorithm family, the _rising sun stitching algorithm_, is here proposed with three algorithm variants (naive reflectance, exhaustive enumeration reflectance and two-step reflectance). The rising sun stitching algorithm and its variants are based on reflectance and multimap. Indeed, the new proposed algorithm uses the 2D reflectance maps generated on the elementary topographic maps to improve the 3D alignment of these elementary maps. These new algorithms are compared to in-plane stitching algorithms described above. As manual stitching is too user-dependent and fiducialization does not preserve surface integrity, only geometric, global optimization of differences and computer vision-based (cross-correlation) in-plane stitching algorithms will be used as references for the comparison of stitching algorithms.