# A Novel 3D Topography Stitching Algorithm Based on Reflectance and Multimap
## 1 Introduction
More precisely, registering two identical overlapping regions is easy: only equality in overlapping regions is to be verified, and searching over multiple translations or rotations is just a question of run-time of the algorithm. Essentially, most algorithms perform perfect stitching of maps with identical overlapping regions. However, in the case of similar but not identical overlapping regions, the goal is to find the transformation to apply on one overlapping region, which results in the least different (or the most similar) regions. In practice, this is the case for every measured map, such as 3D topographies, as noise and uncertainties on the maps to stitch cannot be avoided. This implies that stitching algorithms are complex, as the problem of the registration of measured maps is challenging. In the case of 3D topography stitching, uncertainties appear at two different levels. First, uncertainties exist at the level of the measurement of each elementary map, due to measurement environment, lighting conditions for optical system, the measurement technology, the noise of the metrological system and the nature of the surface to measure (brightness, slopes, materials). Due to uncertainties, it is then impossible to get two identical measures of a surface. At a second level, acquiring multiple elementary maps for stitching while moving between each elementary map position is also classified as an uncertainty due to XYZ positioning, thermal drifting, modification of lighting conditions or surface contamination during the acquisition process (such as dust deposition). Uncertainties of measurement and of the stitching acquisition process make the stitching procedure difficult and, in some more serious cases, impossible. [PERSON] et al. [8] proposed a flowchart of the stitching procedure for 3D topographies. Based on this work, a more detailed and generalized version of this workflow is proposed by the authors of this article in Figure 1. The stitching procedure is composed of two main phases, i.e., the data measurement phase and the stitching algorithm phase, and contains five steps: the data acquisition, the elementary map preprocessing, the in-plane registration (i.e., elementary map alignment for X-translation and Y-translation and \(Z\)-rotation), the out-of-plane registration (for Z-translation, X-rotation and Y-rotation), and the blending (the merging step that aims at hiding visual defects, such as seams, in the resulting overlapping regions of the stitched map). Note that in-plane registration and out-of-plane registration can be performed either simultaneously or consecutively, but both are required for the stitching of 3D topographies. Five categories exist for in-plane registration:  
1. Manual: this can be performed by the user, using either transparency, region pointing or colocalization of overlapping maps. Most manual techniques rely on a visual inspection of all elementary maps, which is a slow process, highly dependent on the user, and prone to registration error. On the other hand, automatic stitching algorithms were historically created for images before topography. Many techniques were first developed for image stitching, also called panorama, and then adapted for topography, with various success rates. Automatic stitching is much faster than manual stitching: [PERSON] et al. [9] explained that the manual stitching of a pair of maps can reach 30 min, while the automatic stitching would only take a few seconds. Thus, larger stitching can be performed in a shorter period of time with automatic stitching. 2. Geometric: this type of stitching uses metadata, such as absolute or relative positions of elementary maps, to perform the registration [10; 11]. This technique is fast, but its precision depends on the accuracy and robustness of the profilometer. Geometric stitching is the most used in commercial profilometers. It can also be used for prepositioning before finer registration with a more accurate technique [12]. 3.