# A Novel 3D Topography Stitching Algorithm Based on Reflectance and Multimap
## 1 Introduction
Fiducialization: these algorithms consist in marking a surface to perform registration on the markers measured in profilometry [13; 14]. Markers on the surface can either be all unique or form a unique pattern all over the surface, but a unique solution must be found by the registration step. Markers can be generated, such as with Focused Ion Beam (FIB) [15], or already on the surface, such as structures in microfluidics [16] and semi-conductors. This technique can be useful for stitching small-scale topographies by adding distinctive features on the surface. This comes at the cost of surface integrity, and a need for post-processing to remove markers before analyzing the original surface. 4. Global optimization of differences: this is generally described as a minimization of differences between overlapping regions of elementary maps, in the least-square method meaning. [PERSON] et al. compute the correct displacements along x, y and z axes to apply on elementary maps in order to perform in-plane registration [17]. Global  
Figure 1: Generalized stitching procedure flowchart. optimization of differences is more accurate than geometric stitching, but is more noise-sensitive, such as in flat or small-scale surfaces. Global optimization algorithms can be used for registration. Simulated annealing has been explained by [PERSON] and [PERSON] [18] using an analogy with the annealing process of solids. A faster version of the simulated annealing optimization algorithm was presented by [PERSON] and [PERSON] [19]. Simulated annealing has been tested by [PERSON] et al. [20] on various combinatory problems. [PERSON] et al. [21] proposed a silhouette-based registration and stitching algorithm using simulation annealing optimization. On the other hand, a genetic algorithm can also be used. Genetic algorithms have been explained by [PERSON] [22], [PERSON] [23], [PERSON] [24] and [PERSON] and [PERSON] [25] as algorithms inspired by the natural selection of genes, using generation of an initial population of solutions to test, selection of best solutions at each iteration, and merging and mutation of parameters to find an optimal solution to a problem. Local search with genetic algorithms has been detailed by [PERSON] [26]. The use of genetic algorithms for image registration and stitching appeared in the works of [PERSON] and [PERSON] [27], [PERSON] et al. [28], [PERSON] and [PERSON] [29] and [PERSON] [30]. Another global optimization algorithm, called particle swarm algorithm, is presented by [PERSON] and [PERSON] [31], [PERSON] and [PERSON] [32], [PERSON] and [PERSON] [33] (in an attempt to define a standard for particle swarm algorithm). An overview of the particle swarm algorithm and its variants was written by [PERSON] et al. [34]. Another variant, called the radius particle swarm optimization, was introduced by [PERSON] and [PERSON] [35]. A 3D surface stitching algorithm based on particle swarm optimization was used by [PERSON] et al. [36] for the stitching of cylindrical surfaces. Combining prepositioning and global optimization of differences reduces errors during registration and reduces run-time of stitching as less solutions need to be explored before finding the optimal solution for the registration. 5. Computer vision-based: this is historically linked to image processing before surface stitching. The goal of these algorithms is to find the maximum number of similarities between two elementary maps. This category is divided into two subsets: direct methods and feature detection methods [37]. Direct methods use all pixels of overlapping regions to perform in-plane registration. Cross-correlation-based registration is an example of a direct method [12]. When the maximum of cross-correlation is found when moving overlapping maps, the correct displacement to apply to each map is determined for the registration [8]. On the other hand, feature detection methods first extract points-of-interests on a map, before performing the in-plane registration on such points, also called features.