# An Overview on the Latest Nature-Inspired and Metaheuristics-Based Image Registration Algorithms
## 2 Image Registration  
It has been proven that there is not a universal design for a hypothetical IR method that could be applicable to every real-world application [2]. However, IR methods consist of the following four components:  
* Two input images named scene \(I_{s}=\{\vec{p}_{1},\vec{p}_{2},\ldots,\vec{p}_{n}\}\) and model \(I_{m}=\{\vec{p}_{1}^{\,\prime},\vec{p}_{2}^{\,\prime},\ldots,\vec{p}_{m}^{\, \prime}\}\), with \(\vec{p}_{i}\) and \(\vec{p}_{j}^{\,\prime}\) being image points. A registration transformation, named \(f\). It corresponds to a geometric/parametric function that relates the coordinate systems of both images. * A similarity metric function, named \(F\). It is aimed at assessing the level of resemblance (i.e., the degree of overlapping) between the transformed scene image (i.e., \(f^{\prime}(l_{s})\)) and the model one. * An optimization procedure. The optimizer regards a method seeking the optimal registration transformation (\(f\)). Likewise, it is necessary to provide a search space for the suitable representation of the IR solutions. As stated, due to the non-linear nature of the inherent optimization procedure of the IR problem, an iterative procedure is often followed. As depicted in Figure 1, such a procedure usually stops once convergence is achieved, specifically, after the \(F\) value (i.e., the similarity metric) is lower than a given tolerance threshold. Then, we focused our attention on the optimization task, because of its vital importance in the success of the whole performance of the IR method. Moreover, two different search space schemes were adopted in the SoTA: (i) The matching-based approach, in which the optimization process is aimed at looking for an optimal set of pairs of similar image points; and (ii) the parameter-based one, which directly explores the search space of the values of IR solutions, i.e., \(f\). The early proposals tackling the IR problem were based on the first approach (i.e., the matching-based). This is the case of the well-known ICP method [5]. Its main pitfall is its sensitiveness to the initial IR transformation (\(f\)) given by the user [13]. Then, ICP is prone to get trapped in local optima solutions. A detailed description of the IR framework is out of the scope of this contribution. We refer the interested reader to [2]. Likewise, the formulation of the IR problem is dependent on the particular environment in which it is involved (remote sensing, medical imaging, CAD, etc.). In our case, the 3D model reconstruction application can be considered in order to formulate the IR problem. Range scanners are 3D image acquisition devices able to capture images of the surface of the sensed object (see Figure 2), named range images. Each range image is acquired by considering a specific view-point different of the previously sensed ones. The full set of range images models the whole geometry of the scanned object. Nevertheless, each of them is in a different coordinate system. Thus, the reconstruction procedure carries out the accurate integration of all the 3D images in order to achieve a complete and reliable model of the physical object. This framework is commonly named  
Figure 1: The flow-diagram of the image registration (IR) optimization process. 3D modeling (see Figure 2) and it concerns the application of, first, successive pair-wise IR steps of adjacent range images. The final stage considers all the range images at once in order to achieve the optimal integration of the whole set ([14]). Notice how the IR problem is present in two stages of the reconstruction procedure, i.e., in the pair-wise alignment and in the final integration of the whole set of range images. Thus, the IR problem can be formulated as follows. Every pair-wise IR step is aimed at finding the optimal Euclidean transformation (\(f\)) that brings the scene view (\(I_{s}\)) into the best possible overlapping onto the model view (\(I_{m}\)).