## 2 Methodology  
The methodology is designed to face the two main issues in DEMs. The first issue is the low variance mentioned in the previous section. The second issue is a general difference, both in scale and position. The latter requires further explanation. Different DEMs may describe the same zones of the surface of the Earth with different resolutions of each cell. This affects not only to the number of cells of the image but the digital levels that represents the height of the DEM. Following the description in the previous paragraph, the methodology is divided into two phases:  
1. Preprocessing: This phase is designed to determine general differences in scale, position, and rotation (rigid transformation). 2. Determination of homologous points (keypoints): This is the main process of the proposed method. It determines the points with the same characteristics in both DEMs using an increasing and rotating ring and a set of pixels surrounding the  
Figure 1: Statistics of datasets IMC-PT and DEMs: (**a**) mean values; (**b**) standard deviations. selected one with a known Manhattan distance for comparison inside a predefined search window. The preprocessing phase, due to low variance, is achieved using an Iterative Closest Point (ICP) algorithm following the ideas of [PERSON] [22] and [PERSON] [23], among others. The last one was used to achieve a difference in the pixel spatial resolution, as was indicated in previous paragraphs. The points used to carry out this alignment between the two DEMs were a set of local maxima and minima with the following criteria: (i) the maximum or minimum must have a distance higher than the diagonal of the image divided by the number of the total local maxima and minima points detected; (ii) maxima and minimum must be absolute inside a defined zone; and (iii) maximum and minimum must be separated to obtain a match. With this approach, we first obtain a transformation to determine the original differences in scale, rotation, and position. We think that this approach is the most interesting because it isolates our proposed algorithm from knowledge about spatial information. However, a general transformation can be performed due to geoposition parameters of each DEM, which can allow us to test the results. Once the preprocessing phase is finished, we determine a more precise match inside a defined area around a cell of the reference image projected into the tested image. The improvement in the keypoint position is achieved using the transformation parameters of the preprocessing phase (Figure 2a). The main idea behind the matching is the use of Pearson chi-squared test value to determine if two rings are similar \"enough\" to be considered the same. Because this test is defined for two sets of data with the same length, as we consider a set of discrete cells, we can compare both rings. In addition, if we define a rotation direction of one of the rings and we match the number of cells of each ring by means of a simple interpolation (Figure 2b), rings with different orientations and different resolutions per pixel can be compared. Figure 2: Methodology proposed in this study: (**a**) workflow; (**b**) example of the procedure for obtaining two sets of pixels to correlate. The acronyms are as follows: DV: Digital value of pixel; n: number of cells in the ring; d: distance in pixels from the center of the ring in the reference image; D: distance of the search window in pixels in the search image; n: number of pixels of the ring of distance d; n’: number of pixels of the ring of distance d’; _f_: relation between approximate pixel spatial resolution from reference image and search image. The proposed procedure is described as Algorithm 1. It is a general iterator in the reference image over the tested image using the transformation obtained in preprocessing and a zone around this position. Then, each ring inside this zone is tested against the original ring of the reference image using a rotation. From all of these rings, the maximum correlation coefficient is retrieved.