## 1 Introduction
For such reasons, in this study, we aim to identify the best monocular RGB methods for 3D reconstruction; so, we included methods from these three disciplines suitable for recovering 3D environment reconstructions. As a complex problem, pure visual monocular 3D reconstruction has been addressed from multiple perspectives combining various techniques that can be classified following different approaches. One early classification is described in the study of [3] defining the feature-based and appearance-based categories; nevertheless, this approach is unsuitable for covering all the SLAM, VO, and SFM techniques available nowadays in the state of the art. A better approach to classify monocular RGB 3D reconstruction systems is the taxonomy described in [9], considering three classifications covering dense, sparse, direct, indirect, classic, and machine learning-based proposals. Moreover, the authors listed 42 methods classified following the proposed extended taxonomy. After a careful reading and analysis of the 42 listed methods, we could identify that many of the existing methods were not adequately evaluated on large datasets [10; 11; 12; 13] or not tested under different motion patterns and illumination changes [11; 14; 15] and not tested for indoors/outdoors [16; 17; 18]; or the results were not obtained on the same metrics [8; 19; 20] hindering comparison and selection. In addition, most of the methods performed comparisons against the currently available methods from the state of the art, providing results in tables summarizing the average mean or median of the algorithm execution on a specific scene, but they did not provide an inferential statistical analysis of the results; thus, the reported differences or improvements cannot be considered significant. Moreover, given the fact that before the extended taxonomy described in [9], there were only general classifications like direct vs. indirect and sparse vs. dense methods [7; 8; 21] or the feature-based and appearance-based classification reported in [3], none of the studies compared their results following a taxonomy that might allow identifying better the advantages and limitations of direct, indirect, dense, and sparse methods. To address the mentioned issues, in this study, we performed a comparison of ten publicly available SLAM and VO methods following a taxonomy, where the main contributions are:  
* A comparison of 10 SLAM and VO methods, following the main classification described in the taxonomy (sparse-indirect, dense-indirect, dense-direct, and sparse-direct), to identify the advantages and limitations of each method of those classifications. * A comparison of three machine learning-based methods against their classic geometric versions to identify whether there are significant improvements in adding neuronal networks to classic approaches. * An inferential statistical analysis describing the procedure to identify significant differences based on the most suitable metrics for testing monocular RGB methods. We also provide video samples of each algorithm's execution as Supplementary material in the GitHub repository: \"[[https://github.com/erickherreraresearch/MonocularPur](https://github.com/erickherreraresearch/MonocularPur)]([https://github.com/erickherreraresearch/MonocularPur](https://github.com/erickherreraresearch/MonocularPur)) eVisualSLAMComparison accessed on 16 June 2023\", along with all the.txt result files of each algorithm run for reproducibility.