## 1 Introduction  
Monocular 3D reconstruction is a complex problem that can be solved from multiple perspectives (commonly requiring combining geometric, probabilistic, and even machine learning techniques), due to the large amount of information to be processed and the scale ambiguity problems that pure monocular sensors imply [1, 2]. This problem has been studied in the past three decades to obtain 3D representations of an environment using a sequence of images as the unique source of information for an algorithm. Previously, multiple researchers have explored the possibility of addressing this problem by using diverse hardware like radars, lasers, GPS, INS, cameras, and any possible combination thereof. Regarding the camera alternative, it can be combined with active or passive infrared sensors as RGB-D input modalities. It can also be structured as an array of cameras registering the same objects from multiple angles to allow triangulation. Monocular RGBsensors can also be used alone to register a frame sequence from which the algorithm can process a scene from multiple views [3; 4]. This last option is known as monocular RBG or monocular pure visual input modality, used in monocular Simultaneous Landing and Mapping (SLAM), Visual Odometry (VO), or Structure from Motion (SFM) to obtain 3D reconstructions of environments and estimate the ego-motion of an agent from such representations. In recent years, the pure monocular input modality has attracted the research community's attention due to the sensors' low price and availability in most handheld devices--smartphones, tablets, and laptops. Thus, monocular SLAM, VO, and SFM systems are not limited as other sensors are (like lasers or radars) to work in a limited range and have demonstrated the ability to recover precise trajectories and 3D reconstructions indoors and outdoors. Simultaneous Localization and Mapping is the process where a robot constructs a map of its surroundings while concurrently figuring out where it is located within that map. It involves determining the positions of landmarks and objects near the robot and its position, commonly utilizing sensors and geometric and Bayesian techniques. Visual Odometry is the process of incrementally estimating the robot's ego-motion (location and orientation) by analyzing the changes between the sequential camera images from the robot, estimating the robot's local trajectory rather than obtaining a comprehensive map. VO is commonly utilized as a front-end in many visual SLAM systems. Structure from Motion refers to a reduction in the 3D structure from 2D image sequences that show a scene from different perspectives. It recovers the 3D location of points matched across multiple images and the camera pose for each image. SFM does not require knowing the camera's motion in advance and is utilized in SLAM for initializing new 3D points [5]. As mentioned before, SLAM, VO, and SFM are three disciplines that can be used to achieve the 3D reconstruction goal. SLAM is a discipline that appeared in the robotics field motivated by the objective of estimating the environment map from where the trajectory of a robot can be calculated, which can be used for autonomous navigation, driving, and flying, among other things. In the computer vision field, multiple systems have been created to address similar problems: SFM and VO. Structure from Motion specializes in recovering an environment geometry, while Visual Odometry focuses on calculating the trajectory and pose of a moving camera. However, it has been demonstrated that instead of solving each problem separately, the best results have always been obtained by solving and optimizing both problems simultaneously [3; 6; 7; 8]. That is why it is common to find VO methods that include SFM modules to improve their performance and SFM methods that use VO to improve estimation or optimization tasks.