Visual SLAM is one of the fundamental problems in robotics, as it enables autonomous operations in real-world scenarios. Unlike other applications such as object detection or speech recognition, deep learning is yet to be the prevailing standard for visual SLAM. This is partly due to the problem's high dimensionality and the limited data availability. It is then essential to identify the problem's geometrical nature to determine which learning-based architectures best encode this information. By first introducing conventional approaches for SLAM, this paper surveys prevailing state-of-the-art algorithms while defining the different taxonomies for SLAM and their underlying geometry. Then, deep learning architectures for computer vision are introduced, defining the geometries encoded by their embeddings. This survey critically analyzes the theory behind visual SLAM algorithms. Furthermore, it evaluates various methods under different environmental conditions, providing insights into the ...

With the rise of deep learning, there is a fundamental change in visual simultaneous localization and mapping (SLAM) algorithms toward developing different modules trained as end-to-end pipelines. However, regardless of the implementation domain, visual SLAM's performance is subject to diverse environmental challenges, such as dynamic elements in outdoor environments, harsh imaging conditions in underwater environments, or blurriness in high-speed setups. These environmental challenges need to be identified to study the real-world viability of SLAM implementations. Motivated by the aforementioned challenges, this article surveys the current state of visual SLAM algorithms according to the two main frameworks: geometry-based and learning-based SLAM. First, we introduce a general formulation of the SLAM pipeline that includes most of the implementations in the literature. Second, those implementations are classified and surveyed for geometry and learning-based SLAM. After that, environme...