The paper introduces LSD-SLAM, a direct (feature-less) monocular SLAM algorithm designed to build large-scale, consistent maps of the environment. Unlike existing direct methods, LSD-SLAM reconstructs the 3D environment in real-time as a pose-graph of keyframes with associated semi-dense depth maps. The key innovations include a novel direct tracking method operating on sim(3) to explicitly detect scale-drift and a probabilistic approach to incorporate noisy depth values into tracking. The system runs in real-time on a CPU and can handle challenging sequences with significant scale variations. The paper also discusses the mathematical foundations, including 3D rigid body and similarity transformations, weighted Gauss-Newton optimization, and uncertainty propagation. Experimental results demonstrate the algorithm's effectiveness on both public datasets and challenging outdoor trajectories, showing its robustness and flexibility.The paper introduces LSD-SLAM, a direct (feature-less) monocular SLAM algorithm designed to build large-scale, consistent maps of the environment. Unlike existing direct methods, LSD-SLAM reconstructs the 3D environment in real-time as a pose-graph of keyframes with associated semi-dense depth maps. The key innovations include a novel direct tracking method operating on sim(3) to explicitly detect scale-drift and a probabilistic approach to incorporate noisy depth values into tracking. The system runs in real-time on a CPU and can handle challenging sequences with significant scale variations. The paper also discusses the mathematical foundations, including 3D rigid body and similarity transformations, weighted Gauss-Newton optimization, and uncertainty propagation. Experimental results demonstrate the algorithm's effectiveness on both public datasets and challenging outdoor trajectories, showing its robustness and flexibility.