Benchmarking and Comparing Popular Visual SLAM Algorithms

This paper contains the performance analysis and benchmarking of two popular visual SLAM Algorithms: RGBD-SLAM and RTABMap. The dataset used for the analysis is the TUM RGBD Dataset from the Computer Vision Group at TUM. The dataset selected has a large set of image sequences from a Microsoft Kinect RGB-D sensor with highly accurate and time-synchronized ground truth poses from a motion capture system. The test sequences selected depict a variety of problems and camera motions faced by Simultaneous Localization and Mapping (SLAM) algorithms for the purpose of testing the robustness of the algorithms in different situations. The evaluation metrics used for the comparison are Absolute Trajectory Error (ATE) and Relative Pose Error (RPE). The analysis involves comparing the Root Mean Square Error (RMSE) of the two metrics and the processing time for each algorithm. This paper serves as an important aid in the selection of SLAM algorithm for different scenes and camera motions. The analysis helps to realize the limitations of both SLAM methods. This paper also points out some underlying flaws in the used evaluation metrics.Comment: 7 pages, 4 figure

Stein fillings of planar open books

We prove that if a contact manifold $(M,\xi)$ is supported by a planar open book, then Euler characteristic and signature of any Stein filling of $(M,\xi)$ is bounded. We also prove a similar finiteness result for contact manifolds supported by spinal open books with planar pages. Moving beyond the geography of Stein fillings, we classify fillings of some lens spaces.Comment: Minor typos fixe

Stein fillings of contact 3-manifolds obtained as Legendrian surgeries

In this note, we classify Stein fillings of an infinite family of contact 3-manifolds up to diffeomorphism. Some contact 3-manifolds in this family can be obtained by Legendrian surgeries on $(S^3,\xi_{std})$ along certain Legendrian 2-bridge knots. We also classify Stein fillings, up to symplectic deformation, of an infinite family of contact 3-manifolds which can be obtained by Legendrian surgeries on $(S^3,\xi_{std})$ along certain Legendrian twist knots. As a corollary, we obtain a classification of Stein fillings of an infinite family of contact hyperbolic 3-manifolds up to symplectic deformation.Comment: Made changes to reflect referee comments. Proofs of some of the key lemmas are expanded. Final version accepted in Journal of Symplectic Geometr