Dense monocular Simultaneous Localization and Mapping by direct surfel optimization

This work presents a novel approach for monocular dense Simultaneous Localization and Mapping. The surface to be estimated is represented as a piecewise planar surface, defined as a group of surfels each having as parameters its position and normal. These parameters are then directly estimated from the raw camera pixels measurements, by a Gauss-Newton iterative process. The representation of the surface as a group of surfels has several advantages. It allows the recovery of robust and accurate pixel depths, without the need to use a computationally demanding depth regularization schema. This has the further advantage of avoiding the use of a physically unlikely surface smoothness prior. New surfels can be correctly initialized from the information present in nearby surfels, avoiding also the need to use an expensive initialization routine commonly needed in Gauss-Newton methods. The method was written in the GLSL shading language, allowing the usage of GPU thus achieving real-time. The method was tested against several datasets, showing both its depth and normal estimation correctness, and its scene reconstruction quality. The results presented here showcase the usefulness of the more physically grounded piecewise planar scene depth prior, instead of the more commonly pixel depth independence and smoothness prior.

New Approach for Secant Update Generalized Version of PSB

Working with Quasi-Newton methods in optimization leads to one important challenge, being to find an estimate of the Hessian matrix as close as possible to the real matrix. While multisecant methods are regularly used to solve root finding problems, they have been little explored in optimization because the symmetry property of the Hessian matrix estimation is generally not compatible with the multisecant property. In this paper, we propose a solution to apply multisecant methods to optimization problems. Starting from the Powell-Symmetric-Broyden (PSB) update formula and adding pieces of information from the previous steps of the optimization path, we want to develop a new update formula for the estimate of the Hessian. A multisecant version of PSB is, however, generally mathematically impossible to build. For that reason, we provide a formula that satisfies the symmetry and is as close as possible to satisfy the multisecant condition and vice versa for a second formula. Subsequently, we add enforcement of the last secant equation to the symmetric formula and present a comparison between the different methods.

Continual Learning with Quasi-Newton Methods

In this paper, we propose CSQN, a new Continual Learning (CL) method which considers Quasi-Newton methods, more specifically, Sampled Quasi-Newton methods, to extend EWC.<div>EWC uses a Bayesian framework to estimate which parameters are important to previous tasks, and it punishes changes made to these parameters. However, it assumes that parameters are independent, as it does not consider interactions between parameters. With CSQN, we aim to overcome this.</div>

Continual Learning with Quasi-Newton Methods

In this paper, we propose CSQN, a new Continual Learning (CL) method which considers Quasi-Newton methods, more specifically, Sampled Quasi-Newton methods, to extend EWC.<div>EWC uses a Bayesian framework to estimate which parameters are important to previous tasks, and it punishes changes made to these parameters. However, it assumes that parameters are independent, as it does not consider interactions between parameters. With CSQN, we aim to overcome this.</div>