The most common way to deal with the uncertainty present in noisy sensorial perception and action is to model the problem with a probabilistic framework. Maximum likelihood estimation is a well-known estimation method used in many robotic and computer vision applications. Under Gaussian assumption, the maximum likelihood estimation converts to a nonlinear least squares problem. Efficient solutions to nonlinear least squares exist and they are based on iteratively solving sparse linear systems until convergence. In general, the existing solutions provide only an estimation of the mean state vector, the resulting covariance being computationally too expensive to recover. Nevertheless, in many simultaneous localization and mapping (SLAM) applications, knowing only the mean vector is not enough. Data association, obtaining reduced state representations, active decisions and next best view are only a few of the applications that require fast state covariance recovery. Furthermore, computer vision and robotic applications are in general performed online. In this case, the state is updated and recomputed every step and its size is continuously growing, therefore, the estimation process may become highly computationally demanding. This paper introduces a general framework for incremental maximum likelihood estimation called SLAM++, which fully benefits from the incremental nature of the online applications, and provides efficient estimation of both the mean and the covariance of the estimate. Based on that, we propose a strategy for maintaining a sparse and scalable state representation for large scale mapping, which uses information theory measures to integrate only informative and non-redundant contributions to the state representation. SLAM++ differs from existing implementations by performing all the matrix operations by blocks. This led to extremely fast matrix manipulation and arithmetic operations used in nonlinear least squares. Even though this paper tests SLAM++ efficiency on SLAM problems, its applicability remains general.

Abstract-Efficiently solving nonlinear least squares (NLS) problems is crucial for many applications in robotics. In online applications, solving the associated nolinear systems every step may become very expensive. This paper introduces online, incremental solutions, which take full advantage of the sparseblock structure of the problems in robotics. In general, the solution of the nonlinear system is approximated by incrementally solving a series of linearized problems. The most computationally demanding part is to assemble and solve the linearized system at each iteration. In our solution, this is mitigated by incrementally updating the factorized form of the linear system and changing the linearization point only if needed. The incremental updates are done using a resumed factorization only on the parts affected by the new information added to the system at every step. The sparsity of the factorized form directly affects the efficiency. In order to obtain an incremental factorization with persistent reduced fill-in, a new incremental ordering scheme is proposed. Furthermore, the implementation exploits the block structure of the problems and offers efficient solutions to manipulate block matrices, including a highly efficient Cholesky factorization on sparse block matrices. In this work, we focus our efforts on testing the method on SLAM applications, but the applicability of the technique remains general. The experimental results show that our implementation outperforms the state of the art SLAM implementations on all the tested datasets.

Many estimation problems in robotics rely on efficiently solving nonlinear least squares (NLS). For example, it is well known that the simultaneous localisation and mapping (SLAM) problem can be formulated as a maximum likelihood estimation (MLE) and solved using NLS, yielding a mean state vector. However, for many applications recovering only the mean vector is not enough. Data association, active decisions, next best view, are only few of the applications that require fast state covariance recovery. The problem is not simple since, in general, the covariance is obtained by inverting the system matrix and the result is dense.The main contribution of this paper is a novel algorithm for fast incremental covariance update, complemented by a highly efficient implementation of the covariance recovery. This combination yields to two orders of magnitude reduction in computation time, compared to the other state of the art solutions. The proposed algorithm is applicable to any NLS solver implementation, and does not depend on incremental strategies described in our previous papers, which are not a subject of this paper.

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One aspect of the EU funded project SAUCE is to explore the possibilities and challenges of integrating light field capturing and processing into media productions. A special light field camera was build by Saarland University [Herfet et al. 2018] and is first tested under production conditions in the test production "Unfolding" as part of the SAUCE project. Filmakademie Baden-Württemberg developed the contentual frame, executed the post-production and prepared a complete previsualization. Calibration and post-processing algorithms are developed by the Trinity College Dublin and the Brno University of Technology. This document describes challenges during building and shooting with the light field camera array, as well as its potential and challenges for the post-production.

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