Scalable Estimation of Precision Maps in a MapReduce Framework

📝 Abstract

This paper presents a large-scale strip adjustment method for LiDAR mobile mapping data, yielding highly precise maps. It uses several concepts to achieve scalability. First, an efficient graph-based pre-segmentation is used, which directly operates on LiDAR scan strip data, rather than on point clouds. Second, observation equations are obtained from a dense matching, which is formulated in terms of an estimation of a latent map. As a result of this formulation, the number of observation equations is not quadratic, but rather linear in the number of scan strips. Third, the dynamic Bayes network, which results from all observation and condition equations, is partitioned into two sub-networks. Consequently, the estimation matrices for all position and orientation corrections are linear instead of quadratic in the number of unknowns and can be solved very efficiently using an alternating least squares approach. It is shown how this approach can be mapped to a standard key/value MapReduce implementation, where each of the processing nodes operates independently on small chunks of data, leading to essentially linear scalability. Results are demonstrated for a dataset of one billion measured LiDAR points and 278,000 unknowns, leading to maps with a precision of a few millimeters.

💡 Analysis

This paper presents a large-scale strip adjustment method for LiDAR mobile mapping data, yielding highly precise maps. It uses several concepts to achieve scalability. First, an efficient graph-based pre-segmentation is used, which directly operates on LiDAR scan strip data, rather than on point clouds. Second, observation equations are obtained from a dense matching, which is formulated in terms of an estimation of a latent map. As a result of this formulation, the number of observation equations is not quadratic, but rather linear in the number of scan strips. Third, the dynamic Bayes network, which results from all observation and condition equations, is partitioned into two sub-networks. Consequently, the estimation matrices for all position and orientation corrections are linear instead of quadratic in the number of unknowns and can be solved very efficiently using an alternating least squares approach. It is shown how this approach can be mapped to a standard key/value MapReduce implementation, where each of the processing nodes operates independently on small chunks of data, leading to essentially linear scalability. Results are demonstrated for a dataset of one billion measured LiDAR points and 278,000 unknowns, leading to maps with a precision of a few millimeters.

📄 Content

Scalable Estimation of Precision Maps in a MapReduce Framework Claus Brenner Institute of Cartography and Geoinformatics Leibniz Universität Hannover Appelstr. 9a, 30167 Hannover, Germany claus.brenner@ikg.uni-hannover.de ABSTRACT This paper presents a large-scale strip adjustment method for LiDAR mobile mapping data, yielding highly precise maps. It uses several concepts to achieve scalability. First, an efficient graph-based pre-segmentation is used, which directly operates on LiDAR scan strip data, rather than on point clouds. Second, observation equations are obtained from a dense matching, which is formulated in terms of an estimation of a latent map. As a result of this formulation, the number of observation equations is not quadratic, but rather linear in the number of scan strips. Third, the dynamic Bayes network, which results from all observation and condition equations, is partitioned into two sub-networks. Consequently, the estimation matrices for all position and orientation corrections are linear instead of quadratic in the number of unknowns and can be solved very efficiently using an alternating least squares approach.
It is shown how this approach can be mapped to a standard key/value MapReduce implementation, where each of the processing nodes operates independently on small chunks of data, leading to essentially linear scalability. Results are demonstrated for a dataset of one billion measured LiDAR points and 278,000 unknowns, leading to maps with a precision of a few millimeters. CCS Concepts • General and reference➝Estimation • Mathematics of com- puting➝Bayesian networks • Mathematics of computing➝ Kalman filters and hidden Markov models • Mathematics of computing➝Maximum likelihood estimation • Information systems➝Geographic information systems • Theory of com- putation➝MapReduce algorithms • Computing methodolo- gies➝Image segmentation • Computing methodologies➝ Matching. Keywords Mobile mapping; LiDAR; least squares adjustment; MapReduce.

1. INTRODUCTION Since more than 20 years, digital maps have been used to support car and personal navigation systems. Recently, the development of highly detailed and accurate maps has gained momentum, since such maps are required for advanced driver assistance systems, as well as partially or fully autonomous cars. In order to collect such maps, mobile mapping systems are employed, which usually combine vision sensors, such as cameras and laser scanners (LiDAR) with a localization subsystem. In case of vehicles, the latter is normally a combination of a global navigation satellite system (GNSS) receiver, an inertial measurement unit (IMU) and an odometer (wheel distance measurement). All measurements are combined by a filter approach to deliver a continuous position and orientation (pose) update, at a typical rate of 200 Hz.

Figure 1. Example results. A large number of single scans (strips) acquired by LiDAR mobile mapping (left) are aligned (middle) using a global optimization. After alignment, systematic errors are removed which allows estimating the surface with a high density and a standard deviation of only a few millimeters. Details such as façade and wall structure and sidewalk pavement become visible (right). Even if highly accurate (and expensive) GNSS/IMU components are employed, and measurements are processed using differential GNSS post-processing, one can typically observe absolute errors in the range of 30 centimeters in urban areas. While this seems to be fairly accurate, it is in large contrast to the accuracy of the LiDAR sensors themselves, which nowadays have down to 5 mm accuracy (and 3 mm precision), a difference of two orders of magnitude. Since contemporary LiDAR mobile mapping systems reach measurement rates of up to 2 million measured points per second, which is 10,000 observations for each pose delivered by the (200 Hz) GNSS/IMU system, it is highly attractive to correct the pose using the LiDAR measurements themselves. 2. RELATED WORK The problem of adjusting sensor poses using measurements is fundamental to geodesy and surveying. In photogrammetry (and lately, computer vision), it is known as bundle adjustment, and after several decades of research, it is still the dominant refinement approach, due to its rigorous formulation of the functional and stochastic error model [19]. In robotics, such problems are usually encountered in the context of simultaneous localization and mapping (SLAM, [7]), where (in-) dependencies © Claus Brenner, 2016. This is the author’s version of the work. It is posted here for your personal use. Not for redistribution. The definitive version was published in: SIGSPATIAL'16, October 31-November 03, 2016, Burlingame, CA, USA. http://dx.doi.org/10.1145/2996913.2996990

between random variables are typically depicted using probabilistic graphical models [12], especially (dynamic) Bayes networ

This content is AI-processed based on ArXiv data.