Real-Time Mapping of Rotationally Symmetric Objects for Mobile Inspection

Abstract

Lifelong monitoring of industrial installations, buildings, and urban settlements as to their thermal energy efficiency requires new, highly automated procedures, for example quantitative geo-referenced thermography. These tools crucially depend on part-based geometric and semantic data models of the sites. There is a lack of CAD models today that are truly up-to-date and readily applicable to such cognitive condition monitoring. Industrial plants and legacy sites also provide an unsafe, sometimes toxic or inaccessible environment to humans. This report proposes and analyzes algorithms to estimate parameterized object representations automatically in real time while capturing point clouds. Mobile platforms and low-cost 3D laser scanners are applied offering a limited field of view and limited spatial resolution. One most important and challenging class of objects are pipe ducts and vessels in chemical plants. This report focuses on methods for the extraction and fitting of rotationally symmetric objects from single range views, their aggregation to linear or branched duct structures, and their relational characterization for matching and merging them. From these partial object descriptions contiguous site maps are composed by the Elastic View Graph (EVG) framework. EVG is an image-based framework for 3D/6DoF SLAM treating as 'observations' relational attributed feature graphs, in other words: pre-segmented 3D images. As to main technical contributions, a new Expectation-Maximization (EM) algorithm is proposed for segmentation and parameter fitting of surfaces-of-revolution (SoR) with piecewise straight axis segments. The E-step implements a Bayesian model of sampling from rotation surfaces. For the M-step, two implemented methods are offered: cone fitting by the geometric distance, implemented by the Levenberg-Marquardt nonlinear optimization algorithm, and an adapted Iterative Closest Point (ICP) algorithm with separately estimated shape parameters. EM converges (empirically) to a local maximum of the posterior probability. Since the optimization space spanning the SoR parameters and the set of point partitions has so many local optima, good starting values are vital. A key focus is therefore on effective hypothesis generation. To this end, three partly new algorithms are developed. The first one, the Chain algorithm, builds a mesh of paths in the directions of principal (Min/Max) curvatures. The second one uses foot point transformations which are local operators contracting a rotation surface to a noisy point representation of its axis curve. By means of an adapted Principal Curve algorithm, this foot point cloud is decomposed into piecewise linear axis segments. The third method exploits the characterizing property of SoR that all normal rays intersect the axis. Using line geometry an axis is estimated in closed form and, by evaluating the degree of rotational symmetry, the point set is recursively subdivided if necessary. In an extensive case study, all algorithms are evaluated and compared on real images from the experimental thermal plant THERESA at KIT North Campus captured by a rotating 3D laser scanner. Quantitative results include the hypothesis evaluation and decimation of false-positive hypotheses, the assessment and comparison of algorithm stability with respect to various input variations (random sampling, Gaussian noise, unknown observer motion during image capture), and the EM convergence speed.