Multi-View Planning for Simultaneous Coverage and Accuracy Optimisation

Multi-View Planning (MVP) for high fidelity three-dimensional (3D) reconstruction and inspection solves the problem of finding an efficient sequence of views allowing complete and high quality reconstruction of complex objects. Given a CAD model – or coarse 3D scan, or time of flight (TOF) 3D scan – of the object, our objective is to jointly evaluate accuracy requirements and coverage during planning, to optimise the reconstruction procedure. In model-based view planning, one fundamental approach is the evaluation of a visibility matrix [4, 5]. This matrix encodes the visibility of discrete surface elements (surface space) from view candidates (view point space). Tarbox’ and Gottschlich’s [5] approach was limited to viewpoint candidate creation on a view sphere around the object. Scott [4] further developed this method by creating arbitrary generalised viewpoints in an optimal scanning zone. The extension of the statistical E-criterion to next best view (NBV) planning was recently introduced by Trummer et al. [6] for online path planning for a 3D reconstruction approach without active illumination. In this paper we present a novel model-based MVP approach, which models measurement uncertainty additionally to coverage. Our paper’s contribution is the accuracy optimising MVP approach using the extended E-criterion, simultaneously taking uncertainty and coverage into account. In the paper we finally evaluate different planning methods using the benchmark object and scheme from [2]. For complex objects, analysis of the viewpoint candidate creation scheme [4] revealed limitations for surfaces in concavities, as well as in the presence of configuration space constraints. We therefore formulated an adaptive viewpoint generation scheme, taking substitute view candidates on a loxodrome (or rhumb line, see [1]) around the optimal, yet unfeasible candidate, into account. To optimise accuracy as well, we extended the statistical E-criterion [3, 6] to model based view planning using active illumination. To predict the measurement uncertainty, we a priori calibrated a model of the sensor’s measurement characteristic covariance matrix Σc. Using eigen decomposition of Σc, we obtain eigenvalues λ (1) c ≥ λ (2) c ≥ λ (3) c and corresponding perpendicular eigenvectors ξ (1) c ,ξ (2) c and ξ (3) c . Applying alignment of ξ (1) c along a candidates viewing direction and scaling λ (1) c according to the determining uncertainty influences, we yield the covariance matrix Σi for scanning a surface from viewpoint vi. The uncertainty from surfaces seen from multiple views can now be estimated by