TVL₁ Planarity Regularization for 3D Shape Approximation

The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within. This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy

Robust Poisson Surface Reconstruction

Abstract. We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator func-tion of the surface’s interior. Compared to previous models, our recon-struction is robust to noise and outliers because it substitutes the least-squares fidelity term by a robust Huber penalty; this allows to recover sharp corners and avoids the shrinking bias of least squares. We choose an implicit parametrization to reconstruct surfaces of unknown topology and close large gaps in the point cloud. For an efficient representation, we approximate the implicit function by a hierarchy of locally supported basis elements adapted to the geometry of the surface. Unlike ad-hoc bases over an octree, our hierarchical B-splines from isogeometric analysis locally adapt the mesh and degree of the splines during reconstruction. The hi-erarchical structure of the basis speeds-up the minimization and efficiently represents clustered data. We also advocate for convex optimization, in-stead isogeometric finite-element techniques, to efficiently solve the min-imization and allow for non-differentiable functionals. Experiments show state-of-the-art performance within a more flexible framework.

A Distributed computing workflow for modelling environmental flows in complex terrain

Numerical modelling of extreme environmental flows such as flash floods, avalanches and mudflows can be used to understand fundamental processes, predict outcomes and assess the loss potential of future events. These extreme flows can produce complicated and dynamic free surfaces as a result of interactions with the terrain and built environment. In order to resolve these features that may affect flows, high resolution, accurate terrain models are required. However, terrain models can be difficult and costly to acquire, and often lack detail of important flow steering structures such as bridges or debris. To overcome these issues we have developed a photogrammetry workflow for reconstructing high spatial resolution three dimensional terrain models. The workflow utilises parallel and distributed computing to provide inexpensive terrain models that can then be used in numerical simulations of environmental flows. A section of Quebrada San Lazaro within the city of Arequipa, Peru is used as a case study to demonstrate the construction and usage of the terrain models and applicability of the workflow for a flash flood scenario.12 page(s