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

SurfelMeshing: Online Surfel-Based Mesh Reconstruction

We address the problem of mesh reconstruction from live RGB-D video, assuming a calibrated camera and poses provided externally (e.g., by a SLAM system). In contrast to most existing approaches, we do not fuse depth measurements in a volume but in a dense surfel cloud. We asynchronously (re)triangulate the smoothed surfels to reconstruct a surface mesh. This novel approach enables to maintain a dense surface representation of the scene during SLAM which can quickly adapt to loop closures. This is possible by deforming the surfel cloud and asynchronously remeshing the surface where necessary. The surfel-based representation also naturally supports strongly varying scan resolution. In particular, it reconstructs colors at the input camera's resolution. Moreover, in contrast to many volumetric approaches, ours can reconstruct thin objects since objects do not need to enclose a volume. We demonstrate our approach in a number of experiments, showing that it produces reconstructions that are competitive with the state-of-the-art, and we discuss its advantages and limitations. The algorithm (excluding loop closure functionality) is available as open source at https://github.com/puzzlepaint/surfelmeshing .Comment: Version accepted to IEEE Transactions on Pattern Analysis and Machine Intelligenc

TVL₁shape approximation from scattered 3D data

With the emergence in 3D sensors such as laser scanners and 3D reconstruction from cameras, large 3D point clouds can now be sampled from physical objects within a scene. The raw 3D samples delivered by these sensors however, contain only a limited degree of information about the environment the objects exist in, which means that further geometrical high-level modelling is essential. In addition, issues like sparse data measurements, noise, missing samples due to occlusion, and the inherently huge datasets involved in such representations makes this task extremely challenging. This paper addresses these issues by presenting a new 3D shape modelling framework for samples acquired from 3D sensor. Motivated by the success of nonlinear kernel-based approximation techniques in the statistics domain, existing methods using radial basis functions are applied to 3D object shape approximation. The task is framed as an optimization problem and is extended using non-smooth L1 total variation regularization. Appropriate convex energy functionals are constructed and solved by applying the Alternating Direction Method of Multipliers approach, which is then extended using Gauss-Seidel iterations. This significantly lowers the computational complexity involved in generating 3D shape from 3D samples, while both numerical and qualitative analysis confirms the superior shape modelling performance of this new framework compared with existing 3D shape reconstruction techniques

A model-based approach to recovering the structure of a plant from images

We present a method for recovering the structure of a plant directly from a small set of widely-spaced images. Structure recovery is more complex than shape estimation, but the resulting structure estimate is more closely related to phenotype than is a 3D geometric model. The method we propose is applicable to a wide variety of plants, but is demonstrated on wheat. Wheat is made up of thin elements with few identifiable features, making it difficult to analyse using standard feature matching techniques. Our method instead analyses the structure of plants using only their silhouettes. We employ a generate-and-test method, using a database of manually modelled leaves and a model for their composition to synthesise plausible plant structures which are evaluated against the images. The method is capable of efficiently recovering accurate estimates of plant structure in a wide variety of imaging scenarios, with no manual intervention

{CurveFusion}: {R}econstructing Thin Structures from {RGBD} Sequences

We introduce CurveFusion, the first approach for high quality scanning of thin structures at interactive rates using a handheld RGBD camera. Thin filament-like structures are mathematically just 1D curves embedded in R^3, and integration-based reconstruction works best when depth sequences (from the thin structure parts) are fused using the object's (unknown) curve skeleton. Thus, using the complementary but noisy color and depth channels, CurveFusion first automatically identifies point samples on potential thin structures and groups them into bundles, each being a group of a fixed number of aligned consecutive frames. Then, the algorithm extracts per-bundle skeleton curves using L1 axes, and aligns and iteratively merges the L1 segments from all the bundles to form the final complete curve skeleton. Thus, unlike previous methods, reconstruction happens via integration along a data-dependent fusion primitive, i.e., the extracted curve skeleton. We extensively evaluate CurveFusion on a range of challenging examples, different scanner and calibration settings, and present high fidelity thin structure reconstructions previously just not possible from raw RGBD sequences

From 3D Models to 3D Prints: an Overview of the Processing Pipeline

Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step, in particular along the Process Planning pipeline, can now count on dozens of methods that prepare the 3D model for fabrication, while analysing and optimizing geometry and machine instructions for various objectives. This report provides a classification of this huge state of the art, and elicits the relation between each single algorithm and a list of desirable objectives during Process Planning. The objectives themselves are listed and discussed, along with possible needs for tradeoffs. Additive Manufacturing technologies are broadly categorized to explicitly relate classes of devices and supported features. Finally, this report offers an analysis of the state of the art while discussing open and challenging problems from both an academic and an industrial perspective.Comment: European Union (EU); Horizon 2020; H2020-FoF-2015; RIA - Research and Innovation action; Grant agreement N. 68044