Geometric Structure Extraction and Reconstruction

Geometric structure extraction and reconstruction is a long-standing problem in research communities including computer graphics, computer vision, and machine learning. Within different communities, it can be interpreted as different subproblems such as skeleton extraction from the point cloud, surface reconstruction from multi-view images, or manifold learning from high dimensional data. All these subproblems are building blocks of many modern applications, such as scene reconstruction for AR/VR, object recognition for robotic vision and structural analysis for big data. Despite its importance, the extraction and reconstruction of a geometric structure from real-world data are ill-posed, where the main challenges lie in the incompleteness, noise, and inconsistency of the raw input data. To address these challenges, three studies are conducted in this thesis: i) a new point set representation for shape completion, ii) a structure-aware data consolidation method, and iii) a data-driven deep learning technique for multi-view consistency. In addition to theoretical contributions, the algorithms we proposed significantly improve the performance of several state-of-the-art geometric structure extraction and reconstruction approaches, validated by extensive experimental results

Efficient moving point handling for incremental 3D manifold reconstruction

As incremental Structure from Motion algorithms become effective, a good sparse point cloud representing the map of the scene becomes available frame-by-frame. From the 3D Delaunay triangulation of these points, state-of-the-art algorithms build a manifold rough model of the scene. These algorithms integrate incrementally new points to the 3D reconstruction only if their position estimate does not change. Indeed, whenever a point moves in a 3D Delaunay triangulation, for instance because its estimation gets refined, a set of tetrahedra have to be removed and replaced with new ones to maintain the Delaunay property; the management of the manifold reconstruction becomes thus complex and it entails a potentially big overhead. In this paper we investigate different approaches and we propose an efficient policy to deal with moving points in the manifold estimation process. We tested our approach with four sequences of the KITTI dataset and we show the effectiveness of our proposal in comparison with state-of-the-art approaches.Comment: Accepted in International Conference on Image Analysis and Processing (ICIAP 2015

Reconstruction of freeform surfaces for metrology

The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces.EMR

A topological comparison of surface extraction algorithms

In many application areas, it is useful to convert the discrete information stored in the nodes of a regular grid into a continuous boundary model. Isosurface extraction algorithms differ on how the discrete information in the grid is generated, on what information does the grid store and on the properties of the output surface. Recent algorithms offer different solutions for the disambiguation problem and for controlling the final topology. Based on a number of properties of the grid’s grey cells and of the reconstruction algorithms, a characterization of several surface extraction strategies is proposed. The classification presented shows the inherent limitations of the different algorithms concerning global topology control and reconstruction of local features like thin portions of the volume and almost non-manifold regions. These limitations can be observed and are illustrated with some practical examples. We review in light of this classification some of the relevant papers in the literature, and see that they cluster in some areas of the proposed hierarchy, making a case for where it might be more interesting to focus in future research.Preprin

3D reconstruction of medical images from slices automatically landmarked with growing neural models

In this study, we utilise a novel approach to segment out the ventricular system in a series of high resolution T1-weighted MR images. We present a brain ventricles fast reconstruction method. The method is based on the processing of brain sections and establishing a fixed number of landmarks onto those sections to reconstruct the ventricles 3D surface. Automated landmark extraction is accomplished through the use of the self-organising network, the growing neural gas (GNG), which is able to topographically map the low dimensionality of the network to the high dimensionality of the contour manifold without requiring a priori knowledge of the input space structure. Moreover, our GNG landmark method is tolerant to noise and eliminates outliers. Our method accelerates the classical surface reconstruction and filtering processes. The proposed method offers higher accuracy compared to methods with similar efficiency as Voxel Grid

3D Point Capsule Networks

In this paper, we propose 3D point-capsule networks, an auto-encoder designed to process sparse 3D point clouds while preserving spatial arrangements of the input data. 3D capsule networks arise as a direct consequence of our novel unified 3D auto-encoder formulation. Their dynamic routing scheme and the peculiar 2D latent space deployed by our approach bring in improvements for several common point cloud-related tasks, such as object classification, object reconstruction and part segmentation as substantiated by our extensive evaluations. Moreover, it enables new applications such as part interpolation and replacement.Comment: As published in CVPR 2019 (camera ready version), with supplementary materia

3D Point Capsule Networks

In this paper, we propose 3D point-capsule networks, an auto-encoder designed to process sparse 3D point clouds while preserving spatial arrangements of the input data. 3D capsule networks arise as a direct consequence of our novel unified 3D auto-encoder formulation. Their dynamic routing scheme and the peculiar 2D latent space deployed by our approach bring in improvements for several common point cloud-related tasks, such as object classification, object reconstruction and part segmentation as substantiated by our extensive evaluations. Moreover, it enables new applications such as part interpolation and replacement