A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

Efficient Surface Reconstruction for Piecewise Smooth Objects

In this report we present a new surface reconstruction technique from unstructured point clouds for piecewise smooth objects, such as scans of architectural and other man-made artifacts. The new technique operates in three conceptual steps: First, a set of basis functions is computed and a topology is established among these functions that respect sharp features using a RANSAC technique. Second, a linearized, statistically motivated optimization problem is solved employing this discretization. Lastly, an implicit function based meshing technique is employed to determine a clean, manifold mesh representation. The main benefit of our new proposal in comparison to previous work is its robustness and efficiency, which we examine by applying the algorithm to a set of synthetic and real-world benchmark data sets

Scan Integration as a Labeling Problem

Integration is a crucial step in the reconstruction of complete 3D surface model from multiple scans. Ever-present registration errors and scanning noise make integration a nontrivial problem. In this paper, we propose a novel method for multi-view scan integration where we solve it as a labelling problem. Unlike previous methods, which have been based on various merging schemes, our labelling-based method is essentially a selection strategy. The overall surface model is composed of surface patches from selected input scans. We formulate the labelling via a higher-order Markov Random Field (MRF) which assigns a label representing an index of some input scan to every point in a base surface. Using a higherorder MRF allows us to more effectively capture spatial relations between 3D points. We employ belief propagation to infer this labelling and experimentally demonstrate that this integration approach provides significantly improved integration via both qualitative and quantitative comparisons

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

Восстановление формы объемных медицинских объектов с помощью дистанционных карт поперечных сечений

Представлены новые методы для реконструкции трехмерной поверхности объекта из нескольких замкнутых, в общем случае неплоских кривых, включая контуры, которые были очерчены вручную. Для восстановления объектов разной формы используются двухмерные дистанционные карты.Представлені нові методи для реконструкції тривимірної поверхні об’єкту з декількох замкнутих, в загальному випадку неплоских кривих, включаючи контури, які були обкреслені уручну. Для відновлення об'єктів різної форми використовуються двомірні дистанційні карти.The new techniques is presented in order to reconstruct 3D object surface from several closed, in general, non-planar curves, including contours that were outlined manually. 2D distance map used to reconstruct object of a different shapes. Branching problem also discussed

Восстановление поверхности трехмерного объекта по обводкам его сечений

В статье предлагаются методы векторного восстановления поверхности и оценки объема медицинских и других трехмерных объектов по нескольким обводкам их поперечных сечений в пространстве. Обводки сечений в пространстве должны быть упорядочены, однако, в общем случае они могут быть не плоскими и не параллельными друг другу. Предложенные методы дают хорошие результаты при восстановлении выпуклых или близких к ним по форме поверхностей. Также предложен способ восстановления поверх- ности разветвляющихся объектов.У статті пропонуються методи векторного відновлення поверхні та оцінки обсягу медичних та інших тривимірних об’єктів за кількома обведеннями їх поперечних перерізів в просторі. Обведення перетинів у просторі повинні бути впорядковані, проте, в загальному випадку вони можуть бути не плоскими і не паралельними один одному. Запропоновані методи дають гарні результати при відновленні опуклих або близьких до них об’єктів. Також описані способи вирішення проблеми розгалуження для об’єктів більш складної форми.A new technique is presented in order to reconstruct 3D surface, represented in a vector form, from several closed, in general, non-planar curves, including contours that were outlined manually. Also approaches to reconstruct branching objects of complex forms are developed

Uncertainty Minimization in Robotic 3D Mapping Systems Operating in Dynamic Large-Scale Environments

This dissertation research is motivated by the potential and promise of 3D sensing technologies in safety and security applications. With specific focus on unmanned robotic mapping to aid clean-up of hazardous environments, under-vehicle inspection, automatic runway/pavement inspection and modeling of urban environments, we develop modular, multi-sensor, multi-modality robotic 3D imaging prototypes using localization/navigation hardware, laser range scanners and video cameras. While deploying our multi-modality complementary approach to pose and structure recovery in dynamic real-world operating conditions, we observe several data fusion issues that state-of-the-art methodologies are not able to handle. Different bounds on the noise model of heterogeneous sensors, the dynamism of the operating conditions and the interaction of the sensing mechanisms with the environment introduce situations where sensors can intermittently degenerate to accuracy levels lower than their design specification. This observation necessitates the derivation of methods to integrate multi-sensor data considering sensor conflict, performance degradation and potential failure during operation. Our work in this dissertation contributes the derivation of a fault-diagnosis framework inspired by information complexity theory to the data fusion literature. We implement the framework as opportunistic sensing intelligence that is able to evolve a belief policy on the sensors within the multi-agent 3D mapping systems to survive and counter concerns of failure in challenging operating conditions. The implementation of the information-theoretic framework, in addition to eliminating failed/non-functional sensors and avoiding catastrophic fusion, is able to minimize uncertainty during autonomous operation by adaptively deciding to fuse or choose believable sensors. We demonstrate our framework through experiments in multi-sensor robot state localization in large scale dynamic environments and vision-based 3D inference. Our modular hardware and software design of robotic imaging prototypes along with the opportunistic sensing intelligence provides significant improvements towards autonomous accurate photo-realistic 3D mapping and remote visualization of scenes for the motivating applications