Implementing the GSOSM algorithm

GSOSM algorithm is a method to reconstruct a surface from a set of scattered points. Implementing this algorithm on a sequential or parallel method contains several interesting questions. In this article we try to give some details on algorithms and problems implementing this method. The aim of the paper is to give ideas and details about the data structures and the implementation, and we draw the attention to possible problems the algorithm may run into. This may help those programmers who implement this type of algorithms for the first time, and will face these challenges. Keywords: growing cell structures; surface reconstruction; mesh generation; shape modeling; MSC: 65D17, 68T20, 97P5

Improving 3D Reconstruction using Deep Learning Priors

Modeling the 3D geometry of shapes and the environment around us has many practical applications in mapping, navigation, virtual/ augmented reality, and autonomous robots. In general, the acquisition of 3D models relies on using passive images or using active depth sensors such as structured light systems that use external infrared projectors. Although active methods provide very robust and reliable depth information, they have limited use cases and heavy power requirements, which makes passive techniques more suitable for day-to-day user applications. Image-based depth acquisition systems usually face challenges representing thin, textureless, or specular surfaces and regions in shadows or low-light environments. While scene depth information can be extracted from the set of passive images, fusion of depth information from several views into a consistent 3D representation remains a challenging task. The most common challenges in 3D environment capture include the use of efficient scene representation that preserves the details, thin structures, and ensures overall completeness of the reconstruction. In this thesis, we illustrate the use of deep learning techniques to resolve some of the challenges of image-based depth acquisition and 3D scene representation. We use a deep learning framework to learn priors over scene geometry and scene global context for solving several ambiguous and ill-posed problems such as estimating depth on textureless surfaces and producing complete 3D reconstruction for partially observed scenes. More specifically, we propose that using deep learning priors, a simple stereo camera system can be used to reconstruct a typical apartment size indoor scene environments with the fidelity that approaches the quality of a much more expensive state-of-the-art active depth-sensing system. Furthermore, we describe how deep learning priors on local shapes can represent 3D environments more efficiently than with traditional systems while at the same time preserving details and completing surfaces.Doctor of Philosoph

Computational Electromagnetism and Acoustics

It is a moot point to stress the significance of accurate and fast numerical methods for the simulation of electromagnetic fields and sound propagation for modern technology. This has triggered a surge of research in mathematical modeling and numerical analysis aimed to devise and improve methods for computational electromagnetism and acoustics. Numerical techniques for solving the initial boundary value problems underlying both computational electromagnetics and acoustics comprise a wide array of different approaches ranging from integral equation methods to finite differences. Their development faces a few typical challenges: highly oscillatory solutions, control of numerical dispersion, infinite computational domains, ill-conditioned discrete operators, lack of strong ellipticity, hysteresis phenomena, to name only a few. Profound mathematical analysis is indispensable for tackling these issues. Many outstanding contributions at this Oberwolfach conference on Computational Electromagnetism and Acoustics strikingly confirmed the immense recent progress made in the field. To name only a few highlights: there have been breakthroughs in the application and understanding of phase modulation and extraction approaches for the discretization of boundary integral equations at high frequencies. Much has been achieved in the development and analysis of discontinuous Galerkin methods. New insight have been gained into the construction and relationships of absorbing boundary conditions also for periodic media. Considerable progress has been made in the design of stable and space-time adaptive discretization techniques for wave propagation. New ideas have emerged for the fast and robust iterative solution for discrete quasi-static electromagnetic boundary value problems