Ordered Statistics Vertex Extraction and Tracing Algorithm (OSVETA)

We propose an algorithm for identifying vertices from three dimensional (3D) meshes that are most important for a geometric shape creation. Extracting such a set of vertices from a 3D mesh is important in applications such as digital watermarking, but also as a component of optimization and triangulation. In the first step, the Ordered Statistics Vertex Extraction and Tracing Algorithm (OSVETA) estimates precisely the local curvature, and most important topological features of mesh geometry. Using the vertex geometric importance ranking, the algorithm traces and extracts a vector of vertices, ordered by decreasing index of importance.Comment: Accepted for publishing and Copyright transfered to Advances in Electrical and Computer Engineering, November 23th 201

FrameNet: Learning Local Canonical Frames of 3D Surfaces from a Single RGB Image

In this work, we introduce the novel problem of identifying dense canonical 3D coordinate frames from a single RGB image. We observe that each pixel in an image corresponds to a surface in the underlying 3D geometry, where a canonical frame can be identified as represented by three orthogonal axes, one along its normal direction and two in its tangent plane. We propose an algorithm to predict these axes from RGB. Our first insight is that canonical frames computed automatically with recently introduced direction field synthesis methods can provide training data for the task. Our second insight is that networks designed for surface normal prediction provide better results when trained jointly to predict canonical frames, and even better when trained to also predict 2D projections of canonical frames. We conjecture this is because projections of canonical tangent directions often align with local gradients in images, and because those directions are tightly linked to 3D canonical frames through projective geometry and orthogonality constraints. In our experiments, we find that our method predicts 3D canonical frames that can be used in applications ranging from surface normal estimation, feature matching, and augmented reality

Deep Depth Completion of a Single RGB-D Image

The goal of our work is to complete the depth channel of an RGB-D image. Commodity-grade depth cameras often fail to sense depth for shiny, bright, transparent, and distant surfaces. To address this problem, we train a deep network that takes an RGB image as input and predicts dense surface normals and occlusion boundaries. Those predictions are then combined with raw depth observations provided by the RGB-D camera to solve for depths for all pixels, including those missing in the original observation. This method was chosen over others (e.g., inpainting depths directly) as the result of extensive experiments with a new depth completion benchmark dataset, where holes are filled in training data through the rendering of surface reconstructions created from multiview RGB-D scans. Experiments with different network inputs, depth representations, loss functions, optimization methods, inpainting methods, and deep depth estimation networks show that our proposed approach provides better depth completions than these alternatives.Comment: Accepted by CVPR2018 (Spotlight). Project webpage: http://deepcompletion.cs.princeton.edu/ This version includes supplementary materials which provide more implementation details, quantitative evaluation, and qualitative results. Due to file size limit, please check project website for high-res pape

Reconstruction of the Antenna Near-Field

Cílem disertační práce je navrhnout efektivně pracující algoritmus, který na základě bezfázového měření v blízkém poli antény bude schopen zrekonstruovat komplexní blízké pole antény resp. vyzařovací diagram antény ve vzdáleném poli. Na základě těchto úvah byly zkoumány vlastnosti minimalizačního algoritmu. Zejména byl analyzován a vhodně zvolen minimalizační přistup, optimalizační metoda a v neposlední řadě i optimalizační funkce tzv. funkcionál. Dále pro urychlení celého minimalizačního procesu byly uvažovány prvotní odhady. A na závěr byla do minimalizačního algoritmu zahrnuta myšlenka nahrazující hledané elektrické pole několika koeficienty. Na základě předchozích analýz byla navržená bezfázová metoda pro charakterizaci vyzařovacích vlastností antén. Tato metoda kombinuje globální optimalizaci s obrazovou kompresní metodou a s lokální metodou ve spojení s konvečním amplitudovým měřením na dvou površích. V našem případě je globální optimalizace použita k nalezení globálního minima minimalizovaného funkcionálu, kompresní metoda k redukci neznámých proměnných na apertuře antény a lokální metoda zajišťuje přesnější nalezení minima. Navržená metoda je velmi robustní a mnohem rychlejší než jiné dostupné minimalizační algoritmy. Další výzkum byl zaměřen na možnosti využití měřených amplitud pouze z jednoho měřícího povrchu pro rekonstrukci vyzařovacích charakteristik antén a využití nového algoritmu pro rekonstrukci fáze na válcové geometrii.The aim of this dissertation thesis is to design a very effective algorithm, which is able to reconstruct the antenna near-field and radiation patterns, respectively, from amplitude-only measurements. Under these circumstances, the properties of minimization algorithm were researched. The selection of the minimization approach, optimization technique and the appropriate functional were investigated and appropriately chosen. To reveal the global minimum area faster, the possibilities in the form of initial estimates for accelerating minimization algorithm were also considered. And finally, the idea to represent the unknown electric field distribution by a few coefficients was implicated into the minimization algorithm. The designed near-field phaseless approach for the antenna far-field characterization combines a global optimization, an image compression method and a local optimization in conjunction with conventional two-surface amplitude measurements. The global optimization method is used to minimize the functional, the image compression method is used to reduce the number of unknown variables, and the local optimization method is used to improve the estimate achieved by the previous method. The proposed algorithm is very robust and faster than comparable algorithms available. Other investigations were focused on possibilities of using amplitude from only single scanning surface for reconstruction of radiation patterns and the application of the novel phase retrieval algorithm for cylindrical geometry.