Biharmonic fields and mesh completion

We discuss bi-harmonic fields which approximate signed distance fields. We conclude that the bi-harmonic field approximation can be a powerful tool for mesh completion in general and complex cases. We present an adaptive, multigrid algorithm to extrapolate signed distance fields. By defining a volume mask in a closed region bounding the area that must be repaired, the algorithm computes a signed distance field in well-defined regions and uses it as an over-determined boundary condition constraint for the biharmonic field computation in the remaining regions. The algorithm operates locally, within an expanded bounding box of each hole, and therefore scales well with the number of holes in a single, complex model. We discuss this approximation in practical examples in the case of triangular meshes resulting from laser scan acquisitions which require massive hole repair. We conclude that the proposed algorithm is robust and general, and is able to deal with complex topological casesPeer ReviewedPostprint (author's final draft

A Complete Method for Reconstructing an Elevation Surface of 3D Point Clouds

Reconstructing the surface of 3D point clouds is a reconstruction from a cloud of 3D points to a triangular mesh. This process approximates a discrete point cloud by a continuous/smooth surface depending on the input data and the applications of users. In this paper, we propose a complete method to reconstruct an elevation surface from 3D point clouds. The method consists of three steps. In the first step, we triangulate an elevation surface of 3D point cloud structured in a 3D grid. In the second step, we remove the outward triangles to deal with concave regions on the boundary of the triangular mesh. In the third step, we reconstruct this surface by filling the hole of triangular mesh. Our method could process very fast for triangulating the surface, preserve the topology and characteristic of the input surface after reconstruction

Dictionary learning-based inpainting on triangular meshes

TesisAnaliza el problema de inpainting el cual consiste en rellenar regiones faltantes o dañados de tal forma que el patrón de llenado no produzca artefactos diferentes o no compatibles con los datos originales. En la presente tesis se propone un nuevo algoritmo de inpainting en superficies basado en el aprendizaje. El resultado obtenido con el método propuesto, elimina el ruido y resalta las características del dato originalTesi

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Characterising pattern asymmetry in pigmented skin lesions

Abstract. In clinical diagnosis of pigmented skin lesions asymmetric pigmentation is often indicative of melanoma. This paper describes a method and measures for characterizing lesion symmetry. The estimate of mirror symmetry is computed first for a number of axes at different degrees of rotation with respect to the lesion centre. The statistics of these estimates are the used to assess the overall symmetry. The method is applied to three different lesion representations showing the overall pigmentation, the pigmentation pattern, and the pattern of dermal melanin. The best measure is a 100% sensitive and 96% specific indicator of melanoma on a test set of 33 lesions, with a separate training set consisting of 66 lesions

Computational Video Enhancement

During a video, each scene element is often imaged many times by the sensor. I propose that by combining information from each captured frame throughout the video it is possible to enhance the entire video. This concept is the basis of computational video enhancement. In this dissertation, the viability of computational video processing is explored in addition to presenting applications where this processing method can be leveraged. Spatio-temporal volumes are employed as a framework for efficient computational video processing, and I extend them by introducing sheared volumes. Shearing provides spatial frame warping for alignment between frames, allowing temporally-adjacent samples to be processed using traditional editing and filtering approaches. An efficient filter-graph framework is presented to support this processing along with a prototype video editing and manipulation tool utilizing that framework. To demonstrate the integration of samples from multiple frames, I introduce methods for improving poorly exposed low-light videos to achieve improved results. This integration is guided by a tone-mapping process to determine spatially-varying optimal exposures and an adaptive spatio-temporal filter to integrate the samples. Low-light video enhancement is also addressed in the multispectral domain by combining visible and infrared samples. This is facilitated by the use of a novel multispectral edge-preserving filter to enhance only the visible spectrum video. Finally, the temporal characteristics of videos are altered by a computational video resampling process. By resampling the video-rate footage, novel time-lapse sequences are found that optimize for user-specified characteristics. Each resulting shorter video is a more faithful summary of the original source than a traditional time-lapse video. Simultaneously, new synthetic exposures are generated to alter the output video's aliasing characteristics