Resolution-Independent Meshes of Superpixels

The over-segmentation into superpixels is an important preprocessing step to smartly compress the input size and speed up higher level tasks. A superpixel was traditionally considered as a small cluster of square-based pixels that have similar color intensities and are closely located to each other. In this discrete model the boundaries of superpixels often have irregular zigzags consisting of horizontal or vertical edges from a given pixel grid. However digital images represent a continuous world, hence the following continuous model in the resolution-independent formulation can be more suitable for the reconstruction problem. Instead of uniting squares in a grid, a resolution-independent superpixel is defined as a polygon that has straight edges with any possible slope at subpixel resolution. The harder continuous version of the over-segmentation problem is to split an image into polygons and find a best (say, constant) color of each polygon so that the resulting colored mesh well approximates the given image. Such a mesh of polygons can be rendered at any higher resolution with all edges kept straight. We propose a fast conversion of any traditional superpixels into polygons and guarantees that their straight edges do not intersect. The meshes based on the superpixels SEEDS (Superpixels Extracted via Energy-Driven Sampling) and SLIC (Simple Linear Iterative Clustering) are compared with past meshes based on the Line Segment Detector. The experiments on the Berkeley Segmentation Database confirm that the new superpixels have more compact shapes than pixel-based superpixels

A fast approximate skeleton with guarantees for any cloud of points in a Euclidean space

The tree reconstruction problem is to find an embedded straight-line tree that approximates a given cloud of unorganized points in $\mathbb{R}^m$ up to a certain error. A practical solution to this problem will accelerate a discovery of new colloidal products with desired physical properties such as viscosity. We define the Approximate Skeleton of any finite point cloud $C$ in a Euclidean space with theoretical guarantees. The Approximate Skeleton ASk$(C)$ always belongs to a given offset of $C$, i.e. the maximum distance from $C$ to ASk$(C)$ can be a given maximum error. The number of vertices in the Approximate Skeleton is close to the minimum number in an optimal tree by factor 2. The new Approximate Skeleton of any unorganized point cloud $C$ is computed in a near linear time in the number of points in $C$. Finally, the Approximate Skeleton outperforms past skeletonization algorithms on the size and accuracy of reconstruction for a large dataset of real micelles and random clouds

Geometric and Topological Methods for Applications to Materials and Data Skeletonisation

Crystal Structure Prediction (CSP) aims to speed up functional materials discovery by using supercomputers to predict whether an input molecule can form stable crystal struc- tures with desirable properties. The process produces large datasets where each entry is a simulated arrangement of copies of the input molecule to form a crystal. However, these datasets have little structure themselves, and it is the aim of this thesis to contribute towards simplifying and analysing such datasets. Crystals are unbounded collections of atoms or molecules, extending infinitely in the space they lie within. As such, rigorously quantifying the geometric similarity of crystal structures, and even just identifying identical structures, is a challenging problem. To solve it, we seek a continuous, complete, isometry classification of crystals. Consequently, by modelling crystals as periodic point sets, we introduce the density fingerprint, which is invariant under isometries, Lipschitz continuous, and complete for an open and dense space of crystal structures. Such a classification will be able to identify and remove near- duplicates from these large CSP datasets, and potentially even guide future searches. We describe how this fingerprint can be computed using periodic higher Voronoi zones. This geometric concept of concentric regions around a fixed centre characterises relative positions of points from the centre in a periodic point set. We present an algorithm to compute these zones in addition to proving key structural properties. We later discuss research into skeletonisation algorithms, proving theoretical guarantees of the homological persistent skeleton (HoPeS), subsequently formulating and performing an experimental comparison of HoPeS with other relevant algorithms. Such algorithms, if effectively used, can be applied to large datasets including those produced by CSP to reveal the shape of the data, helping to highlight regions of interest and branches that merit further study

Surface-guided computing to analyze subcellular morphology and membrane-associated signals in 3D

Signal transduction and cell function are governed by the spatiotemporal organization of membrane-associated molecules. Despite significant advances in visualizing molecular distributions by 3D light microscopy, cell biologists still have limited quantitative understanding of the processes implicated in the regulation of molecular signals at the whole cell scale. In particular, complex and transient cell surface morphologies challenge the complete sampling of cell geometry, membrane-associated molecular concentration and activity and the computing of meaningful parameters such as the cofluctuation between morphology and signals. Here, we introduce u-Unwrap3D, a framework to remap arbitrarily complex 3D cell surfaces and membrane-associated signals into equivalent lower dimensional representations. The mappings are bidirectional, allowing the application of image processing operations in the data representation best suited for the task and to subsequently present the results in any of the other representations, including the original 3D cell surface. Leveraging this surface-guided computing paradigm, we track segmented surface motifs in 2D to quantify the recruitment of Septin polymers by blebbing events; we quantify actin enrichment in peripheral ruffles; and we measure the speed of ruffle movement along topographically complex cell surfaces. Thus, u-Unwrap3D provides access to spatiotemporal analyses of cell biological parameters on unconstrained 3D surface geometries and signals.Comment: 49 pages, 10 figure

UAV-Enabled Surface and Subsurface Characterization for Post-Earthquake Geotechnical Reconnaissance

Major earthquakes continue to cause significant damage to infrastructure systems and the loss of life (e.g. 2016 Kaikoura, New Zealand; 2016 Muisne, Ecuador; 2015 Gorkha, Nepal). Following an earthquake, costly human-led reconnaissance studies are conducted to document structural or geotechnical damage and to collect perishable field data. Such efforts are faced with many daunting challenges including safety, resource limitations, and inaccessibility of sites. Unmanned Aerial Vehicles (UAV) represent a transformative tool for mitigating the effects of these challenges and generating spatially distributed and overall higher quality data compared to current manual approaches. UAVs enable multi-sensor data collection and offer a computational decision-making platform that could significantly influence post-earthquake reconnaissance approaches. As demonstrated in this research, UAVs can be used to document earthquake-affected geosystems by creating 3D geometric models of target sites, generate 2D and 3D imagery outputs to perform geomechanical assessments of exposed rock masses, and characterize subsurface field conditions using techniques such as in situ seismic surface wave testing. UAV-camera systems were used to collect images of geotechnical sites to model their 3D geometry using Structure-from-Motion (SfM). Key examples of lessons learned from applying UAV-based SfM to reconnaissance of earthquake-affected sites are presented. The results of 3D modeling and the input imagery were used to assess the mechanical properties of landslides and rock masses. An automatic and semi-automatic 2D fracture detection method was developed and integrated with a 3D, SfM, imaging framework. A UAV was then integrated with seismic surface wave testing to estimate the shear wave velocity of the subsurface materials, which is a critical input parameter in seismic response of geosystems. The UAV was outfitted with a payload release system to autonomously deliver an impulsive seismic source to the ground surface for multichannel analysis of surface waves (MASW) tests. The UAV was found to offer a mobile but higher-energy source than conventional seismic surface wave techniques and is the foundational component for developing the framework for fully-autonomous in situ shear wave velocity profiling.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145793/1/wwgreen_1.pd

Image decomposition method by topological features

В статье предложен новый метод для разложения изображения на отдельные объекты интереса. В основе разработанного метода лежит использование персистентной гомологии. Показан процесс прямого и обратного преобразования изображения. Исходное изображение после прямого преобразования представляется как набор матриц, которые можно разделить на основные и детализирующие. Основные матрицы содержат информацию об основной структуре объектов на изображениях, а детализирующие включают данные о деталях этих объектов, а также о мелких объектах или шумовой составляющей. Показано, что существует определенная аналогия с Wavelet-преобразованием, но в основе предлагаемого метода заложена принципиально другая теоретическая база. Подробно описан численный пример, отражающий основную суть метода. Описаны свойства разложения, а также возможность использования стандартных алгебраических операций над матрицами разложения. Обратное преобразование позволяет учесть измененные свойства отдельных объектов и синтезировать новое изображение. Продемонстрированы перспективы применения разложения для решения практических задач. Разработаны алгоритмы для бинаризации изображений и удаления текста на неоднородном фоне. Анализ и обработка данных ведется с единых позиций в пространстве матриц разложения. Результаты бинаризации показали, что в сравнении с аналогами разработанный алгоритм покажет себя наилучшим образом в ситуациях, когда бинаризация применяется для выделения множества отдельных объектов. Полученные результаты алгоритма удаления текста на неоднородном фоне подтверждают, что информация полностью удаляется, не задевая остальные области на изображениях.Исследование выполнено в рамках Программы развития ЯрГУ, проект № П2-ГМ3-2021