Multivariate Topology Simplification

Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multivariate (alternatively, multi-field) data, topological analysis requires simultaneous advances both mathematically and computationally. We propose a robust multivariate topology simplification method based on “lip”-pruning from the Reeb space. Mathematically, we show that the projection of the Jacobi set of multivariate data into the Reeb space produces a Jacobi structure that separates the Reeb space into simple components. We also show that the dual graph of these components gives rise to a Reeb skeleton that has properties similar to the scalar contour tree and Reeb graph, for topologically simple domains. We then introduce a range measure to give a scaling-invariant total ordering of the components or features that can be used for simplification. Computationally, we show how to compute Jacobi structure, Reeb skeleton, range and geometric measures in the Joint Contour Net (an approximation of the Reeb space) and that these can be used for visualisation similar to the contour tree or Reeb graph

The Topology ToolKit

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependence-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions. TTK is open source (BSD license) and its code, online documentation and video tutorials are available on TTK's website

Crowd-sourced cadastral geospatial information : defining a workflow from unmanned aerial system (UAS) data to 3D building volumes using opensource applications

Dissertation submitted in partial fulfilment of the requirements for the degree of Master of Science in Geospatial TechnologiesThe surveying field has been impacted over many decades by new inventions and improvements in technology. This has ensured that the profession remains one of high precision with the employment of sophisticated technologies by Cadastral Experts. The use of Unmanned Aerial Systems (UAS) within surveying is not new. However, the standards, technologies, tools and licenses developed by the open source community of developers, have opened new possibilities of utilising UAS within surveying. UASs are being constantly improved to obtain high quality imagery, so efforts were made to find novel ways to add value to the data. This thesis defines a workflow aimed at deriving Cadastral Geospatial Information (Cadastral GI), as three-dimensional (3D) building volumes from the original inputted UAS imagery. To achieve this, an investigation was done to see how crowd-sourced UAS data can be uploaded to open online repositories, downloaded by Cadastral Experts, and then manipulated using open source applications. The Cadastral Experts had to utilise multiple applications and manipulate the data through many data formats, to obtain the (3D) building volumes as final results. Such a product can potentially improve the management of cadastral data by Cadastral Experts, City Managers and National Mapping Agencies. Additionally, an ideal suite of tools is presented, that can be used store, manipulate and share the 3D building volume data while facilitating the contribution of attribute data from the crowd

3D Active Metric-Semantic SLAM

In this letter, we address the problem of exploration and metric-semantic mapping of multi-floor GPS-denied indoor environments using Size Weight and Power (SWaP) constrained aerial robots. Most previous work in exploration assumes that robot localization is solved. However, neglecting the state uncertainty of the agent can ultimately lead to cascading errors both in the resulting map and in the state of the agent itself. Furthermore, actions that reduce localization errors may be at direct odds with the exploration task. We propose a framework that balances the efficiency of exploration with actions that reduce the state uncertainty of the agent. In particular, our algorithmic approach for active metric-semantic SLAM is built upon sparse information abstracted from raw problem data, to make it suitable for SWaP-constrained robots. Furthermore, we integrate this framework within a fully autonomous aerial robotic system that achieves autonomous exploration in cluttered, 3D environments. From extensive real-world experiments, we showed that by including Semantic Loop Closure (SLC), we can reduce the robot pose estimation errors by over 90% in translation and approximately 75% in yaw, and the uncertainties in pose estimates and semantic maps by over 70% and 65%, respectively. Although discussed in the context of indoor multi-floor exploration, our system can be used for various other applications, such as infrastructure inspection and precision agriculture where reliable GPS data may not be available.Comment: Submitted to RA-L for revie

A Fuzzy Approach for Topological Data Analysis

Geometry and topology are becoming more powerful and dominant in data analysis because of their outstanding characteristics. It has emerged recently as a promising research area, known as Topological Data Analysis (TDA), for modern computer science. In recent years, the Mapper algorithm, an outstanding TDA representative, is increasingly completed with a stabilized theoretical foundation and practical applications and diverse, intuitive, user-friendly implementations. From a theoretical perspective, the Mapper algorithm is still a fuzzy clustering algorithm, with a visualization capability to extract the shape summary of data. However, its outcomes are still very sensitive to the parameter choice, including resolution and function. Therefore, there is a need to reduce the dependence on its parameters significantly. This idea is exciting and can be solved thanks to the outstanding characteristics of fuzzy clustering. The Mapper clustering ability is getting more potent by the support from well-known techniques. Therefore, this combination is expected to usefully and powerfully solve some problems encountered in many fields. The main research goal of this thesis is to approach TDA by fuzzy theory to create the interrelationships between them in terms of clustering. Explicitly speaking, the Mapper algorithm represents TDA, and the Fuzzy $C$-Means (FCM) algorithm represents fuzzy theory. They are combined to promote their advantages and overcome their disadvantages. On the one hand, the FCM algorithm helps the Mapper algorithm simplify the choice of parameters to obtain the most informative presentation and is even more efficient in data clustering. On the other hand, the FCM algorithm is equipped with the outstanding features of the Mapper algorithm in simplifying and visualizing data with qualitative analysis. This thesis focuses on conquering and achieving the following aims: (1) Summarizing the theoretical foundations and practical applications of the Mapper algorithm in the flow of literature with improved versions and various implementations. (2) Optimizing the cover choice of the Mapper algorithm in the direction of dividing the filter range automatically into irregular intervals with a random overlapping percentage by using the FCM algorithm. (3) Constructing a novel method for mining data that can exhibit the same clustering ability as the FCM algorithm and reveal some meaningful relationships by visualizing the global shape of data supplied by the Mapper algorithm.Geometrie a topologie se stávají silnějšími a dominantnějšími v analýze dat díky svým vynikajícím vlastnostem. Nedávno se objevila jako slibná výzkumná oblast, známá jako topologická analýza dat (TDA), pro moderní informatiku. V posledních letech je algoritmus Mapper, vynikající představitel TDA, stále více doplněn o stabilizovaný teoretický základ a praktické aplikace a rozmanité, intuitivní a uživatelsky přívětivé implementace. Z teoretického hlediska je algoritmus Mapper stále fuzzy shlukovací algoritmus se schopností vizualizace extrahovat souhrn tvaru dat. Jeho výsledky jsou však stále velmi citlivé na volbu parametrů, včetně rozlišení a funkce. Proto je potřeba výrazně snížit závislost na jeho parametrech. Tato myšlenka je vzrušující a lze ji vyřešit díky vynikajícím vlastnostem fuzzy shlukování. Schopnost shlukování Mapperu je stále silnější díky podpoře známých technik. Proto se očekává, že tato kombinace užitečně a účinně vyřeší některé problémy, se kterými se setkáváme v mnoha oblastech. Hlavním výzkumným cílem této práce je přiblížit TDA pomocí fuzzy teorie a vytvořit mezi nimi vzájemné vztahy z hlediska shlukování. Explicitně řečeno, algoritmus Mapper představuje TDA a algoritmus Fuzzy $C$-Means (FCM) představuje fuzzy teorii. Jsou kombinovány, aby podpořily své výhody a překonaly své nevýhody. Na jedné straně algoritmus FCM pomáhá algoritmu Mapper zjednodušit výběr parametrů pro získání nejinformativnější prezentace a je ještě efektivnější při shlukování dat. Na druhé straně je algoritmus FCM vybaven vynikajícími vlastnostmi algoritmu Mapper pro zjednodušení a vizualizaci dat pomocí kvalitativní analýzy. Tato práce se zaměřuje na dobývání a dosažení následujících cílů: (1) Shrnutí teoretických základů a praktických aplikací Mapperova algoritmu v toku literatury s vylepšenými verzemi a různými implementacemi. (2) Optimalizace volby pokrytí algoritmu Mapper ve směru automatického rozdělení rozsahu filtru do nepravidelných intervalů s náhodně se překrývajícím procentem pomocí algoritmu FCM. (3) Vytvoření nové metody pro těžbu dat, která může vykazovat stejnou schopnost shlukování jako algoritmus FCM a odhalit některé smysluplné vztahy vizualizací globálního tvaru dat poskytovaných algoritmem Mapper.460 - Katedra informatikyvyhově

Mobile Wound Assessment and 3D Modeling from a Single Image

The prevalence of camera-enabled mobile phones have made mobile wound assessment a viable treatment option for millions of previously difficult to reach patients. We have designed a complete mobile wound assessment platform to ameliorate the many challenges related to chronic wound care. Chronic wounds and infections are the most severe, costly and fatal types of wounds, placing them at the center of mobile wound assessment. Wound physicians assess thousands of single-view wound images from all over the world, and it may be difficult to determine the location of the wound on the body, for example, if the wound is taken at close range. In our solution, end-users capture an image of the wound by taking a picture with their mobile camera. The wound image is segmented and classified using modern convolution neural networks, and is stored securely in the cloud for remote tracking. We use an interactive semi-automated approach to allow users to specify the location of the wound on the body. To accomplish this we have created, to the best our knowledge, the first 3D human surface anatomy labeling system, based off the current NYU and Anatomy Mapper labeling systems. To interactively view wounds in 3D, we have presented an efficient projective texture mapping algorithm for texturing wounds onto a 3D human anatomy model. In so doing, we have demonstrated an approach to 3D wound reconstruction that works even for a single wound image