High-Quality Simplification and Repair of Polygonal Models

Because of the rapid evolution of 3D acquisition and modelling methods, highly complex and detailed polygonal models with constantly increasing polygon count are used as three-dimensional geometric representations of objects in computer graphics and engineering applications. The fact that this particular representation is arguably the most widespread one is due to its simplicity, flexibility and rendering support by 3D graphics hardware. Polygonal models are used for rendering of objects in a broad range of disciplines like medical imaging, scientific visualization, computer aided design, film industry, etc. The handling of huge scenes composed of these high-resolution models rapidly approaches the computational capabilities of any graphics accelerator. In order to be able to cope with the complexity and to build level-of-detail representations, concentrated efforts were dedicated in the recent years to the development of new mesh simplification methods that produce high-quality approximations of complex models by reducing the number of polygons used in the surface while keeping the overall shape, volume and boundaries preserved as much as possible. Many well-established methods and applications require "well-behaved" models as input. Degenerate or incorectly oriented faces, T-joints, cracks and holes are just a few of the possible degenaracies that are often disallowed by various algorithms. Unfortunately, it is all too common to find polygonal models that contain, due to incorrect modelling or acquisition, such artefacts. Applications that may require "clean" models include finite element analysis, surface smoothing, model simplification, stereo lithography. Mesh repair is the task of removing artefacts from a polygonal model in order to produce an output model that is suitable for further processing by methods and applications that have certain quality requirements on their input. This thesis introduces a set of new algorithms that address several particular aspects of mesh repair and mesh simplification. One of the two mesh repair methods is dealing with the inconsistency of normal orientation, while another one, removes the inconsistency of vertex connectivity. Of the three mesh simplification approaches presented here, the first one attempts to simplify polygonal models with the highest possible quality, the second, applies the developed technique to out-of-core simplification, and the third, prevents self-intersections of the model surface that can occur during mesh simplification

Fast Exact Booleans for Iterated CSG using Octree-Embedded BSPs

We present octree-embedded BSPs, a volumetric mesh data structure suited for performing a sequence of Boolean operations (iterated CSG) efficiently. At its core, our data structure leverages a plane-based geometry representation and integer arithmetics to guarantee unconditionally robust operations. These typically present considerable performance challenges which we overcome by using custom-tailored fixed-precision operations and an efficient algorithm for cutting a convex mesh against a plane. Consequently, BSP Booleans and mesh extraction are formulated in terms of mesh cutting. The octree is used as a global acceleration structure to keep modifications local and bound the BSP complexity. With our optimizations, we can perform up to 2.5 million mesh-plane cuts per second on a single core, which creates roughly 40-50 million output BSP nodes for CSG. We demonstrate our system in two iterated CSG settings: sweep volumes and a milling simulation

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

A Parallel Feature-preserving Mesh Variable Offsetting Method with Dynamic Programming

Mesh offsetting plays an important role in discrete geometric processing. In this paper, we propose a parallel feature-preserving mesh offsetting framework with variable distance. Different from the traditional method based on distance and normal vector, a new calculation of offset position is proposed by using dynamic programming and quadratic programming, and the sharp feature can be preserved after offsetting. Instead of distance implicit field, a spatial coverage region represented by polyhedral for computing offsets is proposed. Our method can generate an offsetting model with smaller mesh size, and also can achieve high quality without gaps, holes, and self-intersections. Moreover, several acceleration techniques are proposed for the efficient mesh offsetting, such as the parallel computing with grid, AABB tree and rays computing. In order to show the efficiency and robustness of the proposed framework, we have tested our method on the quadmesh dataset, which is available at [https://www.quadmesh.cloud]. The source code of the proposed algorithm is available on GitHub at [https://github.com/iGame-Lab/PFPOffset]

Scalable Realtime Rendering and Interaction with Digital Surface Models of Landscapes and Cities

Interactive, realistic rendering of landscapes and cities differs substantially from classical terrain rendering. Due to the sheer size and detail of the data which need to be processed, realtime rendering (i.e. more than 25 images per second) is only feasible with level of detail (LOD) models. Even the design and implementation of efficient, automatic LOD generation is ambitious for such out-of-core datasets considering the large number of scales that are covered in a single view and the necessity to maintain screen-space accuracy for realistic representation. Moreover, users want to interact with the model based on semantic information which needs to be linked to the LOD model. In this thesis I present LOD schemes for the efficient rendering of 2.5d digital surface models (DSMs) and 3d point-clouds, a method for the automatic derivation of city models from raw DSMs, and an approach allowing semantic interaction with complex LOD models. The hierarchical LOD model for digital surface models is based on a quadtree of precomputed, simplified triangle mesh approximations. The rendering of the proposed model is proved to allow real-time rendering of very large and complex models with pixel-accurate details. Moreover, the necessary preprocessing is scalable and fast. For 3d point clouds, I introduce an LOD scheme based on an octree of hybrid plane-polygon representations. For each LOD, the algorithm detects planar regions in an adequately subsampled point cloud and models them as textured rectangles. The rendering of the resulting hybrid model is an order of magnitude faster than comparable point-based LOD schemes. To automatically derive a city model from a DSM, I propose a constrained mesh simplification. Apart from the geometric distance between simplified and original model, it evaluates constraints based on detected planar structures and their mutual topological relations. The resulting models are much less complex than the original DSM but still represent the characteristic building structures faithfully. Finally, I present a method to combine semantic information with complex geometric models. My approach links the semantic entities to the geometric entities on-the-fly via coarser proxy geometries which carry the semantic information. Thus, semantic information can be layered on top of complex LOD models without an explicit attribution step. All findings are supported by experimental results which demonstrate the practical applicability and efficiency of the methods

Comparing Boolean Operation Methods on 3D Solids

Geometric engines are developed to give answers on geometrical queries, such as, what is the volume of a shape? Developing, testing and maintaining a geometric engine which can be used generically to answer arbitrary geometric queries is a tedious and time consuming task. Thousands of work hours are being spent towards this purpose. A very important element of such geometric engines is the Boolean operations on 3D objects. Boolean operations can be used to develop powerful tools for CAD/CAM applications, by which, end users can save thousands of work hours during modeling. While robust Boolean operations on 3D objects are difficult to implement, once available, many geometric queries can be reduced to a collection of Boolean operations. This reduction would save thousands of hours for the developers of such CAD/CAM applications. The goal of this thesis is to compare the Boolean implementation of Tekla Structures with the Boolean implementation of CGAL and a recently introduced method, EMBER. Using the results of this thesis, Tekla Structures’ currently unidentified vulnerabilities in its Boolean implementation can be identified and thus, improved. Quantitative results showed that Tekla Structures’ Boolean implementation, while being fast, suffered in terms of robustness during the union and difference operations with respect to CGAL and EMBER while doing remarkably well in the intersection operations

GNG based foot reconstruction for custom footwear manufacturing

Custom shoes manufacturing is one of the major challenges facing the footwear industry today. A shoe for everyone: it is a change in the production model in which each individual’s foot is the main focus, replacing traditional size systems based on population means. This paradigm shift represents a major effort for the industry, for which the design and not production becomes the main bottleneck. It is therefore necessary to accelerate the design process by improving the accuracy of current methods. The starting point for making a shoe that fits the client’s foot anatomy is scanning the surface of the foot. Automated foot model reconstruction is accomplished through the use of the self-organising growing neural gas (GNG) network, which is able to topographically map the low dimension of the network to the high dimension of the manifold of the scanner acquisitions without requiring a priori knowledge of the structure of the input space. The GNG obtains a surface representation adapted to the topology of the foot, is accurate, tolerant to noise, and eliminates outliers. It also improves the reconstruction in “dark” areas where the scanner does not obtain information: the heel and toe areas. The method reconstructs the foot surface 4 times more accurately than other well-known methods. The method is generic and easily extensible to other industrial objects that need to be digitized and reconstructed with accuracy and efficiency requirements.This work was partially funded by the Spanish Government DPI2013-40534-R grant, supported with Feder funds, NILS Mobility Project 012-ABEL-CM-2014A, and Fundación Séneca 18946/JLI/13

Context-sensitive interpretation of natural language location descriptions : a thesis submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy in Information Technology at Massey University, Auckland, New Zealand

People frequently describe the locations of objects using natural language. Location descriptions may be either structured, such as 26 Victoria Street, Auckland, or unstructured. Relative location descriptions (e.g., building near Sky Tower) are a common form of unstructured location description, and use qualitative terms to describe the location of one object relative to another (e.g., near, close to, in, next to). Understanding the meaning of these terms is easy for humans, but much more difficult for machines since the terms are inherently vague and context sensitive. In this thesis, we study the semantics (or meaning) of qualitative, geospatial relation terms, specifically geospatial prepositions. Prepositions are one of the most common forms of geospatial relation term, and they are commonly used to describe the location of objects in the geographic (geospatial) environment, such as rivers, mountains, buildings, and towns. A thorough understanding of the semantics of geospatial relation terms is important because it enables more accurate automated georeferencing of text location descriptions than use of place names only. Location descriptions that use geospatial prepositions are found in social media, web sites, blogs, and academic reports, and georeferencing can allow mapping of health, disaster and biological data that is currently inaccessible to the public. Such descriptions have unstructured format, so, their analysis is not straightforward. The specific research questions that we address are: RQ1. Which geospatial prepositions (or groups of prepositions) and senses are semantically similar? RQ2. Is the role of context important in the interpretation of location descriptions? RQ3. Is the object distance associated with geospatial prepositions across a range of geospatial scenes and scales accurately predictable using machine learning methods? RQ4. Is human annotation a reliable form of annotation for the analysis of location descriptions? To address RQ1, we determine the nature and degree of similarity among geospatial prepositions by analysing data collected with a human subjects experiment, using clustering, extensional mapping and t-stochastic neighbour embedding (t-SNE) plots to form a semantic similarity matrix. In addition to calculating similarity scores among prepositions, we identify the senses of three groups of geospatial prepositions using Venn diagrams, t-sne plots and density-based clustering, and define the relationships between the senses. Furthermore, we use two text mining approaches to identify the degree of similarity among geospatial prepositions: bag of words and GloVe embeddings. By using these methods and further analysis, we identify semantically similar groups of geospatial prepositions including: 1- beside, close to, near, next to, outside and adjacent to; 2- across, over and through and 3- beyond, past, by and off. The prepositions within these groups also share senses. Through is recognised as a specialisation of both across and over. Proximity and adjacency prepositions also have similar senses that express orientation and overlapping relations. Past, off and by share a proximal sense but beyond has a different sense from these, representing on the other side. Another finding is the more frequent use of the preposition close to for pairs of linear objects than near, which is used more frequently for non-linear ones. Also, next to is used to describe proximity more than touching (in contrast to other prepositions like adjacent to). Our application of text mining to identify semantically similar prepositions confirms that a geospatial corpus (NCGL) provides a better representation of the semantics of geospatial prepositions than a general corpus. Also, we found that GloVe embeddings provide adequate semantic similarity measures for more specialised geospatial prepositions, but less so for those that have more generalised applications and multiple senses. We explore the role of context (RQ2) by studying three sites that vary in size, nature, and context in London: Trafalgar Square, Buckingham Palace, and Hyde Park. We use the Google search engine to extract location descriptions that contain these three sites with 9 different geospatial prepositions (in, on, at, next to, close to, adjacent to, near, beside, outside) and calculate their acceptance profiles (the profile of the use of a preposition at different distances from the reference object) and acceptance thresholds (maximum distance from a reference object at which a preposition can acceptably be used). We use these to compare prepositions, and to explore the influence of different contexts. Our results show that near, in and outside are used for larger distances, while beside, adjacent to and at are used for smaller distances. Also, the acceptance threshold for close to is higher than for other proximity/adjacency prepositions such as next to, adjacent to and beside. The acceptance threshold of next to is larger than adjacent to, which confirms the findings in ‎Chapter 2 which identifies next to describing a proximity rather than touching spatial relation. We also found that relatum characteristics such as image schema affect the use of prepositions such as in, on and at. We address RQ3 by developing a machine learning regression model (using the SMOReg algorithm) to predict the distance associated with use of geospatial prepositions in specific expressions. We incorporate a wide range of input variables including the similarity matrix of geospatial prepositions (RQ1); preposition senses; semantic information in the form of embeddings; characteristics of the located and reference objects in the expression including their liquidity/solidity, scale and geometry type and contextual factors such as the density of features of different types in the surrounding area. We evaluate the model on two different datasets with 25% improvement against the best baseline respectively. Finally, we consider the importance of annotation of geospatial location descriptions (RQ4). As annotated data is essential for the successful study of automated interpretation of natural language descriptions, we study the impact and accuracy of human annotation on different geospatial elements. Agreement scores show that human annotators can annotate geospatial relation terms (e.g., geospatial prepositions) with higher agreement than other geospatial elements. This thesis advances understanding of the semantics of geospatial prepositions, particularly considering their semantic similarity and the impact of context on their interpretation. We quantify the semantic similarity of a set of 24 geospatial prepositions; identify senses and the relationships among them for 13 geospatial prepositions; compare the acceptance thresholds of 9 geospatial prepositions and describe the influence of context on them; and demonstrate that richer semantic and contextual information can be incorporated in predictive models to interpret relative geospatial location descriptions more accurately

3D reconstruction of medical images from slices automatically landmarked with growing neural models

In this study, we utilise a novel approach to segment out the ventricular system in a series of high resolution T1-weighted MR images. We present a brain ventricles fast reconstruction method. The method is based on the processing of brain sections and establishing a fixed number of landmarks onto those sections to reconstruct the ventricles 3D surface. Automated landmark extraction is accomplished through the use of the self-organising network, the growing neural gas (GNG), which is able to topographically map the low dimensionality of the network to the high dimensionality of the contour manifold without requiring a priori knowledge of the input space structure. Moreover, our GNG landmark method is tolerant to noise and eliminates outliers. Our method accelerates the classical surface reconstruction and filtering processes. The proposed method offers higher accuracy compared to methods with similar efficiency as Voxel Grid