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        "title": "Proximity-Based Point Cloud Reconstruction",
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        "abstract": "Extrapolating information from incomplete data is a key human skill, enabling us to inferpatterns and make predictions from limited observations. A prime example is our ability to perceive coherent shapes from seemingly random point sets, a key aspect of cognition.However, data reconstruction becomes challenging when no predefined rules exist, as it is unclear how to connect the data or infer patterns. In computer graphics, a major goal isto replicate this human ability by developing algorithms that can accurately reconstruct original structures or extract meaningful information from raw, disconnected data.The contributions of this thesis deal with point cloud reconstruction, leveraging proximity-based methods, with a particular focus on a specific proximity-encoding data structure -the spheres-of-influence graph (SIG). We discuss curve reconstruction, where we automate the game of connecting the dots to create contours, providing theoretical guarantees for our method. We obtain the best results compared to similar methods for manifold curves. We extend our curve reconstruction to manifolds, overcoming the challenges of moving to different domains, and extending our theoreticalguarantees. We are able to reconstruct curves from sparser inputs compared to the state-of-the-art, and we explorevarious settings in which these curves can live. We investigate the properties of the SIGas a parameter-free proximity encoding structure of three-dimensional point clouds. We introduce new spatial bounds for the SIG neighbors as a theoretical contribution. We analyze how close the encoding is to the ground truth surface compared to the commonly used kNN graphs, and we evaluate our performance in the context of normal estimationas an application. Lastly, we introduce SING – a stability-incorporated neighborhood graph, a useful tool with various applications, such as clustering, and with a strong theoretical background in topological data analysis.",
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        "title": "SING: Stability-Incorporated Neighborhood Graph",
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        "abstract": "We introduce the Stability-Incorporated Neighborhood Graph (SING), a novel density-aware structure designed to capture the intrinsic geometric properties of a point set. We improve upon the spheres-of-influence graph by incorporating additional features to offer more flexibility and control in encoding proximity information and capturing local density variations. Through persistence analysis on our proximity graph, we propose a new clustering technique and explore additional variants incorporating extra features for the proximity criterion. Alongside the detailed analysis and comparison to evaluate its performance on various datasets, our experiments demonstrate that the proposed method can effectively extract meaningful clusters from diverse datasets with variations in density and correlation. Our application scenarios underscore the advantages of the proposed graph over classical neighborhood graphs, particularly in terms of parameter tuning.",
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        "title": "Reconstructing Curves from Sparse Samples on Riemannian Manifolds",
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        "abstract": "Curve and surface reconstruction from unstructured points represent a fundamental problem in computer graphics and computer vision, with many applications. The quest for better solutions for this ill-posed problem is riddled with various kinds of artifacts such as noise, outliers, and missing data.\n\nMoreover, the reconstruction problem usually implies further input requirements: how many samples do we need for a successful reconstruction, what properties should these samples satisfy and how can we obtain such sets. And once we obtain these point samples, how can we extract connectivity that best approximates the initial surface they have been sampled from?\n\nWe will discuss about various sampling strategies, corresponding reconstruction methods, with multiple applications in automating sketch coloring, adaptive meshing for faster simulations, and cultural heritage.\n",
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        "title": "Distributed Surface Reconstruction",
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        "title": "Visualizing Group Structure in Compound Graphs: The Current State, Lessons Learned, and Outstanding Opportunities",
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