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        "title": "The Sampling-Reconstruction Dual",
        "date": "2025-02",
        "abstract": "Reconstructing surfaces of the real world from scans is an important and challenging problem. Its feasibility is limited by the number of the acquired points and their geometric configuration. The question of how many points exactly are required for the faithful reconstruction of the features leads to its inverse problem, sampling a known surface with the least possible number of points.\r\n \r\nThis talk is about reconstruction algorithms and attempts to prove their theoretical bounds in the number of points required and its dual, sampling curves (as their simpler 2D equivalent) and surfaces with specified bounds from different representations such as meshes, smooth higher-order boundaries, subdivision limit surfaces, and signed distance functions, depending on the application, e.g., lossless reduction of scanned data size, measuring scan error, handling scan artifacts such as noise, outliers, and holes, or secondary goals such as accelerating simulations.\r\n \r\nThe underlying assumption is that the smooth surface (reconstructed, or sampled) is richer than the sparse discrete set of geometric primitives (points + connectivity) it is represented with, leading to the goal of representing object boundaries, e.g., from the physical world, with the least amount of geometry.",
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        "event": "Infinite-dimensional Geometry: Theory and Applications",
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    {
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        "repositum_id": "20.500.12708/208566",
        "title": "SING: Stability-Incorporated Neighborhood Graph",
        "date": "2024-12",
        "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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        "booktitle": "SA '24: SIGGRAPH Asia 2024 Conference Papers",
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        "doi": "10.1145/3680528.3687674",
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        "publisher": "Association for Computing Machinery",
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            "Stipple art editing",
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            "Network topology",
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            "point patterns",
            "similarity metric",
            "discrete distributions",
            "persistence analysis",
            "Neighborhood graph",
            "topological data analysis",
            "K-means",
            "Rips complexes"
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        "title": "Reconstructing Curves from Sparse Samples on Riemannian Manifolds",
        "date": "2024-06",
        "abstract": "Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state-of-the-art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state-of-the-art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non-Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds.",
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        "date_from": "2024-06-24",
        "date_to": "2024-06-26",
        "doi": "10.1111/cgf.15136",
        "event": "Symposium on Geometry Processing",
        "issn": "1467-8659",
        "journal": "Computer Graphics Forum",
        "lecturer": [
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        "location": "Boston",
        "number": "5",
        "pages": "14",
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        "publisher": "WILEY",
        "volume": "43",
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        "keywords": [
            "CCS Concepts",
            "Graph algorithms",
            "Mesh geometry models",
            "Paths and connectivity problems"
        ],
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    {
        "id": "ohrhallinger_stefan-2024-inv",
        "type_id": "talk",
        "tu_id": null,
        "repositum_id": null,
        "title": "Sampling and reconstructing point clouds",
        "date": "2024-05-28",
        "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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        "event": "TU Graz",
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            "surface reconstruction",
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    {
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        "title": "Distributed Surface Reconstruction",
        "date": "2024-04",
        "abstract": "Recent advancements in scanning technologies and their rise in availability have shifted the focus from reconstructing surfaces from point clouds of small areas to large, e.g., city-wide scenes, containing massive amounts of data. We adapt a surface reconstruction method to work in a distributed fashion on a high-performance cluster, reconstructing datasets with millions of vertices in seconds by exploiting the locality of the connectivity required by the reconstruction algorithm to efficiently divide-and-conquer the problem of creating triangulations from very large unstructured point clouds.",
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        "booktitle": "EG 2024 - Posters",
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        "doi": "10.2312/egp.20241037",
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        "event": "45th Annual Conference of the European Association for Computer Graphics (Eurographics 2024)",
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        "location": "Limassol",
        "pages": "2",
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        "keywords": [
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        "title": "Parameter-free connectivity for point clouds",
        "date": "2024-02",
        "abstract": "Determining connectivity in unstructured point clouds is a long-standing problem that has still not been addressed satisfactorily. In this paper, we analyze an alternative to the often-used k-nearest neighborhood (kNN) graph - the Spheres of Influence Graph (SIG). We show that the edges that are neighboring each vertex are spatially bounded, which allows for fast computation of SIG. Our approach shows a better encoding of the ground truth connectivity compared to the kNN for a wide range of k, and additionally, it is parameter-free. Our result for this fundamental task offers potential for many applications relying on kNN, e.g., parameter-free normal estimation, and consequently, surface reconstruction, motion planning, simulations, and many more.",
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    {
        "id": "parakkat-2024-ballmerge",
        "type_id": "journalpaper",
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        "repositum_id": "20.500.12708/197864",
        "title": "BallMerge: High‐quality Fast Surface Reconstruction via Voronoi Balls",
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        "title": "Points2Surf: Learning Implicit Surfaces from Point Clouds",
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        "abstract": "A key step in any scanning-based asset creation workflow is to convert unordered point clouds to a surface. Classical methods (e.g., Poisson reconstruction) start to degrade in the presence of noisy and partial scans. Hence, deep learning based methods have recently been proposed to produce complete surfaces, even from partial scans. However, such data-driven methods struggle to generalize to new shapes with large geometric and topological variations. We present Points2Surf, a novel patch-based learning framework that produces accurate surfaces directly from raw scans without normals.\n\nLearning a prior over a combination of detailed local patches and coarse global information improves generalization performance and reconstruction accuracy.\n\nOur extensive comparison on both synthetic and real data demonstrates a clear advantage of our method over state-of-the-art alternatives on previously unseen classes (on average, Points2Surf brings down reconstruction error by 30% over SPR and by 270%+ over deep learning based SotA methods) at the cost of longer computation times and a slight increase in small-scale topological noise in some cases. \nOur source code, pre-trained model, and dataset are available on: https://github.com/ErlerPhilipp/points2surf\n",
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        "title": "Pose to Seat: Automated design of body-supporting surfaces",
        "date": "2020-04",
        "abstract": "The design of functional seating furniture is a complicated process which often requires extensive manual design effort and empirical evaluation. We propose a computational design framework for pose-driven automated generation of body-supports which are optimized for comfort of sitting. Given a human body in a specified pose as input, our method computes an approximate pressure distribution that also takes frictional forces and body torques into consideration which serves as an objective measure of comfort. Utilizing this information to find out where the body needs to be supported in order to maintain comfort of sitting, our algorithm can create a supporting mesh suited for a person in that specific pose. This is done in an automated fitting process, using a template model capable of supporting a large variety of sitting poses. The results can be used directly or can be considered as a starting point for further interactive design.",
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        "title": "FitConnect: Connecting Noisy 2D Samples by Fitted Neighborhoods",
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        "abstract": "We propose a parameter-free method to recover manifold connectivity in unstructured 2D point clouds with high noise in terms of the local feature size. This enables us to capture the features which emerge out of the noise. To achieve this, we extend the reconstruction algorithm HNN-Crust, which connects samples to two (noise-free) neighbors and has been proven to output a manifold for a relaxed sampling condition. Applying this condition to noisy samples by projecting their k-nearest neighborhoods onto local circular fits leads to multiple candidate neighbor pairs and thus makes connecting them consistently an NP-hard problem. To solve this efficiently, we design an algorithm that searches that solution space iteratively on different scales of k. It achieves linear time complexity in terms of point count plus quadratic time in the size of noise clusters. Our algorithm FitConnect extends HNN-Crust seamlessly to connect both samples with and without noise, performs as local as the recovered features and can output multiple open or closed piece-wise curves. Incidentally, our method simplifies the output geometry by eliminating all but a representative point from noisy clusters. Since local neighborhood fits overlap consistently, the resulting connectivity represents an ordering of the samples along a manifold. This permits us to simply blend the local fits for denoising with the locally estimated noise extent. Aside from applications like reconstructing silhouettes of noisy sensed data, this lays important groundwork to improve surface reconstruction in 3D. Our open-source algorithm is available online.",
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        "abstract": "See right for correct solution of our connect-the-dots game :-)\nOf course, we not only reconstruct members of our institute but also\nhighly noisy point clouds, additionally denoise the reconstruction,\nand specify the minimum number of samples required for that.\nEduard Gröller\nSee here for the mystery present in the crib: youtu.be/-oVwXaaJNtY\n\nDie Auflösung unseres Punkte-verbinden-Spiels ist hier rechts :-)\nWir rekonstruieren nicht nur Institutsmitglieder, sondern auch\nstark verrauschte Punktewolken, entfernen das Rauschen\nund berechnen die Mindestanzahl der benötigten Messpunkte.\nHier ist das Geschenk in der Krippe zu sehen: youtu.be/-oVwXaaJNtY",
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        "id": "Radwan-2017-Occ",
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        "title": "Cut and Paint: Occlusion-Aware Subset Selection for Surface Processing",
        "date": "2017-05",
        "abstract": "User-guided surface selection operations are straightforward for visible regions on a convex model. However, concave surfaces present a challenge because self-occlusions require multiple camera positions to get unobstructed views. Therefore, users often have to locate and switch to new unobstructed views in order to continue the operation. Our novel approach enables operations like painting or cutting in a single view, even on the backside of objects and for arbitrary depth complexity, with interactive performance. Continuous projection of a curve drawn in screen space onto the mesh guarantees seamless brush strokes or manifold cuts, unaffected by any occlusions.\n\nOur occlusion-aware surface-processing method enables a number of applications in an easy way. As examples, we show continuous painting on the surface, selecting regions for texturing, creating illustrative cutaways from nested models and animation of cutaways.",
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    {
        "id": "ohrhallinger-2016-sgp",
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        "title": "Curve Reconstruction with Many Fewer Samples",
        "date": "2016",
        "abstract": "We consider the problem of sampling points from a collection of smooth curves in the plane, such that the Crust family of proximity-based reconstruction algorithms can rebuild the curves. Reconstruction requires a dense sampling of local features, i.e., parts of the curve that are close in Euclidean distance but far apart geodesically.\nWe show that epsilon<0.47-sampling is sufficient for our proposed HNN-CRUST variant, improving upon the \nstate-of-the-art requirement of epsilon<1/3-sampling.\nThus we may reconstruct curves with many fewer samples.\nWe also present a new sampling scheme that reduces the required density even further than epsilon<0.47-sampling.\nWe achieve this by better controlling the spacing between geodesically consecutive points.\nOur novel sampling condition is based on the reach, the minimum local feature size along intervals between samples.\nThis is mathematically closer to the reconstruction density requirements, particularly near sharp-angled features.\nWe prove lower and upper bounds on reach rho-sampling density in terms of lfs epsilon-sampling and demonstrate that we typically reduce the required number of samples for reconstruction by more than half.\n",
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        "event": "Symposium on Geometry Processing",
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        "title": "Efficient Collision Detection While Rendering Dynamic Point Clouds",
        "date": "2014-05",
        "abstract": "A recent trend in interactive environments is the use of unstructured\nand temporally varying point clouds. This is driven by both\naffordable depth cameras and augmented reality simulations. One\nresearch question is how to perform collision detection on such\npoint clouds. State-of-the-art methods for collision detection create\na spatial hierarchy in order to capture dynamic point cloud surfaces,\nbut they require O(NlogN) time for N points. We propose\na novel screen-space representation for point clouds which exploits\nthe property of the underlying surface being 2D. In order for dimensionality\nreduction, a 3D point cloud is converted into a series\nof thickened layered depth images. This data structure can be constructed\nin O(N) time and allows for fast surface queries due to\nits increased compactness and memory coherency. On top of that,\nparts of its construction come for free since they are already handled\nby the rendering pipeline. As an application we demonstrate\nonline collision detection between dynamic point clouds. It shows\nsuperior accuracy when compared to other methods and robustness\nto sensor noise since uncertainty is hidden by the thickened boundary.",
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        "booktitle": "Proceedings of the 2014 Graphics Interface Conference",
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        "event": "Graphics Interface 2014",
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        "title": "The Intrinsic Shape of Point Clouds",
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        "abstract": "Given a point cloud, in the form of unorganized points, the problem of automatically connecting the dots to obtain an aesthetically pleasing and piecewise-linear closed interpolating boundary shape has been extensively researched for over three decades. In R3 , it is even more complicated to find an aesthetic closed oriented surface. Most previous methods for shape reconstruction exclusively from coordinates work well only when the point spacing on the shape boundary is dense and locally uniform. The problem of shape construction from non-dense and locally non-uniformly spaced point sets is in our opinion not yet satisfactorily solved. Various extensions to earlier methods do not work that well and do not provide any performance guarantees either.\nOur main thesis in this research is that a point set, even with non-dense and locally non-uniform spacing, has an intrinsic shape which optimizes in some way the Gestalt principles of form perception. This shape can be formally defined as the minimum of an energy function over all possible closed linear piece-wise interpolations of this point set. Further, while finding this optimal shape is NP-hard, it is possible to heuristically search for an acceptable approximation within reasonable time.\nOur minimization objective is guided by Gestalt’s laws of Proximity, Good Continuity and Closure. Minimizing curvature tends to satisfy proximity and good continuity. For computational simplification, we globally minimize the longest-edge-in-simplex, since it is intrinsic to a single facet and also a factor in mean curvature. And we require a closed shape.\nUsing such an intrinsic criterion permits the extraction of an approximate shape with a linearithmic algorithm as a simplicial complex, which we have named the Minimum Boundary Complex. Experiments show that it seems to be a very close approximation to the desired boundary shape and that it retains its genus. Further it can be constructed locally and can also handle sensor data with significant noise. Its quick construction is due to not being restricted by the manifold property, required in the boundary shape. Therefore it has many applications where a manifold shape is not necessary, e.g. visualization, shape retrieval, shadow mapping, and topological data analysis in higher dimensions. The definition of the Minimum Boundary Complex is our first major contribution.\nOur next two contributions include new methods for constructing boundary shapes by transforming the boundary complex into a close approximation of the minimum boundary shape. These algorithms vary a topological constraint to first inflate the boundary complex to recover a manifold hull and then sculpture it to extract a Minimum Boundary approximation, which interpolates all the points. In the R3 method, we show how local minima can be avoided by covering holes in the hull. Finally, we apply a mesh fairing step to optimize mean curvature directly. We present results for shape construction in R2 and R3 , which clearly demonstrate that our methods work better than the best performing earlier methods for non-dense and locally non-uniformly spaced point sets, while maintaining competitive linearithmic complexity.\n",
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        "title": "Minimising Longest Edge for Closed Surface Construction from Unorganised 3D Point Sets",
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        "abstract": "Given an unorganised 3D point set with just coordinate data, we formulate the problem of closed surface construction as one requiring minimisation of longest edge in triangles, a criterion derivable from Gestalt laws for shape perception. Next we define the Minimum Boundary Complex (BCmin ), which resembles the desired surface Bmin considerably, by slightly relaxing the topological constraint to make it at least two triangles per edge instead of exactly two required by Bmin . A close approximation of BCmin can be computed fast using a greedy algorithm. This provides a very good starting shape which can be transformed by a few steps into the desired shape, close to Bmin. Our method runs in O(n log n) time, with Delaunay Graph construction as largest run-time factor. We show considerable improvement over previous methods, especially for sparse, non-uniform point spacing.\n",
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