Fast and Robust QEF Minimization using Probabilistic Quadrics

Trettner, Philip; Kobbelt, Leif

doi:10.1111/cgf.13933

Cited by 12 publications

(8 citation statements)

References 17 publications

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“…This function is ill-conditioned in coplanar cases and, therefore, requires robust linear solvers or high numeric precision. In this work, we use the recently introduced probabilistic extension for QEF by Trettner and Kobbelt [68] for better robustness.…”

Section: Simplification Via Octree-based Vertex Clusteringmentioning

confidence: 99%

“…We use the probabilistic extension of quadratic error functions introduced by Trettner and Kobbelt [68] for our bottom-up simplification due to better robustness and expose a single standard deviation σ n to configure the normal variance Σ n = σ 2 n I. The plane position variance Σ p is set to 0 because it does not influence the position of the representative vertex and only increases the expectancy value of the simplification error.…”

Section: Topology and Silhouette-preserving Simplificationmentioning

confidence: 99%

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Real-Time 3D Reconstruction Pipeline for Room-Scale, Immersive, Medical Teleconsultation

Eck,

Wechner,

Pankratz

et al. 2023

Applied Sciences

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Medical teleconsultation was among the initial use cases for early telepresence research projects since medical treatment often requires timely intervention by highly specialized experts. When remote medical experts support interventions, a holistic view of the surgical site can increase situation awareness and improve team communication. A possible solution is the concept of immersive telepresence, where remote users virtually join the operating theater that is transmitted based on a real-time reconstruction of the local site. Enabled by the availability of RGB-D sensors and sufficient computing capability, it becomes possible to capture such a site in real time using multiple stationary sensors. The 3D reconstruction and simplification of textured surface meshes from the point clouds of a dynamic scene in real time is challenging and becomes infeasible for increasing capture volumes. This work presents a tightly integrated, stateless 3D reconstruction pipeline for dynamic, room-scale environments that generates simplified surface meshes from multiple RGB-D sensors in real time. Our algorithm operates directly on the fused, voxelized point cloud instead of populating signed-distance volumes per frame and using a marching cube variant for surface reconstruction. We extend the formulation of the dual contouring algorithm to work for point cloud data stored in an octree and interleave a vertex-clustering-based simplification before extracting the surface geometry. Our 3D reconstruction pipeline can perform a live reconstruction of six incoming depth videos at their native frame rate of 30 frames per second, enabling the reconstruction of smooth movement. Arbitrarily complex scene changes are possible since we do not store persistent information between frames. In terms of mesh quality and hole filling, our method falls between the direct mesh reconstruction and expensive global fitting of implicit functions.

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Section: Simplification Via Octree-based Vertex Clusteringmentioning

confidence: 99%

Section: Topology and Silhouette-preserving Simplificationmentioning

confidence: 99%

Real-Time 3D Reconstruction Pipeline for Room-Scale, Immersive, Medical Teleconsultation

Eck,

Wechner,

Pankratz

et al. 2023

Applied Sciences

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show abstract

“…In order to determine the unique point, there are at least three different planes in the sum of 𝑄 matrices, otherwise a unique solution that minimizes the quadratic error will not be obtained. We use probabilistic quadrics [14] to avoid this problem.…”

Section: Serial Approaches 31 Quadric Error Matrixmentioning

confidence: 99%

Fast and robust parallel simplification algorithm for triangular mesh

Yan,

Yang,

Wang

2023

Third International Conference on Computer Graphics, Image, and Virtualization (ICCGIV 2023)

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Mesh simplification is a fundamental problem in geometry processing. Since general simplification algorithms are difficult to parallelize, the main challenge is to process meshes of tens of millions of faces with fast and low memory consumption and maintain high-quality output. In this paper, we propose a multi-threaded algorithmic framework for mesh simplification. First, we design a robust and fast serial simplification model based on edge collapsing with low memory consumption. We implement a simplified algorithm based on Probabilistic QEM, and we take strict measures to protect the mesh topology as well as a greedy strategy to speed up the algorithm. Then we design a parallel simplification algorithm framework based on the idea of divide-and-conquer followed by global optimization. This method can execute the algorithm much faster with the same memory consumption as the serial method and maintain high-quality output results. Experiments show that our parallel algorithm outperforms current open-source software in terms of speed and memory consumption, and maintains good output for all models tested.

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“…Higher-than-necessary triangle counts are undesired, as they increase the problem complexity for the thermal optimizer. Therefore, a simple mesh decimation [41] is applied to reduce the output complexity while limiting the output error, which is followed by an iteration of Laplacian smoothing to improve the surface quality.…”

Section: Post-processingmentioning

confidence: 99%

Variable Offset Computation Space for Automatic Cooling Dimensioning

et al. 2022

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The injection mold is one of the most important elements for the part precision of this important mass production process. The thermal mold design is realized by cooling channels around the cavity and poses as a decisive factor for the part quality. Thus, the objective but specific design of the cooling channel layout is crucial for a reproducible part with high-dimensional accuracy in production. Consequently, knowledge-based and automated methods are used to create the optimal heat management in the mold. One of these methods is the inverse thermal mold design, which uses a specific calculation space. The geometric boundary conditions of the optimization algorithm influence the resulting thermal balance within the mold. As the calculation area in the form of an offset around the molded part is one of these boundary conditions, its influence on the optimization result is determined. The thermal optimizations show a dependency on different offset shapes due to the offset thickness and coalescence of concave geometries. An algorithm is developed to generate an offset for this thermal mold design methodology considering the identified influences. Hence, a reproducible and adaptive offset is generated automatically for a complex geometry, and the quality function result improves by 43% in this example.

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Fast and Robust QEF Minimization using Probabilistic Quadrics

Cited by 12 publications

References 17 publications

Real-Time 3D Reconstruction Pipeline for Room-Scale, Immersive, Medical Teleconsultation

Real-Time 3D Reconstruction Pipeline for Room-Scale, Immersive, Medical Teleconsultation

Fast and robust parallel simplification algorithm for triangular mesh

Variable Offset Computation Space for Automatic Cooling Dimensioning

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