Fast and Robust QEF Minimization using Probabilistic Quadrics

Error quadrics are a fundamental and powerful building block in many geometry processing algorithms. However, finding the minimizer of a given quadric is in many cases not robust and requires a singular value decomposition or some ad‐hoc regularization. While classical error quadrics measure the squ...

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Vydané v:Computer graphics forum Ročník 39; číslo 2; s. 325 - 334
Hlavní autori: Trettner, P., Kobbelt, L.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Oxford Blackwell Publishing Ltd 01.05.2020
Predmet:
Algorithms
CCS Concepts
Computing methodologies → Mesh models; Mesh geometry models
Error analysis
Ground truth
Normal distribution
Optimization
Random noise
Regularization
Robustness
Singular value decomposition
Triangles
ISSN:0167-7055, 1467-8659
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Shrnutí:Error quadrics are a fundamental and powerful building block in many geometry processing algorithms. However, finding the minimizer of a given quadric is in many cases not robust and requires a singular value decomposition or some ad‐hoc regularization. While classical error quadrics measure the squared deviation from a set of ground truth planes or polygons, we treat the input data as genuinely uncertain information and embed error quadrics in a probabilistic setting (“probabilistic quadrics”) where the optimal point minimizes the expected squared error. We derive closed form solutions for the popular plane and triangle quadrics subject to (spatially varying, anisotropic) Gaussian noise. Probabilistic quadrics can be minimized robustly by solving a simple linear system — 50× faster than SVD. We show that probabilistic quadrics have superior properties in tasks like decimation and isosurface extraction since they favor more uniform triangulations and are more tolerant to noise while still maintaining feature sensitivity. A broad spectrum of applications can directly benefit from our new quadrics as a drop‐in replacement which we demonstrate with mesh smoothing via filtered quadrics and non‐linear subdivision surfaces.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13933