Philip Trettner, M.Sc.
Room 106
Phone: +49 241 8021808
Fax: +49 241 8022899
Email: trettner@cs.rwth-aachen.de


Fast and Robust QEF Minimization using Probabilistic Quadrics

Philip Trettner, Leif Kobbelt
Computer Graphics Forum (Proc. EUROGRAPHICS 2020)

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 - 50x 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.

» Show BibTeX

@article {10.1111:cgf.13933,
journal = {Computer Graphics Forum},
title = {{Fast and Robust QEF Minimization using Probabilistic Quadrics}},
author = {Trettner, Philip and Kobbelt, Leif},
year = {2020},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.13933}

High-Performance Image Filters via Sparse Approximations

Kersten Schuster, Philip Trettner, Leif Kobbelt
Proceedings of the ACM on Computer Graphics and Interactive Techniques, Vol. 3, No. 2, 2020

We present a numerical optimization method to find highly efficient (sparse) approximations for convolutional image filters. Using a modified parallel tempering approach, we solve a constrained optimization that maximizes approximation quality while strictly staying within a user-prescribed performance budget. The results are multi-pass filters where each pass computes a weighted sum of bilinearly interpolated sparse image samples, exploiting hardware acceleration on the GPU. We systematically decompose the target filter into a series of sparse convolutions, trying to find good trade-offs between approximation quality and performance. Since our sparse filters are linear and translation-invariant, they do not exhibit the aliasing and temporal coherence issues that often appear in filters working on image pyramids. We show several applications, ranging from simple Gaussian or box blurs to the emulation of sophisticated Bokeh effects with user-provided masks. Our filters achieve high performance as well as high quality, often providing significant speed-up at acceptable quality even for separable filters. The optimized filters can be baked into shaders and used as a drop-in replacement for filtering tasks in image processing or rendering pipelines.

A Three-Level Approach to Texture Mapping and Synthesis on 3D Surfaces

Kersten Schuster, Philip Trettner, Patric Schmitz, Leif Kobbelt
Proceedings of the ACM on Computer Graphics and Interactive Techniques, Vol. 3, No. 1, 2020

We present a method for example-based texturing of triangular 3D meshes. Our algorithm maps a small 2D texture sample onto objects of arbitrary size in a seamless fashion, with no visible repetitions and low overall distortion. It requires minimal user interaction and can be applied to complex, multi-layered input materials that are not required to be tileable. Our framework integrates a patch-based approach with per-pixel compositing. To minimize visual artifacts, we run a three-level optimization that starts with a rigid alignment of texture patches (macro scale), then continues with non-rigid adjustments (meso scale) and finally performs pixel-level texture blending (micro scale). We demonstrate that the relevance of the three levels depends on the texture content and type (stochastic, structured, or anisotropic textures).

» Show BibTeX

author = {Schuster, Kersten and Trettner, Philip and Schmitz, Patric and Kobbelt, Leif},
title = {A Three-Level Approach to Texture Mapping and Synthesis on 3D Surfaces},
year = {2020},
issue_date = {Apr 2020},
publisher = {The Association for Computers in Mathematics and Science Teaching},
address = {USA},
volume = {3},
number = {1},
url = {https://doi.org/10.1145/3384542},
doi = {10.1145/3384542},
journal = {Proc. ACM Comput. Graph. Interact. Tech.},
month = apr,
articleno = {1},
numpages = {19},
keywords = {material blending, surface texture synthesis, texture mapping}

City Reconstruction and Visualization from Public Data Sources

Jan Robert Menzel, Sven Middelberg, Philip Trettner, Bastian Jonas, Leif Kobbelt
Eurographics Workshop on Urban Data Modelling and Visualisation (UDMV 2016)

We present a city reconstruction and visualization framework that integrates geometric models reconstructed with a range of different techniques. The framework generates the vast majority of buildings procedurally, which yields plausible visualizations for structurally simple buildings, e.g. residential buildings. For structurally complex landmarks, e.g. churches, a procedural approach does not achieve satisfactory visual fidelity. Thus, we also employ image-based techniques to reconstruct the latter in a more realistic, recognizable way. As the manual acquisition of data required for the procedural and image-based reconstructions is practically infeasible for whole cities, we rely on publicly available data as well as crowd sourcing projects. This enables our framework to render views from cities without any dedicated data acquisition as long as there are sufficient public data sources available. To obtain a more lively impression of a city, we also visualize dynamic features like weather conditions and traffic based on publicly available real-time data.

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