Inter-Surface Maps via Constant-Curvature Metrics

Patrick Schmidt, Marcel Campen, Janis Born, Leif Kobbelt

We propose a novel approach to represent maps between two discrete surfaces of the same genus and to minimize intrinsic mapping distortion. Our maps are well-defined at every surface point and are guaranteed to be continuous bijections (surface homeomorphisms). As a key feature of our approach, only the images of vertices need to be represented explicitly, since the images of all other points (on edges or in faces) are properly defined implicitly. This definition is via unique geodesics in metrics of constant Gaussian curvature. Our method is built upon the fact that such metrics exist on surfaces of arbitrary topology, without the need for any cuts or cones (as asserted by the uniformization theorem). Depending on the surfaces' genus, these metrics exhibit one of the three classical geometries: Euclidean, spherical or hyperbolic. Our formulation handles constructions in all three geometries in a unified way. In addition, by considering not only the vertex images but also the discrete metric as degrees of freedom, our formulation enables us to simultaneously optimize the images of these vertices and images of all other points.

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author = {Schmidt, Patrick and Campen, Marcel and Born, Janis and Kobbelt, Leif},
title = {Inter-Surface Maps via Constant-Curvature Metrics},
journal = {ACM Transactions on Graphics},
issue_date = {July 2020},
volume = {39},
number = {4},
month = jul,
year = {2020},
articleno = {119},
url = {https://doi.org/10.1145/3386569.3392399},
doi = {10.1145/3386569.3392399},
publisher = {ACM},
address = {New York, NY, USA},

Rilievo: Artistic Scene Authoring via Interactive Height Map Extrusion in VR

Sevinc Eroglu, Patric Schmitz, Carlos Aguilera Martinez, Jana Rusch, Leif Kobbelt, Torsten Wolfgang Kuhlen
ACM SIGGRAPH 2020 Art Papers. Published in Leonardo Journal.

The authors present a virtual authoring environment for artistic creation in VR. It enables the effortless conversion of 2D images into volumetric 3D objects. Artistic elements in the input material are extracted with a convenient VR-based segmentation tool. Relief sculpting is then performed by interactively mixing different height maps. These are automatically generated from the input image structure and appearance. A prototype of the tool is showcased in an analog-virtual artistic workflow in collaboration with a traditional painter. It combines the expressiveness of analog painting and sculpting with the creative freedom of spatial arrangement in VR.

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title={Rilievo: Artistic Scene Authoring via Interactive Height Map Extrusion in VR},
author={Eroglu, Sevinc and Schmitz, Patric and Martinez, Carlos Aguilera and Rusch, Jana and Kobbelt, Leif and Kuhlen, Torsten W},
publisher={MIT Press}

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.

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@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-Fidelity Point-Based Rendering of Large-Scale 3D Scan Datasets

Patric Schmitz, Timothy Blut, Christian Mattes, Leif Kobbelt
IEEE Computer Graphics and Applications

Digitalization of 3D objects and scenes using modern depth sensors and high-resolution RGB cameras enables the preservation of human cultural artifacts at an unprecedented level of detail. Interactive visualization of these large datasets, however, is challenging without degradation in visual fidelity. A common solution is to fit the dataset into available video memory by downsampling and compression. The achievable reproduction accuracy is thereby limited for interactive scenarios, such as immersive exploration in Virtual Reality (VR). This degradation in visual realism ultimately hinders the effective communication of human cultural knowledge. This article presents a method to render 3D scan datasets with minimal loss of visual fidelity. A point-based rendering approach visualizes scan data as a dense splat cloud. For improved surface approximation of thin and sparsely sampled objects, we propose oriented 3D ellipsoids as rendering primitives. To render massive texture datasets, we present a virtual texturing system that dynamically loads required image data. It is paired with a single-pass page prediction method that minimizes visible texturing artifacts. Our system renders a challenging dataset in the order of 70 million points and a texture size of 1.2 terabytes consistently at 90 frames per second in stereoscopic VR.

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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.

Cost Minimizing Local Anisotropic Quad Mesh Refinement

Max Lyon, David Bommes, Leif Kobbelt
Eurographics Symposium on Geometry Processing 2020

Quad meshes as a surface representation have many conceptual advantages over triangle meshes. Their edges can naturally be aligned to principal curvatures of the underlying surface and they have the flexibility to create strongly anisotropic cells without causing excessively small inner angles. While in recent years a lot of progress has been made towards generating high quality uniform quad meshes for arbitrary shapes, their adaptive and anisotropic refinement remains difficult since a single edge split might propagate across the entire surface in order to maintain consistency. In this paper we present a novel refinement technique which finds the optimal trade-off between number of resulting elements and inserted singularities according to a user prescribed weighting. Our algorithm takes as input a quad mesh with those edges tagged that are prescribed to be refined. It then formulates a binary optimization problem that minimizes the number of additional edges which need to be split in order to maintain consistency. Valence 3 and 5 singularities have to be introduced in the transition region between refined and unrefined regions of the mesh. The optimization hence computes the optimal trade-off and places singularities strategically in order to minimize the number of consistency splits — or avoids singularities where this causes only a small number of additional splits. When applying the refinement scheme iteratively, we extend our binary optimization formulation such that previous splits can be undone if this prevents degenerate cells with small inner angles that otherwise might occur in anisotropic regions or in the vicinity of singularities. We demonstrate on a number of challenging examples that the algorithm performs well in practice.

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title = {Cost Minimizing Local Anisotropic Quad Mesh Refinement},
author = {Lyon, Max and Bommes, David and Kobbelt, Leif},
journal = {Computer Graphics Forum},
volume = {39},
number = {5},
year = {2020},
doi = {10.1111/cgf.14076}

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).

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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}

PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models

Lin Gao, Ling-Xiao Zhang, Hsien-Yu Meng, Yi-Hui Ren, Yu-Kun Lai, Leif Kobbelt
IEEE Transactions on Visualization and Computer Graphics

In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces.

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author = {Lin Gao and
Ling{-}Xiao Zhang and
Hsien{-}Yu Meng and
Yi{-}Hui Ren and
Yu{-}Kun Lai and
Leif Kobbelt},
title = {PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models},
journal = {CoRR},
volume = {abs/1910.06511},
year = {2019},
url = {http://arxiv.org/abs/1910.06511},
archivePrefix = {arXiv},
eprint = {1910.06511},

Unsupervised Segmentation of Indoor 3D Point Cloud: Application to Object-based Classification

Florent Poux, Christian Mattes, Leif Kobbelt
3D GeoInfo Conference 2020

Point cloud data of indoor scenes is primarily composed of planar-dominant elements. Automatic shape segmentation is thus valuable to avoid labour intensive labelling. This paper provides a fully unsupervised region growing segmentation approach for efficient clustering of massive 3D point clouds. Our contribution targets a low-level grouping beneficial to object-based classification. We argue that the use of relevant segments for object-based classification has the potential to perform better in terms of recognition accuracy, computing time and lowers the manual labelling time needed. However, fully unsupervised approaches are rare due to a lack of proper generalisation of user-defined parameters. We propose a self-learning heuristic process to define optimal parameters, and we validate our method on a large and richly annotated dataset (S3DIS) yielding 88.1% average F1-score for object-based classification. It permits to automatically segment indoor point clouds with no prior knowledge at commercially viable performance and is the foundation for efficient indoor 3D modelling in cluttered point clouds.

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author = {Poux, F. and Mattes, C. and Kobbelt, L.},
journal = {ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences},
volume = {XLIV-4/W1-2020},
year = {2020},
pages = {111--118},
url = {https://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XLIV-4-W1-2020/111/2020/},
doi = {10.5194/isprs-archives-XLIV-4-W1-2020-111-2020}

Initial User-Centered Design of a Virtual Reality Heritage System: Applications for Digital Tourism

Florent Poux, Quentin Valembois, Christian Mattes, Leif Kobbelt, Roland Billen
Remote Sensing

Reality capture allows for the reconstruction, with a high accuracy, of the physical reality of cultural heritage sites. Obtained 3D models are often used for various applications such as promotional content creation, virtual tours, and immersive experiences. In this paper, we study new ways to interact with these high-quality 3D reconstructions in a real-world scenario. We propose a user-centric product design to create a virtual reality (VR) application specifically intended for multi-modal purposes. It is applied to the castle of Jehay (Belgium), which is under renovation, to permit multi-user digital immersive experiences. The article proposes a high-level view of multi-disciplinary processes, from a needs analysis to the 3D reality capture workflow and the creation of a VR environment incorporated into an immersive application. We provide several relevant VR parameters for the scene optimization, the locomotion system, and the multi-user environment definition that were tested in a heritage tourism context.

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title={Initial User-Centered Design of a Virtual Reality Heritage System: Applications for Digital Tourism},
journal={Remote Sensing},
publisher={MDPI AG},
author={Poux, Florent and Valembois, Quentin and Mattes, Christian and Kobbelt, Leif and Billen, Roland},

SEG-MAT: 3D Shape Segmentation Using Medial Axis Transform

Cheng Lin, Lingjie Liu, Changjian Li, Leif Kobbelt, Bin Wang, Shiqing Xin, Wenping Wang
IEEE Transactions on Visualization and Computer Graphics

Segmenting arbitrary 3D objects into constituent parts that are structurally meaningful is a fundamental problem encountered in a wide range of computer graphics applications. Existing methods for 3D shape segmentation suffer from complex geometry processing and heavy computation caused by using low-level features and fragmented segmentation results due to the lack of global consideration. We present an efficient method, called SEG-MAT, based on the medial axis transform (MAT) of the input shape. Specifically, with the rich geometrical and structural information encoded in the MAT, we are able to develop a simple and principled approach to effectively identify the various types of junctions between different parts of a 3D shape. Extensive evaluations and comparisons show that our method outperforms the state-of-the-art methods in terms of segmentation quality and is also one order of magnitude faster.

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author={C. {Lin} and L. {Liu} and C. {Li} and L. {Kobbelt} and B. {Wang} and S. {Xin} and W. {Wang}},
journal={IEEE Transactions on Visualization and Computer Graphics},
title={SEG-MAT: 3D Shape Segmentation Using Medial Axis Transform},

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