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C05
Computational and structural aspects in multi-scale shape interpolation


Shape analysis is of central interest in computer vision and geometry processing. Three major computational and theoretical challenges in shape analysis are the computation of correspondences (shape registration or matching), the definition of similarity measures (metrics in shape space), and the generation of intermediate shapes (shape morphing).

Scientific Details+

Shape analysis is of central interest in computer vision and geometry processing. Three major computational and theoretical challenges in shape analysis are the computation of correspondences (shape registration or matching), the definition of similarity measures (metrics in shape space), and the generation of intermediate shapes (shape morphing). While there have been numerous solutions proposed to these challenges over the years, existing approaches suffer from various shortcomings–most importantly the computed solutions often require good initial registrations (with human interaction), have outlier solutions, or the respective algorithms are computationally too demanding which prohibits processing of complex, high-resolution shapes. Moreover, respective methods are often designed for perfect meshes and hardly generalize to other shape representations, for example, to noisy point cloud geometries. The aim of this project is to study the above challenges in the framework of shape interpolation: Given two or more shapes create a family of interpolating shapes. Such an interpolation will invariably entail metrics and correspondences. In particular, we will devise shape interpolation methods for a variety of different shape representations such as point clouds, meshes, or signed distance functions.

Publications+

Papers
  • Florian Hofherr, Lukas Koestler, Florian Bernard, and Daniel Cremers.
    Neural Implicit Representations for Physical Parameter Inference From a Single Video.
    Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 2093–2103, 2023.
    arXiv:2204.14030.
  • Martin Skrodzki, Ulrich Reitebuch, and Eric Zimmermann.
    Investigations of structures in the parameter space of three-dimensional Turing-like patterns.
    HAL, July 2021.
    URL: https://hal.science/hal-03270664/file/AUTOMATA2021-exploratory15.pdf.
  • "Martin Skrodzki and Eric Zimmermann".
    "A Large-Scale Evaluation Of Shape-Aware Neighborhood Weights And Neighborhood Sizes".
    "Computer-Aided Design", 141:103107, 2021.
    doi:10.1016/j.cad.2021.103107.
  • Sunil Kumar Yadav, Martin Skrodzki, Eric Zimmermann, and Konrad Polthier.
    "Surface Denoising Based on Normal Filtering in a Robust Statistics Framework".
    "Proceedings of the Forum "Math-for-Industry" 2018", 35:103–132, 2021.
    doi:10.1007/978-981-16-5576-0_6.
  • Martin Skrodzki, Eric Zimmermann, and Konrad Polthier.
    Variational shape approximation of point set surfaces.
    Computer Aided Geometric Design, June 2020.
    arXiv:2005.01003, doi:10.1016/j.cagd.2020.101875.
  • Martin Skrodzki, Ulrike Bath, Kevin Guo, and Konrad Polthier.
    A leap forward: a user study on gestural geometry exploration.
    Journal of Mathematics and the Arts, 13(4):369–382, 2019.
    doi:10.1080/17513472.2019.1667209.
  • Sunil Kumar Yadav, Ulrich Reitebuch, and Konrad Polthier.
    Mesh Denoising Based on Normal Voting Tensor and Binary Optimization.
    IEEE Transactions on Visualization and Computer Graphics, 24(8):2366–2379, August 2018.
    doi:10.1109/TVCG.2017.2740384.
  • Martin Skrodzki, Ulrich Reitebuch, Konrad Polthier, and Shagnik Das.
    Combinatorial and Asymptotical Results on the Neighborhood Grid Data Structure.
    Eurographics Conference on Computer Graphics 2018, 2018.
    URL: https://conference.imp.fu-berlin.de/eurocg18/download/paper_30.pdf.
  • Sunil Kumar Yadav, Ulrich Reitebuch, Martin Skrodzki, Eric Zimmermann, and Konrad Polthier.
    Constraint-based point set denoising using normal voting tensor and restricted quadratic error metrics.
    Computers and Graphics, 74:234 – 243, 2018.
    doi:10.1016/j.cag.2018.05.014.
  • Martin Skrodzki, Johanna Jansen, and Konrad Polthier.
    Directional density measure to intrinsically estimate and counteract non-uniformity in point clouds.
    Computer Aided Geometric Design, 64:73 – 89, 2018.
    URL: http://www.sciencedirect.com/science/article/pii/S0167839618300256, doi:10.1016/j.cagd.2018.03.011.
  • Martin Skrodzki and Konrad Polthier.
    Mondrian Revisited: A Peek Into The Third Dimension.
    In Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture, 99–106. Phoenix, Arizona, 2018. Tessellations Publishing.
    URL: http://archive.bridgesmathart.org/2018/bridges2018-99.pdf.
  • Eric Zimmermann Ulrich Reitebuch and Konrad Polthier.
    Two-Layer Woven Surfaces with Planar Faces.
    In Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture, 147–154. Phoenix, Arizona, 2018. Tessellations Publishing.
    URL: http://archive.bridgesmathart.org/2018/bridges2018-147.pdf.
  • Konstantin Poelke and Konrad Polthier.
    Discrete Topology-Revealing Vector Fields on Simplicial Surfaces with Boundary.
    In Proc. of TopoInVis 2017. 2017.
    URL: https://www.semanticscholar.org/paper/Discrete-Topology-Revealing-Vector-Fields-on-with-Poelke-Polthier/e21049641234976a56bbb668287b382412ccdfe1.
  • Martin Skrodzki and Konrad Polthier.
    Turing-Like Patterns Revisited: A Peek Into The Third Dimension.
    In David Swart, Carlo H. Séquin and Kristóf Fenyvesi, editors, Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture, 415–418. Phoenix, Arizona, 2017. Tessellations Publishing.
    URL: http://archive.bridgesmathart.org/2017/bridges2017-415.pdf.
  • Konstantin Poelke and Konrad Polthier.
    Boundary-aware Hodge decompositions for piecewise constant vector fields.
    Computer-Aided Design, 78:126 – 136, 2016.
    doi:10.1016/j.cad.2016.05.004.
  • Martin Skrodzki, Ulrich Reitebuch, and Konrad Polthier.
    Chladni Figures Revisited: A Peek Into The Third Dimension.
    In Eve Torrence, Bruce Torrence, Carlo Séquin, Douglas McKenna, Kristóf Fenyvesi, and Reza Sarhangi, editors, Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, 481–484. Phoenix, Arizona, 2016. Tessellations Publishing.
    URL: http://archive.bridgesmathart.org/2016/bridges2016-481.html.

Posters

Team+

Prof. Dr. Konrad Polthier   +

Projects: C05
University: FU Berlin
E-Mail: konrad.polthier[at]fu-berlin.de
Website: http://page.mi.fu-berlin.de/polthier/

Prof. Dr. Daniel Cremers   +

Projects: C05, C09
University: TU München, Department of Computer Science, Informatik 9, 02.09.054
Address: Boltzmannstrasse 3, 85748 Garching, GERMANY
Tel: +49 89 28917755
Fax: +49 89 28917757
E-Mail: cremers[at]tum.de
Website: https://vision.in.tum.de/members/cremers

Marvin Eisenberger   +

Projects: C05
University: TU München, Informatik 9, 02.09.058
Address: Boltzmannstrasse 3, 85748 Garching, GERMANY
Tel: +49 89 28917790
Fax: +49 89 28917757
E-Mail: marvin.eisenberger[at]in.tum.de
Website: https://vision.in.tum.de/members/eisenber

Florian Hofherr   +

Projects: C05
University: TU München, Informatik 9
Address: Boltzmannstrasse 3, 85748 Garching, GERMANY
Tel: +49 89 28917757
E-Mail: florian.hofherr[at]posteo.de
Website: https://vision.in.tum.de/members/hofherrf

Christian Koke   +

Projects: C05
University: TU München
E-Mail: christian.koke[at]tum.de

Ulrich Reitebuch   +

Projects: C05
University: FU Berlin, AG Mathematical Geometry Processing, 106
Address: Arnimallee 6, 14195 Berlin, GERMANY
Tel: +49 30 83875874
E-Mail: Ulrich.Reitebuch[at]fu-berlin.de
Website: https://page.mi.fu-berlin.de/reitebuc/

Eric Zimmermann   +

Projects: C05
University: FU Berlin
E-Mail: eric.zimmermann[at]fu-berlin.de