Abstract
Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional fields from data relies on complex optimization procedures, which are usually poorly formalizable, require a considerable computational effort, and do not transfer across applications. In this work, we propose a deep learning-based approach and study the expressive power and generalization ability.
M. Taktasheva and A. Matveev—These two authors contribute equally to the work.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Barabanau, I., Artemov, A., Murashkin, V., Burnaev, E.: Monocular 3D object detection via geometric reasoning on keypoints (2019). arXiv preprint arXiv:1905.05618
Bessmeltsev, M., Solomon, J.: Vectorization of line drawings via polyvector fields. ACM Trans. Graph. (TOG) 38(1), 9 (2019)
Bokhovkin, A., Burnaev, E.: Boundary loss for remote sensing imagery semantic segmentation. In: Lu, H., Tang, H., Wang, Z. (eds.) ISNN 2019. LNCS, vol. 11555, pp. 388–401. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-22808-8_38
Bommes, D., et al.: Quad-mesh generation and processing: a survey. Comput. Graph. Forum 32, 51–76 (2013)
Burnaev, E., Cichocki, A., Osin, V.: Fast multispectral deep fusion networks. Bull. Pol. Acad. Tech. 66(4), 875–880 (2018)
Diamanti, O., Vaxman, A., Panozzo, D., Sorkine-Hornung, O.: Designing N-PolyVector fields with complex polynomials. Comput. Graph. Forum 33, 1–11 (2014)
de Goes, F., Desbrun, M., Tong, Y.: Vector field processing on triangle meshes. In: ACM SIGGRAPH 2016 Courses, p. 27. ACM (2016)
Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw. 2(5), 359–366 (1989)
Ignatiev, V., Trekin, A., Lobachev, V., Potapov, G., Burnaev, E.: Targeted change detection in remote sensing images. In: Proceedings of SPIE (2019)
Koch, S., et al.: ABC: a big CAD model dataset for geometric deep learning. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9601–9611 (2019)
Kolos, M., Marin, A., Artemov, A., Burnaev, E.: Procedural synthesis of remote sensing images for robust change detection with neural networks. In: Lu, H., Tang, H., Wang, Z. (eds.) ISNN 2019. LNCS, vol. 11555, pp. 371–387. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-22808-8_37
Mhaskar, H.N., Poggio, T.: Deep vs. shallow networks: an approximation theory perspective. Anal. Appl. 14(06), 829–848 (2016)
Notchenko, A., Kapushev, Y., Burnaev, E.: Large-scale shape retrieval with sparse 3D convolutional neural networks. In: van der Aalst, W.M.P., et al. (eds.) AIST 2017. LNCS, vol. 10716, pp. 245–254. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-73013-4_23
Novikov, G., Trekin, A., Potapov, G., Ignatiev, V., Burnaev, E.: Satellite imagery analysis for operational damage assessment in emergency situations. In: Abramowicz, W., Paschke, A. (eds.) BIS 2018. LNBIP, vol. 320, pp. 347–358. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93931-5_25
Paszke, A., et al.: Automatic differentiation in PyTorch (2017)
Ray, N., Nivoliers, V., Lefebvre, S., Lévy, B.: Invisible seams. Comput. Graph. Forum 29, 1489–1496 (2010)
Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28
Vaxman, A., et al.: Directional field synthesis, design, and processing. Comput. Graph. Forum 35, 545–572 (2016)
Voinov, O., et al.: Perceptual deep depth super-resolution (2018). arXiv preprint arXiv:1812.09874
Acknowlegement
The work was supported by the Russian Science Foundation under Grant 19-41-04109.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Taktasheva, M., Matveev, A., Artemov, A., Burnaev, E. (2019). Learning to Approximate Directional Fields Defined Over 2D Planes. In: van der Aalst, W., et al. Analysis of Images, Social Networks and Texts. AIST 2019. Lecture Notes in Computer Science(), vol 11832. Springer, Cham. https://doi.org/10.1007/978-3-030-37334-4_33
Download citation
DOI: https://doi.org/10.1007/978-3-030-37334-4_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-37333-7
Online ISBN: 978-3-030-37334-4
eBook Packages: Computer ScienceComputer Science (R0)