doc. Ing. Tomáš Pajdla, Ph.D.


Dissertation theses

Learning to solve multiple view geometry

Topic of dissertation thesis
Topic description

Multiple view geometry is an important field in computer vision and robotics, which provides understanding to the foundations of the subject. The development of this field has, however, not yet been greatly influenced by the recent advances in machine learning and geometrical machine learning in particular. We aim at using machine learning to address long-standing problems in multiple view geometry that have not been solved by traditional techniques. For instance, current methods for computing camera geometry from image matches can cope efficiently with only relatively simple problems in two-view geometry. Thus, there are still no really efficient solvers even for three-view geometry. The classical approach to solver design leads in this case to very complicated computation procedures due to trying to solve exact algebraic problems. Recent advances in numerical algebraic geometry start providing a practical alternative to the elimination-based approaches. In particular, we believe that these approaches can be greatly improved in efficiency and robustness by learning optimal strategies of solving, efficient problem analysis, and fitting the problem to the data. Our plan is to develop a new approach to solving hard problems in multiple-view geometry that would use machine learning to tune solving techniques to the data and thus making them tractable and efficient.

  • [MB] M. Bronstein et alt. “Geometric deep learning: going beyond Euclidean data”. IEEE Signal Processing Magazine, vol. 34, no. 4, pp. 18-42, 2017.
  • [NS] D. Nister and F. Schaffalitzky. “Four Points in Two or Three Calibrated Views: Theory and Practice”. International Journal of Computer Vision (IJCV), vol. 67, pp. 211-231, 2006.
  • [Fal] R Fabbri et al. “TRPLP – Trifocal Relative Pose From Lines at Points”. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 12070-12080, 2020.
  • [PLMPl] T Duff et al. “PLMP - Point-Line Minimal Problems in Complete Multi-View Visibility”. IEEE International Conference on Computer Vision (ICCV), pp. 1675-1684, 2019.
  • [PL1P] T Duff et al. “PL1P - Point-line Minimal Problems under Partial Visibility in Three Views”. European Conference on Computer Vision (ECCV), pp. 175-192, 2020.
  • [BGrob] V Larsson et al. "Beyond Grobner Bases: Basis Selection for Minimal Solvers". IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3945-3954, 2018.
  • [Pfeifer] D Peifer et al. “Learning selection strategies in Buchberger's algorithm”. International Conference on Machine Learning (ICML), pp. 7575-7585, 2020.
  • [Bernal] E. Bernal et al. “Machine learning the real discriminant locus”. ArXiv preprint, June 2020.
  • [DSAC] E Brachmann et al. "DSAC – Differentiable RANSAC for Camera Localization", CVPR 2017.
  • [Ranftl] R Ranftl, V Koltun. Deep Fundamental Matrix Estimation. ECCV 2018.