Speakers
TatJun Chin Associate Professor The University of Adelaide 
Anders Eriksson ARC Future Fellow Queensland University of Technology 
Fredrik Kahl Professor Chalmers University of Technology 
Course description
Stemming from its roots in photogrammetry, the theory and practice of multiple view geometry has traditionally focussed on L2 minimisation, i.e., minimising sum of squared errors. However, due to the projective nature of the imaging process, many of the optimisation problems associated with L2 minimisation (e.g., bundle adjustment) involve objective functions that are plagued by multiple local minima [1]. This prevents algorithms that are tractable (i.e., able to efficiently and verifiably find the globally optimal solution), and necessitates careful preprocessing and/or initialisation to ensure success.
The situation changes dramatically, however, if we perform Linfinity minimisation. Pioneered by Hartley and Kahl in the mid2000’s for multiple view geometry [2][3], it can be shown that many geometric problems (e.g., triangulation, homography estimation) are amenable to tractable solutions if we minimise the largest error. Since then, there has been significant progress in the “Linfinity way”, encompassing aspects such as robust estimation [4][5][6], largescale optimisation [7][8], and guaranteed approximations [9]most of which can be performed better due to the fundamental advantages of Linfinity minimisation. The intimate connection between Linfinity minimisation and quasiconvex programming [10] also enables theory and methods from the discrete geometry literature to be leveraged for computer vision.
This tutorial aims to give an indepth introduction of Linfinity optimisation in geometric vision. We emphasise on the basic mathematical and algorithmic concepts, so as to convey deeper understanding and appreciation of the approach. We also survey important recent advances in the area, which contribute towards making the Linfinity way a bona fide alternative to current methods for geometric vision. It is hoped that the tutorial will inspire more researchers to incorporate Linfinity methods into their applications.
Detailed topics and schedule
Time  Topic  Slides  Presenter 

13301340  Arrival and welcome  Chin  
13401430 

Kahl  
14301520 

Chin  
15201600  Coffee break  
16001650 

Eriksson 
References
 R. Hartley, F. Kahl: Optimal Algorithms in Multiview Geometry. ACCV 2007.
 R. Hartley, F. Schaffalitzky: Linfinity Minimization in Geometric Reconstruction Problems. CVPR 2004.
 F. Kahl: Multiple View Geometry and the Linfinitynorm. ICCV 2005.
 K. Sim, R. Hartley: Removing Outliers Using The Linfty Norm. CVPR 2006.
 O. Enqvist, E. Ask, F. Kahl, K. Åström: Tractable Algorithms for Robust Model Estimation. IJCV 112(1): 115129 (2015).
 T.J. Chin, P. Purkait, A. Eriksson, D. Suter: Efficient globally optimal consensus maximisation with tree search. CVPR 2015.
 A. Eriksson, M. Isaksson: Pseudoconvex Proximal Splitting for Linfinity Problems in Multiview Geometry. CVPR 2014.
 A. Eriksson, J. Bastian, T.J. Chin, M. Isaksson: A ConsensusBased Framework for Distributed Bundle Adjustment. CVPR 2016.
 Q. Zhang, T.J. Chin: Coresets for Triangulation. TPAMI 2017.
 D. Eppstein: Quasiconvex Programming. CoRR abs/cs/0412046 (2004).
 C. Olsson, A. Eriksson, F. Kahl: Efficient Optimization for Lproblems using Pseudoconvexity. ICCV 2007.
 S. Agarwal, N. Snavely, S. M. Seitz: Fast Algorithms for Linfinity Problems in Multiview Geometry. CVPR 2008.
 Z. Dai, Y. Wu, F. Zhang, and H. Wang: A Novel Fast Method for Linfinity Problems in Multiview Geometry. ECCV 2012.
 S Donné, B Goossens, W Philips. Point Triangulation Through Polyhedron Collapse Using the linfinity Norm. ICCV 2015.
 T.J. Chin, D. Suter: The Maximum Consensus Problem: Recent Algorithmic Advances. Synthesis Lectures on Computer Vision, Morgan & Claypool Publishers 2017.
 H. Le, T.J. Chin, D. Suter: RATSAC  Random Tree Sampling for Maximum Consensus Estimation. DICTA 2017.
 Q. Zhang, T.J. Chin, H. Le: A Fast ResectionIntersection Method for the Known Rotation Problem. CVPR 2018.
 D. Martinec, T. Pajdla: Robust Rotation and Translation Estimation in Multiview Reconstruction. CVPR 2007.
 A. Eriksson, C. Olsson, F. Kahl, T.J. Chin: Rotation Averaging and Strong Duality. CVPR 2018.
 H. Le, T.J. Chin, D. Suter: An Exact Penalty Method for Locally Convergent Maximum Consensus. CVPR 2017.
 Q. Zhang, T.J. Chin and D. Suter: Quasiconvex Plane Sweep for Triangulation with Outliers. ICCV 2017.
 J. Yu, A. Eriksson, T.J. Chin, and D. Suter: An Adversarial Optimization Approach to Efficient Outlier Removal. ICCV 2011.