[. Benmansour and L. D. Cohen, Tubular Structure Segmentation Based on Minimal Path Method and Anisotropic Enhancement, International Journal of Computer Vision, vol.31, issue.2???3, pp.192-210, 2010.
DOI : 10.1023/A:1008009714131
URL : https://hal.archives-ouvertes.fr/hal-00662296

M. Bardi and I. Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, 2008.
DOI : 10.1007/978-0-8176-4755-1

J. Boissonnat, A. Cérézo, and J. Leblond, Shortest paths of bounded curvature in the plane, Journal of Intelligent & Robotic Systems, vol.145, issue.2, pp.5-20, 1994.
DOI : 10.1007/BF01258291

J. Benamou, F. Collino, and J. Mirebeau, Monotone and consistent discretization of the Monge-Amp??re operator, Mathematics of Computation, vol.85, issue.302, pp.2743-2775, 2016.
DOI : 10.1090/mcom/3080

[. Benmansour, . Carlier, F. Peyré, and . Santambrogio, Derivatives with respect to metrics and applications: subgradient marching algorithm, Numerische Mathematik, vol.2, issue.2, pp.357-381, 2010.
DOI : 10.4310/CMS.2006.v4.n1.a10
URL : https://hal.archives-ouvertes.fr/hal-00360794

J. Erik, R. Bekkers, A. Duits, G. R. Mashtakov, and . Sanguinetti, A PDE approach to data-driven sub-Riemannian geodesics in SE (2), SIAM Journal on Imaging Sciences, vol.8, issue.4, pp.2740-2770, 2015.

U. Boscain, R. Duits, F. Rossi, and Y. Sachkov, Curve cuspless reconstruction via sub-Riemannian geometry. ESAIM: Control, Optimisation and Calculus of Variations, pp.748-770, 2014.
DOI : 10.1051/cocv/2013082
URL : https://hal.archives-ouvertes.fr/hal-00763141

[. Bardi and L. Evans, On Hopf's formulas for solutions of Hamilton-Jacobi equations. Nonlinear Analysis. Theory, Methods and Applications, An International Multidisciplinary Journal. Series A: Theory and Methods, vol.8, issue.11, pp.1373-1381, 1984.

J. Bost and K. Künnemann, Hermitian vector bundles and extension groups on arithmetic schemes. I. Geometry of numbers, Advances in Mathematics, vol.223, issue.3, pp.987-1106, 2010.
DOI : 10.1016/j.aim.2009.09.005
URL : https://doi.org/10.1016/j.aim.2009.09.005

J. Frederic-bonnans, E. Ottenwaelter, and H. Zidani, A fast algorithm for the two dimensional HJB equation of stochastic control, ESAIM: Mathematical Modelling and Numerical Analysis, vol.27, issue.4, pp.723-735, 2004.
DOI : 10.1137/0327031

[. Bornemann and C. Rasch, Finite-element Discretization of Static Hamilton-Jacobi Equations based on a Local Variational Principle, Computing and Visualization in Science, vol.40, issue.9, pp.57-69, 2006.
DOI : 10.1515/9781400873173

D. Laurent, R. Cohen, and . Kimmel, Global minimum for active contour models: A minimal path approach, International Journal of Computer Vision, vol.24, issue.1, pp.57-78, 1997.

[. Chen, J. Mirebeau, and L. D. Cohen, Global Minimum for Curvature Penalized Minimal Path Method, Procedings of the British Machine Vision Conference 2015, pp.86-81, 2015.
DOI : 10.5244/C.29.86
URL : https://hal.archives-ouvertes.fr/hal-01250048

D. Chen, J. Mirebeau, and L. D. Cohen, A New Finsler Minimal Path Model with Curvature Penalization for Image Segmentation and Closed Contour Detection, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp.355-363, 2016.
DOI : 10.1109/CVPR.2016.45
URL : https://hal.archives-ouvertes.fr/hal-01415044

[. Chen, J. Mirebeau, D. Laurent, and . Cohen, Finsler Geodesics Evolution Model for Region based Active Contours, Procedings of the British Machine Vision Conference 2016, 2016.
DOI : 10.5244/C.30.22

[. Chen, J. Mirebeau, and L. D. Cohen, Global Minimum for a Finsler Elastica Minimal Path Approach, International Journal of Computer Vision, vol.57, issue.2, pp.458-483, 2017.
DOI : 10.1007/s10915-013-9710-3
URL : https://hal.archives-ouvertes.fr/hal-01403941

J. , C. , and N. Sloane, Low-Dimensional Lattices. VI. Voronoi Reduction of Three-Dimensional Lattices, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, pp.43655-68, 1896.

S. Jennifer, K. Campbell, . Siddiqi, V. Vladimir, . Rymar et al., Flow-based fiber tracking with diffusion tensor and q-ball data: Validation and comparison to principal diffusion direction techniques, NeuroImage, vol.27, issue.4, pp.725-736, 2005.

[. Chan and L. Vese, Active contours without edges, IEEE Transactions on Image Processing, vol.10, issue.2, pp.266-277, 2001.
DOI : 10.1109/83.902291
URL : http://www.math.ucla.edu/~lvese/PAPERS/IEEEIP2001.pdf

[. Duits, . Boscain, Y. Rossi, and . Sachkov, Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2), Journal of Mathematical Imaging and Vision, vol.73, issue.1, pp.384-417, 2013.
DOI : 10.1016/j.spl.2005.02.013
URL : https://hal.archives-ouvertes.fr/hal-00924469

[. Duits, P. Stephan, J. Meesters, . Mirebeau, M. Jorg et al., Optimal Paths for Variants of the 2D and 3D Reeds-Shepp Car with Applications in Image Analysis, 2016.

L. Dubins, On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents, American Journal of Mathematics, vol.79, issue.3, pp.497-516, 1957.
DOI : 10.2307/2372560

L. Euler, Methodus inveniendi Lineas curvas maximi minive proprietate gaudentes

A. Fuster, T. D. Haije, A. Tristán-vega, B. Plantinga, C. Westin et al., Adjugate Diffusion Tensors for Geodesic Tractography in White Matter, Journal of Mathematical Imaging and Vision, vol.25, issue.4, pp.1-14, 2016.
DOI : 10.1016/S1053-8119(03)00236-2
URL : https://link.springer.com/content/pdf/10.1007%2Fs10851-015-0586-8.pdf

[. Féjer, On the infinite sequences arising in the theories of harmonic analysis, of interpolation, and of mechanical quadratures, Bulletin of the American Mathematical Society, vol.39, issue.8, 1933.
DOI : 10.1090/S0002-9904-1933-05677-X

J. Fehrenbach and J. Mirebeau, Sparse Non-negative Stencils for Anisotropic Diffusion, Journal of Mathematical Imaging and Vision, vol.24, issue.10, pp.123-147, 2014.
DOI : 10.1016/j.acha.2007.05.004
URL : https://hal.archives-ouvertes.fr/hal-00776860

S. Jbabdi, . Bellec, . Toro, M. Daunizeau, H. Pélégrini-issac et al., Accurate Anisotropic Fast Marching for Diffusion-Based Geodesic Tractography, International Journal of Biomedical Imaging, vol.2, issue.1-2, pp.2-12, 2008.
DOI : 10.1016/j.biopsych.2005.05.015
URL : https://doi.org/10.1155/2008/320195

R. Kimmel, N. Kiryati, and A. M. Bruckstein, Multivalued distance maps for motion planning on surfaces with moving obstacles, IEEE Transactions on Robotics and Automation, vol.14, issue.3, pp.427-436, 1998.
DOI : 10.1109/70.678452
URL : http://www.cs.technion.ac.il/~freddy/JournalPapers/00678452.pdf

M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, pp.321-331, 1988.
DOI : 10.1007/BF00133570
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.124.5318

W. Liao, K. Rohr, and S. W. Rz, Globally Optimal Curvature- Regularized Fast Marching For Vessel Segmentation. Medical Image Computing and Computer-Assisted Interventation-MICCAI 2013, pp.550-557, 2013.
DOI : 10.1007/978-3-642-40811-3_69

H. Li and A. Yezzi, Vessels as 4-D Curves: Global Minimal 4-D Paths to Extract 3-D Tubular Surfaces and Centerlines, IEEE Transactions on Medical Imaging, vol.26, issue.9, pp.1213-1223, 2007.
DOI : 10.1109/TMI.2007.903696
URL : http://users.ece.gatech.edu/~huali/minpath/minpath.pdf

[. Mirebeau and J. Dreo, Automatic differentiation of nonholonomic fast marching for computing most threatening trajectories under sensors surveillance, Geometrical Science of Information, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01503607

J. Mirebeau, Anisotropic Fast-Marching on Cartesian Grids Using Lattice Basis Reduction, SIAM Journal on Numerical Analysis, vol.52, issue.4, pp.1573-1599, 2014.
DOI : 10.1137/120861667
URL : https://hal.archives-ouvertes.fr/hal-00657608

J. Mirebeau, Efficient fast marching with Finsler metrics, Numerische Mathematik, vol.74, issue.250, pp.515-557, 2014.
DOI : 10.1090/S0025-5718-04-01678-3
URL : https://hal.archives-ouvertes.fr/hal-00736431

J. Mirebeau, Minimal Stencils for Discretizations of Anisotropic PDEs Preserving Causality or the Maximum Principle, SIAM Journal on Numerical Analysis, vol.54, issue.3, pp.1582-1611, 2016.
DOI : 10.1137/16M1064854
URL : https://hal.archives-ouvertes.fr/hal-01086369

J. Mirebeau, Anisotropic fast-marching on cartesian grids using Voronoi's first reduction of quadratic forms, 2017.

R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications, 2006.
DOI : 10.1090/surv/091

[. Melonakos, . Pichon, A. Angenent, and . Tannenbaum, Finsler Active Contours, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.3, pp.412-423, 2008.
DOI : 10.1109/TPAMI.2007.70713
URL : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2796633/pdf

D. Mumford, Elastica and Computer Vision, Algebraic geometry and its applications, pp.491-506, 1994.
DOI : 10.1007/978-1-4612-2628-4_31

Q. Phong, D. Nguyen, and . Stehlé, Low-dimensional lattice basis reduction revisited, ANTS, pp.338-357, 2004.

]. Obe06 and . Oberman, Convergent Difference Schemes for Degenerate Elliptic and Parabolic Equations: Hamilton?Jacobi Equations and Free Boundary Problems, SIAM Journal on Numerical Analysis, vol.44, issue.2, pp.879-895, 2006.

M. Pechaud, G. Keriven, and . Peyré, Extraction of tubular structures over an orientation domain, 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp.336-342, 2009.
DOI : 10.1109/CVPR.2009.5206782
URL : https://hal.archives-ouvertes.fr/hal-00365599

[. Peyré, R. Pechaud, and . Keriven, Geodesic methods in computer vision and graphics. Foundations and Trends R in Computer Graphics and Vision

G. Parker, C. Wheeler-kingshott, and G. Barker, Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging, IEEE Transactions on Medical Imaging, vol.21, issue.5, pp.505-512, 2002.
DOI : 10.1109/TMI.2002.1009386

G. Randers, On an Asymmetrical Metric in the Four-Space of General Relativity, Physical Review, vol.13, issue.2, pp.195-199, 1941.
DOI : 10.1007/BF01390677

[. Reeds and L. Shepp, Optimal paths for a car that goes both forwards and backwards, Pacific Journal of Mathematics, vol.145, issue.2, pp.367-393, 1990.
DOI : 10.2140/pjm.1990.145.367
URL : http://msp.org/pjm/1990/145-2/pjm-v145-n2-p06-s.pdf

E. Rouy and A. Tourin, A Viscosity Solutions Approach to Shape-From-Shading, SIAM Journal on Numerical Analysis, vol.29, issue.3, pp.867-884, 1992.
DOI : 10.1137/0729053

L. Yuri and . Sachkov, Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane ESAIM: Control, Optimisation and Calculus of Variations, pp.293-321, 2011.

A. Schürmann, Computational geometry of positive definite quadratic forms, 2009.
DOI : 10.1090/ulect/048

[. Selling, Ueber die binären und ternären quadratischen Formen, Journal fur die Reine und Angewandte Mathematik, pp.143-229, 1874.

[. Strandmark, J. Ulen, F. Kahl, and L. Grady, Shortest Paths with Curvature and Torsion, 2013 IEEE International Conference on Computer Vision, pp.2024-2031, 2013.
DOI : 10.1109/ICCV.2013.253

J. N. Tsitsiklis, Efficient algorithms for globally optimal trajectories, IEEE Transactions on Automatic Control, vol.40, issue.9, pp.1528-1538, 1995.
DOI : 10.1109/9.412624
URL : http://www.mit.edu/people/jnt/Papers/J058-95-jnt-traj.pdf

. Weber, S. Yohai, . Devir, M. Alexander, . Bronstein et al., Parallel algorithms for approximation of distance maps on parametric surfaces, ACM Transactions on Graphics, vol.27, issue.4, pp.104-120, 2008.
DOI : 10.1145/1409625.1409626

C. Zach, L. Shan, M. Niethammer-takeo-kanade, J. Kittler, J. M. Kleinberg et al., Globally Optimal Finsler Active Contours, DAGM-Symposium, pp.552-561, 2009.
DOI : 10.1109/CVPR.2009.5206608
URL : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4339059/pdf