M. Carlo and E. , 30 3.2.1 Estimation of an integral, p.31

.. Local-path-sampling, 38 4.1.1 Light sub-paths and eye-sub paths, p.43

P. Tracing and .. , 44 4.2.1 Basic algorithm, p.45

M. Markov-chain and .. Carlo-methods, 57 4.6.1 Metropolis sampling, Metropolis Light Transport, p.59

D. Results, 113 8.5.1 Visual comparisons, p.114

L. Opening, 144 10.3.2 The opening labeling, p.150

J. Arvo and D. Kirk, Particle transport and image synthesis, Proceedings of the 17th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '90, pp.63-66, 1990.

[. Azriel and R. Klette, Digital Geometry: Geometric Methods for Digital Picture Analysis. The Morgan Kaufmann Series in Computer Graphics, 2004.

[. Van-antwerpen, Recursive mis computation for streaming bdpt on the gpu, 2011.

J. M. Airey, J. H. Rohlf, F. P. Brooks, and J. , Towards image realism with interactive update rates in complex virtual building environments, ACM SIGGRAPH Computer Graphics, vol.24, issue.2, pp.41-50, 1990.
DOI : 10.1145/91394.91416

S. Brabec, T. Annen, and H. Peter-seidel, Shadow Mapping for Hemispherical and Omnidirectional Light Sources, Proc. of Computer Graphics International, pp.397-408, 2002.
DOI : 10.1007/978-1-4471-0103-1_25

[. Barák, J. Bittner, and V. Havran, Temporally Coherent Adaptive Sampling for Imperfect Shadow Maps, Computer Graphics Forum, vol.32, issue.7-8, 2013.
DOI : 10.1111/cgf.12154

[. Bertrand and M. Couprie, A New 3D Parallel Thinning Scheme Based on Critical Kernels, Discrete Geometry for Computer Imagery, pp.580-591, 2006.
DOI : 10.1007/11907350_49

URL : https://hal.archives-ouvertes.fr/hal-00622000

[. Bertrand and M. Couprie, On Parallel Thinning Algorithms: Minimal Non-simple Sets, P-simple Points and Critical Kernels, Journal of Mathematical Imaging and Vision, vol.2, issue.2, pp.23-35, 2009.
DOI : 10.1007/s10851-009-0152-3

URL : https://hal.archives-ouvertes.fr/hal-00731784

[. Biri and J. Chaussard, Skeleton based importance sampling for path tracing, proceedings of Eurographics 2012, pp.1-4, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00681570

[. Bertrand and M. Couprie, Powerful Parallel and Symmetric 3D Thinning Schemes Based on Critical Kernels, Journal of Mathematical Imaging and Vision, vol.2, issue.2, pp.134-148, 2014.
DOI : 10.1007/s10851-012-0402-7

URL : https://hal.archives-ouvertes.fr/hal-00828450

[. Bertrand and M. Couprie, Isthmus based parallel and symmetric 3D thinning algorithms, Graphical Models, vol.80, pp.1-15, 2015.
DOI : 10.1016/j.gmod.2015.05.001

URL : https://hal.archives-ouvertes.fr/hal-01217936

G. Bertrand, On critical kernels Comptes Rendus de l'Académie des Sciences, pp.363-367, 2007.

H. Blum, A transformation for extracting new descriptors of shape, Proc. Models for the Perception of Speech and Visual Form, pp.362-380, 1967.

[. Bertrand and G. Malandain, A new characterization of three-dimensional simple points, Pattern Recognition Letters, vol.15, issue.2, pp.169-175, 1994.
DOI : 10.1016/0167-8655(94)90046-9

URL : https://hal.archives-ouvertes.fr/inria-00615050

M. Couprie and G. Bertrand, New Characterizations of Simple Points, Minimal Non-simple Sets and P-Simple Points in 2D, 3D and 4D Discrete Spaces, Discrete Geometry for Computer Imagery, 14th IAPR International Conference. Proceedings, pp.105-116, 2008.
DOI : 10.1007/978-3-540-79126-3_11

URL : https://hal.archives-ouvertes.fr/hal-00622026

M. Couprie and G. Bertrand, New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.31, issue.4, pp.637-648, 2009.
DOI : 10.1109/TPAMI.2008.117

URL : https://hal.archives-ouvertes.fr/hal-00622393

M. Couprie and G. Bertrand, Isthmus-Based Parallel and Asymmetric 3D Thinning Algorithms, Discrete Geometry for Computer Imagery -18th IAPR International Conference, DGCI 2014 Proceedings, pp.51-62, 2014.
DOI : 10.1007/978-3-319-09955-2_5

URL : https://hal.archives-ouvertes.fr/hal-01112000

J. Chaussard and M. Couprie, Surface Thinning in 3D Cubical Complexes, Proceedings of the 13th International Workshop on Combinatorial Image Analysis, IWCIA '09, pp.135-148, 2009.
DOI : 10.1007/978-3-642-10210-3_11

URL : https://hal.archives-ouvertes.fr/hal-00622486

J. Chaussard, M. Couprie, and H. Talbot, A Discrete ??-Medial Axis, Discrete Geometry for Computer Imagery, pp.421-433, 2009.
DOI : 10.1007/BFb0038202

URL : https://hal.archives-ouvertes.fr/hal-00622407

J. Chaussard, M. Couprie, and H. Talbot, Robust skeletonization using the discrete lambda-medial axis, Pattern Recognition Letters, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00622523

J. Chaussard, M. Couprie, and H. Talbot, Robust skeletonization using the discrete lambda-medial axis, Pattern Recognition Letters, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00622523

D. Michel-couprie, R. Coeurjolly, and . Zrour, Discrete bisector function and Euclidean skeleton in 2D and 3D, Image and Vision Computing, vol.25, issue.10, pp.1543-1556, 2007.
DOI : 10.1016/j.imavis.2006.06.020

J. Chaussard, Topological tools for discrete shape analysis, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00587411

J. Chaussard, L. Noël, V. Biri, and M. Couprie, A 3D Curvilinear Skeletonization Algorithm with Application to Path Tracing, Discrete Geometry for Computer Imagery, pp.119-130, 2013.
DOI : 10.1007/978-3-642-37067-0_11

URL : https://hal.archives-ouvertes.fr/hal-00796545

F. Crassin, M. Neyret, S. Sainz, E. Green, and . Eisemann, Interactive Indirect Illumination Using Voxel Cone Tracing, Computer Graphics Forum, vol.28, issue.3, pp.1921-1930, 2011.
DOI : 10.1111/j.1467-8659.2011.02063.x

URL : https://hal.archives-ouvertes.fr/hal-00650173

Y. [. Cohen-or, C. T. Chrysanthou, F. Silva, and . Durand, A survey of visibility for walkthrough applications, IEEE Transactions on Visualization and Computer Graphics, vol.9, issue.3, pp.412-431, 2003.
DOI : 10.1109/TVCG.2003.1207447

[. Coeurjolly, Fast and accurate approximation of digital shape thickness distribution in arbitrary dimension, Computer Vision and Image Understanding, vol.116, issue.12, pp.1159-1167, 2012.
DOI : 10.1016/j.cviu.2012.08.006

URL : https://hal.archives-ouvertes.fr/hal-00758070

M. Couprie, Hierarchic Euclidean Skeletons in Cubical Complexes, Discrete Geometry for Computer Imagery -16th IAPR International Conference Proceedings, pp.141-152, 2011.
DOI : 10.1007/978-3-642-19867-0_12

URL : https://hal.archives-ouvertes.fr/hal-00729055

[. Devroye, Non-uniform random variate generation, 1986.
DOI : 10.1007/978-1-4613-8643-8

[. Dong, T. Grosch, T. R. Kautz, and H. Seidel, Real-time indirect illumination with clustered visibility, VMV, pp.187-196, 2009.

]. E. Dij71 and . Dijkstra, EWD316: A Short Introduction to the Art of Programming, 1971.

C. Dachsbacher, J. K?ivánek, M. Ha?an, A. Arbree, B. Walter et al., Scalable Realistic Rendering with Many-Light Methods, Computer Graphics Forum, vol.4, issue.1, pp.88-104, 2014.
DOI : 10.1111/cgf.12256

[. Dutré, E. P. Lafortune, and Y. D. Willems, Monte carlo light tracing with direct computation of pixel intensities, 3rd International Conference on Computational Graphics and Visualisation Techniques, pp.128-137, 1993.

C. Dachsbacher and M. Stamminger, Reflective shadow maps, Proceedings of the 2005 symposium on Interactive 3D graphics and games , SI3D '05, pp.203-231, 2005.
DOI : 10.1145/1053427.1053460

[. Fradin, D. Meneveaux, and S. Horna, Out of core photonmapping for large buildings, Proceedings of the Sixteenth Eurographics Conference on Rendering Techniques, EGSR '05, pp.65-72, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00337795

I. Georgiev, J. Krivánek, T. Davidovi?, and P. Slusallek, Light transport simulation with vertex connection and merging, ACM Transactions on Graphics, vol.31, issue.6, pp.1-19210, 2012.
DOI : 10.1145/2366145.2366211

[. Georgiev, J. K?ivánek, S. Popov, and P. Slusallek, Importance Caching for Complex Illumination, Computer Graphics Forum, vol.0, issue.7-9, pp.701-710, 2012.
DOI : 10.1111/j.1467-8659.2012.03049.x

[. Georgiev and P. Slusallek, Simple and robust iterative importance sampling of virtual point lights, Proceedings of Eurographics 2010, pp.57-60, 2010.

E. Heitz, Understanding the masking-shadowing function in microfacet-based brdfs, Journal of Computer Graphics Techniques (JCGT), vol.3, issue.2, pp.48-107, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00942452

]. C. Hil69 and . Hilditch, Linear skeletons from square cupboards, Machine Intelligence, 1969.

M. Ha?an, J. K?ivánek, B. Walter, and K. Bala, Virtual spherical lights for many-light rendering of glossy scenes, In ACM Transactions on Graphics, vol.28, p.143, 2009.

[. Hachisuka, S. Ogaki, and H. W. Jensen, Progressive photon mapping, In ACM Transactions on Graphics, vol.27, p.130, 2008.

H. Hey, P. Ha?an, F. Pellacini, and K. Bala, Importance sampling with hemispherical particle footprints Matrix row-column sampling for the many-light problem, Spring Conference on Computer Graphics, 2002.

[. Hachisuka, J. Pantaleoni, and H. W. Jensen, A path space extension for robust light transport simulation, ACM Transactions on Graphics, vol.31, issue.6, p.31191, 2012.
DOI : 10.1145/2366145.2366210

H. Wim, J. B. Hesselink, and . Roerdink, Euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.12, pp.2204-2217, 2008.

M. Hollander, T. Ritschel, E. Eisemann, and T. Boubekeur, ManyLoDs: Parallel Many-View Level-of-Detail Selection for Real-Time Global Illumination, Computer Graphics Forum, pp.1233-1240, 2011.
DOI : 10.1111/j.1467-8659.2011.01982.x

W. Jakob, Mitsuba renderer, 2010.

H. Wann, J. , and N. J. Christensen, Photon maps in bidirectional monte carlo ray tracing of complex objects, Computers & Graphics, vol.19, issue.2, pp.215-224, 1995.

[. Jensen, Importance Driven Path Tracing using the Photon Map, Eurographics Rendering Workshop, pp.326-335, 1995.
DOI : 10.1007/978-3-7091-9430-0_31

[. Jensen, Global Illumination using Photon Maps, Rendering Techniques' 96, pp.21-30, 1996.
DOI : 10.1007/978-3-7091-7484-5_3

[. Jensen, Realistic Image Synthesis Using Photon Mapping, 2001.
DOI : 10.1201/b10685

J. T. Kajiya, The rendering equation, ACM SIGGRAPH Computer Graphics, vol.20, issue.4, pp.143-150, 1986.
DOI : 10.1145/15886.15902

A. Keller, Instant radiosity, Proceedings of the 24th annual conference on Computer graphics and interactive techniques , SIGGRAPH '97, pp.49-56, 1997.
DOI : 10.1145/258734.258769

]. A. Kff-+-15, L. Keller, M. Fascione, I. Fajardo, P. Georgiev et al., The path tracing revolution in the movie industry, ACM SIGGRAPH 2015 Courses, SIGGRAPH '15, pp.1-24, 2015.

A. Keller and W. Heidrich, Interleaved Sampling, Proceedings of the 12th Eurographics Workshop on Rendering Techniques, pp.269-276, 2001.
DOI : 10.1007/978-3-7091-6242-2_25

T. Kollig and A. Keller, Illumination in the Presence of Weak Singularities, MCQMC Methods, 2004.
DOI : 10.1007/3-540-31186-6_15

R. Kopperman, . Paulr, R. Meyer, and . Wilson, A Jordan surface theorem for three-dimensional digital spaces, Discrete & Computational Geometry, vol.86, issue.2, pp.155-161, 1991.
DOI : 10.1007/BF02574681

]. T. Kon97 and . Kong, Topology-preserving deletion of 1's from 2-, 3-and 4-dimensional binary images, Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery, DGCI '97, pp.3-18, 1997.

[. Kelemen and L. Szirmay-kalos, Simple and robust mutation strategy for metropolis light transport algorithm, 2001.

L. Liu, E. W. Chambers, D. Letscher, and T. Ju, A simple and robust thinning algorithm on cell complexes, Computer Graphics Forum (Proceedings of Pacific Graphics 2010), 2010.
DOI : 10.1111/j.1467-8659.2010.01814.x

A. Lieutier, has the same homotopy type than its medial axis, Proceedings of the eighth ACM symposium on Solid modeling and applications , SM '03, pp.65-75, 2003.
DOI : 10.1145/781606.781620

[. Lohou, Contribution à l'analyse topologique des images: étude d'algorithmes de squelettisation pour images 2D et 3D, selon une approche topologie digitale ou topologie discrète, 2001.

P. Eric, Y. D. Lafortune, and . Willems, Bi-directional path tracing, Proceedings of the 3rd international conference on computational graphics and visualization techniques, pp.145-153, 1993.

P. Eric, Y. D. Lafortune, and . Willems, Using the modified phong reflectance model for physically based rendering, 1994.

P. Eric, Y. D. Lafortune, and . Willems, Reducing the number of shadow rays in bidirectional path tracing, Proceedings of The Winter School of Computer Graphics and Visualisation '95, pp.384-392, 1995.

[. Matheron, Eléments pour une Théorie des Milieux Poreux, 1967.

M. Maria, S. Horna, and L. Aveneau, Topological Space Partition for Fast Ray Tracing in Architectural Models, GRAPP 2014 -9th International Joint Conference on Computer Graphics Theory and Applications, pp.225-235, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00938335

[. Malgouyres and A. Lenoir, Topology Preservation Within Digital Surfaces, Graphical Models, vol.62, issue.2, pp.71-84, 2000.
DOI : 10.1006/gmod.1999.0517

URL : https://hal.archives-ouvertes.fr/hal-01318725

D. Meneveaux, E. Maisel, and K. Bouatouch, A new partitioning method for architectural environments, The Journal of Visualization and Computer Animation, vol.9, issue.4, pp.195-213, 1998.
DOI : 10.1002/(SICI)1099-1778(1998100)9:4<195::AID-VIS179>3.0.CO;2-Z

URL : https://hal.archives-ouvertes.fr/hal-00337792

[. Matusik, H. Pfister, M. Brand, and L. Mcmillan, A data-driven reflectance model, ACM Transactions on Graphics, vol.22, issue.3, pp.759-769, 2003.
DOI : 10.1145/882262.882343

A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1092, 1953.

N. Metropolis and S. Ulam, The Monte Carlo Method, Journal of the American Statistical Association, vol.44, issue.247, pp.335-341, 1949.
DOI : 10.1080/01621459.1949.10483310

L. Noël and V. Biri, Skeleton based Vertex Connection Resampling for Bidirectional Path Tracing, 23rd Pacific Conference on Computer Graphics and Applications, Pacific Graphics, 2015.
DOI : 10.1111/cgf.12768

L. Noël, Skeleton based vertex connection resampling for bidirectional path tracing -code, 2015. https://github.com/Celeborn2BeAlive, p.2015

[. Olsson, M. Billeter, and U. Assarsson, Clustered deferred and forward shading, HPG '12: Proceedings of the Conference on High Performance Graphics 2012, 2012.

J. Ou and F. Pellacini, Lightslice: Matrix slice sampling for the manylights problem, ACM Trans. Graph, vol.301798, issue.6, pp.1-179, 2011.

[. Olsson, E. Persson, and M. Billeter, Real-time many-light management and shadows with clustered shading, ACM SIGGRAPH 2015 Courses on, SIGGRAPH '15, pp.1-12, 2015.
DOI : 10.1145/2776880.2792712

O. Olsson, E. Sintorn, V. Kämpe, M. Billeter, and U. Assarsson, Efficient virtual shadow maps for many lights, Proceedings of the 18th meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, pp.87-96, 2014.

[. Palágyi, A Subiteration-Based Surface-Thinning Algorithm with a Period of Three, Pattern Recognition, pp.294-303, 2007.
DOI : 10.1007/978-3-540-74936-3_30

A. Pajot, L. Barthe, M. Paulin, and P. Poulin, Combinatorial Bidirectional Path-Tracing for Efficient Hybrid CPU/GPU Rendering, Computer Graphics Forum, vol.27, issue.5, pp.315-324, 2011.
DOI : 10.1111/j.1467-8659.2011.01863.x

M. Pharr and G. Humphreys, Physically Based Rendering, Second Edition: From Theory To Implementation, 2010.

[. Palágyi and A. Kuba, A 3D 6-subiteration thinning algorithm for extracting medial lines, Pattern Recognition Letters, vol.19, issue.7, pp.613-627, 1998.
DOI : 10.1016/S0167-8655(98)00031-2

[. Peter, G. Pietrek, and F. Informatik, Importance Driven Construction of Photon Maps, Rendering Techniques '98 (Proceedings of the 9th Eurographics Workshop on Rendering, pp.269-280, 1998.
DOI : 10.1007/978-3-7091-6453-2_25

S. Popov, R. Ramamoorthi, F. Durand, and G. Drettakis, Probabilistic Connections for Bidirectional Path Tracing, Computer Graphics Forum, p.12, 2015.
DOI : 10.1111/cgf.12680

URL : https://hal.archives-ouvertes.fr/hal-01164842

[. Raynal and M. Couprie, Isthmus-Based 6-Directional Parallel Thinning Algorithms, Discrete Geometry for Computer Imagery -16th IAPR International Conference, DGCI 2011 Proceedings, pp.175-186, 2011.
DOI : 10.1007/978-3-642-19867-0_15

URL : https://hal.archives-ouvertes.fr/hal-00729053

E. Tobias-ritschel, I. Eisemann, . Ha, D. James, H. Kim et al., Making imperfect shadow maps view-adaptive: High-quality global illumination in large dynamic scenes, Computer Graphics Forum, pp.2258-2269, 2011.

T. Tobias-ritschel, M. H. Grosch, H. Kim, C. Seidel, J. Dachsbacher et al., Imperfect shadow maps for efficient computation of indirect illumination, p.129, 2008.

W. T. Reeves, D. H. Salesin, and R. L. Cook, Rendering antialiased shadows with depth maps, ACM SIGGRAPH Computer Graphics, vol.21, issue.4, pp.283-291, 1987.
DOI : 10.1145/37402.37435

[. Simon, J. Hanika, and C. Dachsbacher, Rich-VPLs for Improving the Versatility of Many-Light Methods, Proceedings of Eurographics), pp.575-584, 2015.
DOI : 10.1111/cgf.12585

]. B. Simp06a, J. C. Segovia, R. Iehl, B. Mitanchey, and . Péroche, Bidirectional instant radiosity, Proceedings of the 17th Eurographics Conference on Rendering Techniques, EGSR '06, pp.389-397, 2006.

]. B. Simp06b, J. C. Segovia, R. Iehl, B. Mitanchey, and . Péroche, Non-interleaved deferred shading of interleaved sample patterns, Proceedings of the 21st ACM SIG- GRAPH/EUROGRAPHICS Symposium on Graphics Hardware, GH '06, pp.53-60, 2006.

J. [. Segovia, B. Iehl, and . Péroche, Metropolis Instant Radiosity, Computer Graphics Forum, vol.26, issue.3, pp.425-434, 2007.
DOI : 10.1111/j.1467-8659.2007.01065.x

URL : https://hal.archives-ouvertes.fr/hal-01501494

A. [. Steinhurst and . Lastra, Global Importance Sampling of Glossy Surfaces Using the Photon Map, 2006 IEEE Symposium on Interactive Ray Tracing, pp.133-138, 2006.
DOI : 10.1109/RT.2006.280224

M. Schwarz and H. Seidel, Fast parallel surface and solid voxelization on GPUs, ACM Transactions on Graphics, vol.29, issue.6, pp.1-17910, 2010.
DOI : 10.1145/1882261.1866201

[. Saha, R. Strand, and G. Borgefors, Digital Topology and Geometry in Medical Imaging: A Survey, IEEE Transactions on Medical Imaging, vol.34, issue.9, 2015.
DOI : 10.1109/TMI.2015.2417112

J. F. Talbot, D. Cline, and P. Egbert, Importance resampling for global illumination, Proceedings of the Sixteenth Eurographics conference on Rendering Techniques, pp.139-146, 2005.

[. Teller, C. Fowler, T. Funkhouser, and P. Hanrahan, Partitioning and ordering large radiosity computations, Proceedings of the 21st annual conference on Computer graphics and interactive techniques , SIGGRAPH '94, pp.443-450, 1994.
DOI : 10.1145/192161.192279

Y. Tokuyoshi, Virtual spherical gaussian lights for real-time glossy indirect illumination, SIGGRAPH Asia 2014 Technical Briefs, SA '14, pp.1-17, 2014.

J. Seth, C. H. Teller, and . Séquin, Visibility preprocessing for interactive walkthroughs, SIGGRAPH Comput. Graph, vol.25, issue.4, pp.61-70, 1991.

E. Veach, Robust Monte Carlo Methods for Light Transport Simulation, 1997.

E. Veach and L. J. Guibas, Optimally combining sampling techniques for Monte Carlo rendering, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques , SIGGRAPH '95, pp.419-428, 1995.
DOI : 10.1145/218380.218498

E. Veach and L. J. Guibas, Metropolis light transport, Proceedings of the 24th annual conference on Computer graphics and interactive techniques , SIGGRAPH '97, pp.65-76, 1997.
DOI : 10.1145/258734.258775

L. Vincent, Fast opening functions and morphological granulometries, Proc. SPIE 2300, Image Algebra and Morphological Image Processing V, pp.253-267, 1994.

J. Vorba, O. Karlík, M. ?ik, T. Ritschel, and J. K?ivánek, On-line learning of parametric mixture models for light transport simulation, ACM Transactions on Graphics, vol.33, issue.4, pp.1-11, 2014.
DOI : 10.1145/2601097.2601203

B. Walter, A. Arbree, K. Bala, and D. P. Greenberg, Multidimensional lightcuts, ACM Transactions on Graphics, vol.25, issue.3, pp.1081-1088, 2006.
DOI : 10.1145/1141911.1141997

[. Walter, S. Fernandez, A. Arbree, K. Bala, M. Donikian et al., Lightcuts, ACM Transactions on Graphics, vol.24, issue.3, pp.1098-1107, 2005.
DOI : 10.1145/1073204.1073318