, On the singularities of convex functions, Manuscripta Mathematica, vol.4, issue.1, pp.421-435, 1992.
DOI : 10.1007/BF02567770
, Surface reconstruction by Voronoi filtering, Discrete and Computational Geometry, vol.22, issue.42, pp.481-504, 1999.
DOI : 10.1007/pl00009475
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.71
, Stability and computation of medial axes-a state-of-the-art report, Mathematical Foundations of Scientific Visualization Computing the volume of the union of spheres, The Visual Computer, Computer Graphics, and Massive Data Exploration, vol.3, issue.6, pp.18-323, 1988.
, Voronoibased variational reconstruction of unoriented point sets, Proceedings of the Eurographics Symposium on Geometry Processing, pp.39-48, 2007.
, Functions of bounded variation and free discontinuity problems Defining point-set surfaces On the structure of singular sets of convex functions, ACM Transactions on Graphics Calculus of Variations and Partial Differential Equations, vol.56, issue.2 1, pp.57-264, 1994.
, Almost everywhere existence of second differentials of convex functions and convex surfaces connected with it, Leningrad State Univ, Annals [Uchenye Zapiski] Math. Ser, vol.6, pp.3-35, 1939.
, Cohen-Or, 4-points congruent sets for robust pairwise surface registration, ACM Transactions on Graphics, vol.27, issue.3, p.70, 2008.
DOI : 10.1145/1399504.1360684
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.4881
, An optimal algorithm for approximate nearest neighbor searching fixed dimensions Computation of surface geometry and segmentation using covariance techniques, Sets with positive reach, Archiv der Mathematik, pp.891-923, 1982.
, Quantitative concentration inequalities for empirical measures on non-compact spaces, Probability Theory and Related Fields, pp.541-593, 2007.
DOI : 10.1007/s00440-006-0004-7
URL : http://arxiv.org/abs/math/0503123
, Hölder regularity of the normal distance with an application to a PDE model for growing sandpiles, Transactions of the American Mathematical Society, vol.359, issue.06, pp.2741-2769, 2007.
DOI : 10.1090/S0002-9947-07-04259-6
, Molecular shape analysis based upon the morse-smale complex and the connolly function, Proceedings of the nineteenth conference on Computational geometry , SCG '03, pp.351-360, 2003.
DOI : 10.1145/777792.777845
, Normal cone approximation and offset shape isotopy, Computational Geometry, vol.42, issue.6-7, pp.47-80, 2008.
DOI : 10.1016/j.comgeo.2008.12.002
URL : https://hal.archives-ouvertes.fr/inria-00124825
, Stability of Curvature Measures, Computer Graphics Forum, vol.26, issue.2, pp.1485-1496, 2009.
DOI : 10.1111/j.1467-8659.2009.01525.x
URL : https://hal.archives-ouvertes.fr/inria-00344903
, Stability of boundary measures, Preprint, vol.54, issue.104, p.111, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00154798
, Analysis of scalar fields over point cloud data, Proceedings of the ACM/SIAM Symposium on Discrete Algorithms, pp.1021-1030, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00294591
, The ?????-medial axis???, Graphical Models, vol.67, issue.4, pp.304-331, 2005.
DOI : 10.1016/j.gmod.2005.01.002
, Mean shift: a robust approach toward feature space analysis Towards persistence-based reconstruction in Euclidean spaces Measurement of protein surface shape by solid angles, Con86] ML Connolly [CP05] F. Cazals and M. Pouget, Estimating differential quantities using polynomial fitting of osculating jets, pp.603-619, 1986.
, Regularity properties of the distance functions to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometry, ESAIM: Control, Optimisation and Calculus of Variations, p.28, 2009.
, Robust feature detection and local classification for surfaces based on moment analysis, IEEE Transactions on Visualization and Computer Graphics, vol.10, issue.5, pp.1000-9999, 2004.
DOI : 10.1109/TVCG.2004.34
, Stability of Persistence Diagrams, Discrete & Computational Geometry, vol.37, issue.1, pp.103-120, 2007.
DOI : 10.1007/s00454-006-1276-5
, Restricted Delaunay triangulations and normal cycle Shape segmentation and matching with flow discretization, ACM Symposium on Computational Geometry, pp.312-321, 2003.
, Normal and feature estimations from noisy point clouds, Report, vol.78, pp.91-121, 1992.
DOI : 10.1007/11944836_5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.8964
, Persistent homology -? a survey, Surveys on discrete and computational geometry, Computational Geometry, vol.13, issue.52, pp.415-440, 1946.
, Robust moving least-squares fitting with sharp features, ACM Transactions on Graphics, vol.24, issue.3, pp.544-552, 2005.
DOI : 10.1145/1073204.1073227
, Curvature measures, Transactions of the, pp.418-491, 1959.
, Tubular neighborhoods in Euclidean spaces, Duke Math, Critical point theory for distance functions, Proc. of Symposia in Pure Mathematics, pp.64-1025, 1969.
, Curvature-driven modeling and rendering of point-based surfaces, Braz. Symp. Comp. Graph. Imag. Proc, pp.27-36, 2006.
, Surface reconstruction from unorganized points, Computer Graphics, vol.26, issue.2, pp.71-78, 1992.
, Does polynomial parallel volume imply convexity?, Last, and W. Weil, A local Steiner?type formula for general closed sets and applications, pp.469-479, 2004.
DOI : 10.1007/s00208-003-0497-7
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.688.192
, Combinatorial manifold mesh reconstruction and optimization from unorganized points with arbitrary topology, Computer-Aided Design, vol.34, issue.2, pp.149-165, 2002.
DOI : 10.1016/S0010-4485(01)00079-3
, Mean Curvature and Asymptotic Volume of Small Balls, The American Mathematical Monthly, vol.110, issue.10, pp.947-950, 2003.
DOI : 10.2307/3647968
, Spline-based feature curves from point-sampled geometry, The Visual Computer, pp.449-462, 2008.
, The Lipschitz continuity of the distance function to the cut locus, Transactions of the, pp.21-40, 2001.
, Über den kleinsten Kreis, der eine ebene Figur einschließt Straßer, Patch-graph reconstruction for piecewise smooth surfaces, Proceedings Vision, Modeling and Visualization Convexity and the unique footpoint property in Riemannian geometry, Archiv der Mathematik, pp.310-313, 1910.
, Data-dependent mls for faithful surface approximation Any open bounded subset of R n has the same homotopy type as its medial axis The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations, Proceedings of the Eurographics Symposium on Geometry ProcessingLie04] A. Lieutier, pp.59-67, 2004.
, Anisotropic smoothing of point sets, Laboratoire des Sciences de l'Information et des Systemes, pp.680-692, 1995.
DOI : 10.1016/j.cagd.2005.06.010
, Robust Voronoi-based Curvature and Feature Estimation Geometric Measure Theory: A Beginner's Guide, Proc. SIAM/ACM Joint Conference on Geometric and Physical Modeling Magid, O. Soldea, and E. Rivlin, A comparison of Gaussian and mean curvature estimation methods on triangular meshes of range image data, Computer Vision and Visual Understanding, pp.1-12, 1988.
, Finding the homology of submanifolds with confidence from random samples, Discrete and Computational Geometry, vol.4, p.11, 2006.
, Semiconcave functions in Alexandrov's geometry, Surveys in differential geometry Gross, Multi-scale feature extraction on point-sampled surfaces, Computer Graphics Forum, vol.22, pp.137-201, 2003.
, Discovering structural regularity in 3d geometry, ACM Transactions on Graphics, vol.27, issue.3, p.70, 2008.
, Integral invariants for robust geometry processing, Computer Aided Geometric Design, vol.26, issue.1, pp.37-60, 2009.
DOI : 10.1016/j.cagd.2008.01.002
, A unified approach to the change of resolution: space and gray-level, Riv01] A. Rivière, Dimension de Hausdorff de la Nervure Image Processing, Analysis, and Machine Vision, pp.739-742, 1963.
DOI : 10.1109/34.192468
, A sampling framework for accurate curvature estimation in discrete surfaces Robust estimation of adaptive tensors of curvature by tensor voting, IEEE Transactions on Visualization and Computer Graphics IEEE Trans. Pattern Analysis and Machine Intelligence, vol.11, issue.45, pp.573-583, 2003.
, On the volume of tubes, American Journal of Mathematics, vol.61, issue.2, pp.461-472, 1939.
, Direct computing of surface curvatures for point-set surfaces On the cut locus in Alexandrov spaces and applications to convex surfaces, Proceedings of the IEEE/Eurographics Symposium on Point-based Graphics, pp.71-217, 2004.