The discontinuity issue of total orders on metric spaces and its consequences for mathematical morphology Accepted for publication in Journal of Mathematical Imaging and Vision. URL https, 2014. ,
Image adapted total ordering for mathematical morphology on multivariate images, 2014 IEEE International Conference on Image Processing (ICIP), p.29432947, 2014. ,
DOI : 10.1109/ICIP.2014.7025595
Probability density estimation on the hyperbolic space applied to radar processing. Accepted at GSI 2015. URL https, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01121090
Computing Histogram of Tensor Images Using Orthogonal Series Density Estimation and Riemannian Metrics, 2014 22nd International Conference on Pattern Recognition, p.900905, 2014. ,
DOI : 10.1109/ICPR.2014.165
URL : https://hal.archives-ouvertes.fr/hal-00941147
Histograms of images valued in the manifold of colours endowed with perceptual metrics Accepted at GSI 2015. URL https://hal.archives-ouvertes.fr/hal-01121213/document An extended version of Chevallier et al. (2015b) has been submitted to the journalMathematical Morphology -Theory and Applications". The chapterNon-parametric probability density estimation on spaces of Gaussian laws" is currently being transformed into a journal article, 2015. ,
Barycenters in the Wasserstein Space, SIAM Journal on Mathematical Analysis, vol.43, issue.2, p.904924, 2011. ,
DOI : 10.1137/100805741
URL : https://hal.archives-ouvertes.fr/hal-00637399
Methods of information geometry, nachdr. Edition. No. 191 in Translations of mathematical monographs, 2007. ,
Morphological colour operators in totally ordered lattices based on distances: Application to image filtering, enhancement and analysis, Computer Vision and Image Understanding, vol.107, issue.1-2, p.5673, 2007. ,
DOI : 10.1016/j.cviu.2006.11.008
Geometric algebra colour image representations and derived total orderings for morphological operators ??? Part I: Colour quaternions, Journal of Visual Communication and Image Representation, vol.21, issue.1, p.3348, 2010. ,
DOI : 10.1016/j.jvcir.2009.10.002
URL : https://hal.archives-ouvertes.fr/hal-00835974
Morphological Processing of Univariate Gaussian Distribution-Valued Images Based on Poincar?? Upper-Half Plane Representation, Geometric Theory of Information. Signals and Communication Technology, p.331366, 2014. ,
DOI : 10.1007/978-3-319-05317-2_12
Mathematical morphology: The Hamilton-Jacobi connection, 1993 (4th) International Conference on Computer Vision, p.215219, 1993. ,
DOI : 10.1109/ICCV.1993.378217
Riemannian Medians and Means With Applications to Radar Signal Processing, IEEE Journal of Selected Topics in Signal Processing, vol.7, issue.4, p.595604, 2013. ,
DOI : 10.1109/JSTSP.2013.2261798
Log-Euclidean metrics for fast and simple calculus on diusion tensors, Magnetic Resonance in Medicine, vol.56, issue.2, p.411421, 2006. ,
Kernel Density Estimation on Symmetric Spaces, 2014. ,
DOI : 10.1007/978-3-319-25040-3_83
Super Resolution Spectrum Analysis Regularization: Burg, Capon and Ago-antagonistic Algorithms, 1996. ,
Information Geometry of Covariance Matrix: Cartan-Siegel Homogeneous Bounded Domains, Mostow/Berger Fibration and Fr??chet Median, Matrix Information Geometry, 2013. ,
DOI : 10.1007/978-3-642-30232-9_9
Koszul Information Geometry and Souriau Geometric Temperature/Capacity of Lie Group Thermodynamics, Entropy, vol.16, issue.8, p.45214565, 2014. ,
DOI : 10.3390/e16084521
A Panoramic View of Riemannian Geometry, 2003. ,
DOI : 10.1007/978-3-642-18245-7
Visual determination of suprathreshold color-dierence tolerances using probit analysis, Color Research & Application, vol.16, issue.5, p.297316, 1991. ,
Computing the Karcher mean of symmetric positive denite matrices, Linear Algebra and its Applications, vol.438, issue.4, p.17001710, 2013. ,
Duality vs. adjunction for fuzzy mathematical morphology and general form of fuzzy erosions and dilations. Fuzzy Sets and Systems, p.18581867, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00650338
Morphology for Color Images via Loewner Order for Matrix Fields, Mathematical Morphology and Its Applications to Signal and Image Processing. No. 7883 in Lecture Notes in Computer Science, p.243254, 2013. ,
DOI : 10.1007/978-3-642-38294-9_21
Morphological Operations for Color-Coded Images, Computer Graphics Forum, vol.14, issue.3, 1995. ,
A Color Tree of Shapes with Illustrations on Filtering, Simplication, and Segmentation, Mathematical Morphology and Its Applications to Signal and Image Processing. No. 9082 in Lecture Notes in Computer Science, p.363374, 2015. ,
Approches vectorielles ou marginales pour le traitement d'images multi-composantes, 1998. ,
Total Ordering Based on Space Filling Curves for Multivalued Morphology, Proceedings of the Fourth International Symposium on Mathematical Morphology and Its Applications to Image and Signal Processing. ISMM '98, 1998. ,
The Irregularity Issue of Total Orders on Metric Spaces and Its Consequences for Mathematical Morphology, Journal of Mathematical Imaging and Vision, vol.154, issue.1, 2015. ,
DOI : 10.1007/s10851-015-0607-7
URL : https://hal.archives-ouvertes.fr/hal-01446907
Histograms of Images Valued in the Manifold of Colours Endowed with Perceptual Metrics, 2015. ,
DOI : 10.1007/978-3-319-25040-3_81
URL : https://hal.archives-ouvertes.fr/hal-01121213
Grey-Scale Morphology Based on Fuzzy Logic, Journal of Mathematical Imaging and Vision, vol.16, issue.2, p.155171, 2002. ,
Integrating Isosurface Statistics and Histograms, IEEE Transactions on Visualization and Computer Graphics, vol.19, issue.2, p.263277, 2013. ,
On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions, IEEE Transactions on Computers, vol.25, issue.11, p.11751179, 1976. ,
DOI : 10.1109/TC.1976.1674577
Development and Testing of a Color Space (IPT) with Improved Hue Uniformity, Final Program and Proceedings -IS and T/SID Color Imaging Conference, 1998. ,
Hyperbolic geometry for colour metrics, Optics Express, vol.22, issue.10, p.1236912378, 2014. ,
DOI : 10.1364/OE.22.012369
Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors, Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis. No. 3117 in Lecture Notes in Computer Science, p.8798, 2004. ,
DOI : 10.1007/978-3-540-27816-0_8
Ordering of the RGB Space with a Growing Self-organizing Network. Application to Color Mathematical Morphology, Articial Neural Networks: Biological Inspirations ICANN 2005. No. 3696 in Lecture Notes in Computer Science, p.385390, 2005. ,
DOI : 10.1007/11550822_60
Topology-Preserving Ordering of the RGB Space with an Evolutionary Algorithm, Applications of Evolutionary Computation. No. 9028 in Lecture Notes in Computer Science, p.517528, 2015. ,
DOI : 10.1007/978-3-319-16549-3_42
Ordering on the Probability Simplex of Endmembers for Hyperspectral Morphological Image Processing, Mathematical Morphology and Its Applications to Signal and Image Processing. No. 9082 in Lecture Notes in Computer Science, p.410421, 2015. ,
DOI : 10.1007/978-3-319-18720-4_35
URL : https://hal.archives-ouvertes.fr/hal-01104250
The estimation of the gradient of a density function, with applications in pattern recognition, IEEE Transactions on Information Theory, vol.21, issue.1, p.3240, 1975. ,
DOI : 10.1109/TIT.1975.1055330
A concept of the mass center of a system of material points in the constant curvature spaces, Communications in Mathematical Physics, vol.65, issue.No. 5, p.6384, 1993. ,
DOI : 10.1007/BF02096832
Sur l'estimation d'une densité dans un espace métrique, 1974. ,
Image indexing and retrieval based on color histograms, Multimedia Tools and Applications, vol.43, issue.No. 10, p.133156, 1996. ,
DOI : 10.1007/BF00672252
The volume of a small geodesic ball of a Riemannian manifold., The Michigan Mathematical Journal, vol.20, issue.4, p.329344, 1974. ,
DOI : 10.1307/mmj/1029001150
Heat Kernel and Analysis on Manifolds, 2009. ,
Group-Invariant Frames for Colour Morphology, Mathematical Morphology and Its Applications to Signal and Image Processing. No. 7883 in Lecture Notes in Computer Science, p.267278, 2013. ,
Morphological operators on the unit circle, IEEE Transactions on Image Processing, vol.10, issue.12, p.18421850, 2001. ,
DOI : 10.1109/83.974569
The algebraic basis of mathematical morphology I. Dilations and erosions, Computer Vision, Graphics, and Image Processing, vol.50, issue.245, p.295, 1990. ,
Morphological image operators, 1994. ,
Geometric Analysis on Symmetric Spaces, 1993. ,
DOI : 10.1090/surv/039
Dierential Geometry, Lie Groups, and Symmetric Spaces, 2001. ,
Non-Euclidean Analysis, Non- Euclidean Geometries. No. 581 in Mathematics and Its Applications, p.367384, 2006. ,
DOI : 10.1007/0-387-29555-0_18
Versuch einer erweiterten Anwendung des Fechnerschen Gesetzes im farbensystem, Z. Psychol. Physiol. Sinnesorg, vol.130, 1891. ,
Nonparametric Estimation of a Probability Density on a Riemannian Manifold Using Fourier Expansions, The Annals of Statistics, vol.18, issue.2, 1990. ,
DOI : 10.1214/aos/1176347628
k-Nearest neighbor density estimation on Riemannian Manifolds, 2011. ,
Möbius deconvolution on the hyperbolic plane with application to impedance density estimation, The Annals of Statistics, vol.38, issue.4, p.24652498, 2010. ,
How to specify or identify the most accurate multispectral distance function for mathematical morphology?, 2013 Colour and Visual Computing Symposium (CVCS), p.17, 2013. ,
DOI : 10.1109/CVCS.2013.6626273
URL : https://hal.archives-ouvertes.fr/hal-00877422
Statistics on the Manifold of Multivariate Normal Distributions: Theory and Application to Diffusion Tensor MRI Processing, Journal of Mathematical Imaging and Vision, vol.12, issue.1, p.423444, 2006. ,
DOI : 10.1007/s10851-006-6897-z
Graph-based ordering scheme for color image ltering, International Journal of Image and Graphics, vol.08, issue.03, p.473493, 2008. ,
Multivariate Normal Distributions Parametrized as a Riemannian Symmetric Space, Journal of Multivariate Analysis, vol.74, issue.1, p.3648, 2000. ,
DOI : 10.1006/jmva.1999.1853
The development of the CIE 2000 colour-dierence formula: CIEDE2000, Color Research & Application, vol.26, issue.5, p.340350, 2001. ,
Chromaticity-discrimination ellipses for surface colours, Color Research & Application, vol.97, issue.1, p.2542, 1986. ,
DOI : 10.1002/col.5080110107
Visual Sensitivities to Color Differences in Daylight*, Journal of the Optical Society of America, vol.32, issue.5, p.247, 1942. ,
DOI : 10.1364/JOSA.32.000247
Random sets and integral geometry Wiley series in probability and mathematical statistics, 1974. ,
Adjunctions on the lattice of hierarchies, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00566714
Mémoire sur la théorie des déblais et des remblais, 1781. ,
Geometric measure theory: a beginner's guide, 4th Edition, 2009. ,
Elementary Dierential Topology, 1966. ,
Hyperbolic Voronoi Diagrams Made Easy, 2010 International Conference on Computational Science and Its Applications, p.7480, 2010. ,
DOI : 10.1109/ICCSA.2010.37
A Topological Approach to Hierarchical Segmentation using Mean Shift, 2007 IEEE Conference on Computer Vision and Pattern Recognition, p.18, 2007. ,
DOI : 10.1109/CVPR.2007.383228
Kernel density estimation on Riemannian manifolds, Statistics & Probability Letters, vol.73, issue.3, p.297304, 2005. ,
DOI : 10.1016/j.spl.2005.04.004
Probabilities and Statistics on Riemannian Manifolds : A Geometric approach, 2004. ,
URL : https://hal.archives-ouvertes.fr/inria-00071490
Deconvolution Density Estimation on the Space of Positive Denite Symmetric Matrices, Nonparametric Statistics and Mixture Models. WORLD SCIENTIFIC, p.147168, 2011. ,
A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coecients, International Journal of Computer Vision, vol.40, issue.1, p.4970, 2000. ,
Segmentation of DTI based on tensorial morphological gradient, Medical Imaging 2009: Image Processing, pp.72591-72591, 2009. ,
DOI : 10.1117/12.811754
The CIE 1976 Color-Dierence Formulae, Color Research & Application, vol.2, issue.1, p.711, 1977. ,
Ordering Partial Partitions for Image Segmentation and Filtering: Merging, Creating and Inflating Blocks, Journal of Mathematical Imaging and Vision, vol.30, issue.7, p.202233, 2013. ,
DOI : 10.1007/s10851-013-0455-2
Morphology on Label Images: Flat-Type Operators and Connections, Journal of Mathematical Imaging and Vision, vol.299, issue.10, p.283307, 2005. ,
DOI : 10.1007/s10851-005-4895-1
Space-lling curves. Universitext, 1994. ,
Flat zones ltering, connected operators, and lters by reconstruction. IEEE transactions on image processing: a publication of the, IEEE Signal Processing Society, vol.4, issue.8, p.11531160, 1995. ,
Implementing continuous-scale morphology via curve evolution, Pattern Recognition, vol.26, issue.9, p.13631372, 1993. ,
DOI : 10.1016/0031-3203(93)90142-J
Anamorphoses and function lattices, p.211, 1993. ,
Image analysis and mathematical morphology, 1982. ,
Density Estimation for Statistics and Data Analysis, 1986. ,
DOI : 10.1007/978-1-4899-3324-9
A Riemannian Geometry of the Multivariate Normal Model, Scandinavian Journal of Statistics, vol.11, issue.4, p.211223, 1984. ,
Morphological Image Analysis, 2004. ,
A modified Helmholtz line-element in brightness-colour space, Proceedings of the Physical Society, vol.58, issue.1, p.41, 1946. ,
DOI : 10.1088/0959-5309/58/1/305
Nonlinear Mean Shift over Riemannian Manifolds, International Journal of Computer Vision, vol.22, issue.11, 2009. ,
DOI : 10.1007/s11263-008-0195-8
Nonlinear Mean Shift over Riemannian Manifolds, International Journal of Computer Vision, vol.22, issue.11, 2009. ,
DOI : 10.1007/s11263-008-0195-8
Wasserstein geometry of Gaussian measures, Osaka Journal of Mathematics -OSAKA J MATH, vol.48, 2011. ,
An Introduction to Measure Theory, 2011. ,
DOI : 10.1090/gsm/126
Harmonic Analysis on Symmetric Spaces and Applications II, 1988. ,
DOI : 10.1007/978-1-4612-3820-1
An Algorithm for the Inversion of Finite Toeplitz Matrices, Journal of the Society for Industrial and Applied Mathematics, vol.12, issue.3, p.2946327, 1964. ,
DOI : 10.1137/0112045
Topics in mathematical morphology for multivariate images. phdthesis, 2012. ,
URL : https://hal.archives-ouvertes.fr/pastel-00820581
Supervised Ordering in : Application to Morphological Processing of Hyperspectral Images, IEEE Transactions on Image Processing, vol.20, issue.11, p.33013308, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00833508
Random Projection Depth for Multivariate Mathematical Morphology, IEEE Journal of Selected Topics in Signal Processing, vol.6, issue.7, p.753763, 2012. ,
DOI : 10.1109/JSTSP.2012.2211336
URL : https://hal.archives-ouvertes.fr/hal-00751347
of Grundlehren der mathematischen Wissenschaften, Optimal Transport, vol.338, 2009. ,
Invariant measures on groups and their use in statistics. No. v. 14 in Lecture notes-monograph series, 1990. ,
Abstract, LMS Journal of Computation and Mathematics, vol.43, 2009. ,
DOI : 10.1112/S1461157020090531
URL : https://hal.archives-ouvertes.fr/hal-01153717
Control Theory and Optimization I Homogeneous Spaces and the Riccati Equation in the Calculus of Variations, 2000. ,