Calcul des matrices de rigidité des modèles déformables Bibliographie Numerical differentiation procedures for nonexact data, Numerische Mathematik, vol.22, pp.157-182, 1974. ,
A time series approach to numerical differentiation, Technometrics, vol.16, issue.1, pp.69-75, 1974. ,
Steps Toward the Automatic Interpretation of 3D Images, Proceedings of the NATO Advanced Research Workshop on 3D Imaging in Medicine, pp.60-107, 1990. ,
DOI : 10.1007/978-3-642-84211-5_6
Medical image tracking, 1992. ,
URL : https://hal.archives-ouvertes.fr/inria-00615545
The Theory of Splines and their Applications, 1967. ,
Non-rigid motion models for tracking the left ventricular wall. Lecture notes in computer science: Information processing in medical images, 1991. ,
Analyse non linéaire et ses motivationséconomiquesmotivationséconomiques, 1984. ,
Using dynamic programming for solving variational problems in vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.9, pp.855-867, 1990. ,
DOI : 10.1109/34.57681
Exponential and polynomial methods for applying tension to an interpolating spline curve, Computer Vision, Graphics, and Image Processing, vol.27, pp.1-18, 1984. ,
An introduction to splines for use in computer graphics and geometric modeleling, 1987. ,
Error bounds for spline interpolation, Journal of Math. and Mech, vol.13, pp.827-835, 1964. ,
Les contours actifs: modélisation, comportement et convergence ,
The generation of interelementcompatible stiffness and mass matrices by the use of interpolation formulae, Proc. Conf. Matrix Methods in Struct. Mech., Air Force Inst. of Tech, 1965. ,
Formulae for numerical differentiation, Math. Gaz, vol.25, pp.19-27, 1941. ,
Towards autonomy in active contour models, [1990] Proceedings. 10th International Conference on Pattern Recognition, pp.847-851, 1990. ,
DOI : 10.1109/ICPR.1990.118228
URL : https://hal.archives-ouvertes.fr/inria-00548463
Shape reconstruction from planar cross-sections, Computer Vision, Graphics, and Image Processing, vol.44, pp.1-29, 1988. ,
Distance transformations in arbitrary dimensions, Computer Vision , Graphics, and Image Processing, pp.321-345, 1984. ,
Analyse Fonctionnelle, Théorie et applications, 1983. ,
Tracking points on deformable objects using curvature information, Proceedings of the Second European Conference on Computer Vision 1992, pp.458-466, 1992. ,
DOI : 10.1007/3-540-55426-2_51
URL : https://hal.archives-ouvertes.fr/inria-00074965
A finite element method applied to new active contour models and 3-D reconstruction from cross sections, IEEE Proceedings of the Third International Conference on Computer Vision, pp.587-591, 1990. ,
Finite element methods for active contour models and balloons from 2-D to 3-D, 1991. ,
Using a finite element method for active contour models and 3-D reconstruction from cross sections, Artificial Intelligence and Computer Vision Also published in the Proceedings of the Seventh Israeli Conference on Artificial Intelligence and Computer Vision, pp.237-247, 1990. ,
Finite element methods for active contour models and balloons from 2-D to 3-D, IEEE Proceedings of Computer Vision and Pattern Recognition, pp.592-598, 1992. ,
Segmenting 3-D images with energy minimizing surfaces, Proceedings of the Eight Israeli Conference on Artificial Intelligence and Computer Vision, 1991. ,
Introducing new deformable surfaces to segment 3D images, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.738-739, 1991. ,
DOI : 10.1109/CVPR.1991.139807
Using deformable surface to segment 3-D images and infer differential structures, Proceedings of the Second European Conference on Computer Vision 1992, pp.648-652, 1992. ,
URL : https://hal.archives-ouvertes.fr/inria-00615561
Using deformable surfaces to segment 3-D images and infer differential structures, Computer Vision, Graphics, and Image Processing: Image Understanding, pp.242-263, 1992. ,
URL : https://hal.archives-ouvertes.fr/inria-00615537
A geometric model for active contours in image processing, Numerische Mathematik, vol.36, issue.4 ,
DOI : 10.1007/BF01385685
Truncation error in interpolation and numerical differentiation, Numerische Mathematik, vol.3, pp.279-284, 1961. ,
IntroductionàIntroductionà l'analyse Matricielle etàet`età l'Optimisation, 1985. ,
The finite element methods for elliptic problems. NORTH- HOLLAND, 1987. ,
Scalar-and Planar-valued curve fitting using splines under tension, Communication of the ACM, Numerical Mathematics, vol.17, issue.4, 1974. ,
Etude des modèles de contours actifs et d'autres techniques de traitement d'Images, 1990. ,
On active contour models and balloons. Computer Vision, Graphics, and Image Processing: Image Understanding, pp.211-218, 1991. ,
DOI : 10.1016/1049-9660(91)90028-n
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.8722
Measurement and integration of 3-D structures by tracking edge lines, Proceedings of the First European Conference on Computer Vision Lecture Notes in Computer Science: Computer Vision ? ECCV90, pp.269-280, 1990. ,
Numerical Differentiation and Regularization, SIAM Journal on Numerical Analysis, vol.8, issue.2, pp.254-265, 1971. ,
DOI : 10.1137/0708026
-D Imaging in Medicine, 1989. ,
URL : https://hal.archives-ouvertes.fr/insu-01355727
Smoothing noisy data with spline functions, Numerische Mathematik, vol.4, issue.4 ,
DOI : 10.1007/BF01404567
Euclidean distance mapping Computer Vision, Graphics, and Image Processing [dB62] Carl de Boor. Bicubic spline interpolation, Journal of Mathematical Physics, vol.14, issue.41, pp.227-248212, 1962. ,
Differential Geometry of Curves and Surfaces, 1976. ,
Extraction de composantes connexes basée sur une détection optimale des contours, CESTA, 1987. ,
Using Canny's criteria to derive a recursively implemented optimal edge detector, International Journal of Computer Vision, vol.1, issue.2, pp.167-187, 1987. ,
DOI : 10.1007/BF00123164
Fast algorithms for low level vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989. ,
Tracking line segments, Proceedings of the First European Conference on Computer Vision Lecture Notes in Computer Science: Computer Vision ? ECCV90, pp.259-268, 1990. ,
DOI : 10.1016/0262-8856(90)80002-B
An efficient method for calculating smoothing splines using orthogonal transformations, Numerische Mathematik, vol.45, issue.3, pp.311-319, 1987. ,
DOI : 10.1007/BF01390708
Shape representation and image segmentation using deformable surfaces, IEEE Proceedings of Computer Vision and Pattern Recognition, pp.467-472, 1991. ,
Measurement of nonrigid motion using contour shape descriptors, IEEE Proceedings of Computer Vision and Pattern Recognition, pp.318-324, 1991. ,
Free-form surface modelling using tensor product Bezier patches: A review with new solutions, 1989. ,
On the G1 smooth connection between triangular Bernstein-Bezier patches, 1989. ,
Etude sur la représentation de surfaces complexes: ApplicationàApplication`Applicationà la reconstruction de surfaceséchantillonnéessurfaceséchantillonnées, pp.88-102, 1988. ,
Contour extraction by mixture density description obtained from region clustering, Proceedings of the Second European Conference on Computer Vision 1992, pp.24-32, 1992. ,
DOI : 10.1007/3-540-55426-2_3
Model driven edge detection, DARPA Image Understanding Workshop, 1988. ,
DOI : 10.1007/BF01211451
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.175.2057
Interpolation with interval and point tension controls using cubic weighted ?-Splines, ACM Transactions on Mathematical Software, vol.13, issue.1, pp.68-96, 1987. ,
Weighted bicubic spline interpolation to rapidly varying data ,
Smoothing and matching of 3D-space curves, Proceedings of the Second European Conference on Computer Vision 1992, pp.620-629, 1992. ,
An efficient edge chaining algorithm, Fifth Scandinavian Conference on Image Analysis, 1987. ,
Détection de discontinuités dans un signal (ou une image) par Inf- Convolution spline et validation croisée: Un algorithme rapide non paramétré, 1988. ,
Face recognition from depth and curvature, Proceedings SPIE Conference on Geometric Methods in Computer Vision, 1991. ,
An implementation of a computational theory of visual surface interpolation, Computer Vision, Graphics, and Image Processing, vol.22, pp.39-69, 1983. ,
Features extraction and analysis methods for sequences of ultrasound images, Proceedings of the Second European Conference on Computer Vision 1992, pp.43-57, 1992. ,
URL : https://hal.archives-ouvertes.fr/inria-00615562
The Measurement of Visual Motion, 1984. ,
Recovery of non-rigid motion and structure, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.325-330, 1991. ,
DOI : 10.1109/CVPR.1991.139710
A least-squares smooth fitting for irregularly spaced data: Finiteelement approach using the cubic B-spline basis, Geophysics, vol.51, issue.11, pp.2051-2066, 1986. ,
An error formula for numerical differentiation, Numerische Mathematik, vol.5, pp.439-442, 1963. ,
Snakes: Active contour models, International Journal of Computer Vision, vol.5, issue.6035, pp.321-331, 1987. ,
DOI : 10.1007/BF00133570
Snakes: Active contour models, Proceedings of the First International Conference on Computer Vision, pp.259-268, 1987. ,
DOI : 10.1007/BF00133570
La méthode de validation croisée ,
Approximation et Optimisation, 1972. ,
Complex topology 3D-objects segmentation, Proceedings of SPIE, 1991. ,
Dynamic segmentation: Detecting complex topology 3D-object, Proceedings of International Conference of the IEEE Engineering in Medicine and Biology Society, pp.295-296, 1991. ,
Visual Monitoring of Glaucoma, 1991. ,
Théorie de l'´ elasticité, 1967. ,
Theory of Elasticity, 1986. ,
Dynamic Segmentation: Finding the Edge With Snake Splines, Curves and Surfaces, pp.279-284, 1991. ,
DOI : 10.1016/B978-0-12-438660-0.50044-3
Optimal contour approximation by deformable piecewise cubic splines, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.638-643, 1991. ,
DOI : 10.1109/CVPR.1991.139767
From voxel to curvature, IEEE Proceedings of Computer Vision and Pattern Recognition, pp.644-649, 1991. ,
URL : https://hal.archives-ouvertes.fr/inria-00075203
Using third order derivatives to extract ridge lines in 3-D images, IEEE Proceedings of Computer Vision and Pattern Recognition, 1992. ,
3-D edge detection using recursive filtering ,
URL : https://hal.archives-ouvertes.fr/inria-00075626
Recursive filtering and edge closing: Two primary tools for 3D edge detection, First European Conference on Computer Vision (ECCV), 1990. ,
DOI : 10.1007/BFb0014850
URL : https://hal.archives-ouvertes.fr/inria-00075456
Methods for Solving Incorrectly Posed Problems, 1984. ,
Active contour models: overview, implementation and applications, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings, pp.194-199, 1990. ,
DOI : 10.1109/ICSMC.1990.142091
Constrained deformable superquadrics and nonrigid motion tracking, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.337-343, 1991. ,
DOI : 10.1109/CVPR.1991.139712
Finding corners, Proceedings of Alvey Vision Conference, pp.267-274, 1987. ,
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
A technique for the numerical solution of certain integral equations of the first kind, J. Assoc. Comput. Mach, vol.9, pp.84-97, 1961. ,
Closed-form solutions for physically based shape modelling and recognition A regularized solution to edge detection, IEEE Transactions on Pattern Analysis and [ Technical Report A.I. Memo, vol.833, 1985. ,
Smoothing by spline functions I, Numerische Mathematik, vol.10, pp.177-183, 1967. ,
Smoothing by spline functions II, Numerische Mathematik, vol.16, pp.451-454, 1971. ,
Segmentation dynamique en imagerie cardiaque, Congrés sur la recherche en imagerie médicale, 1990. ,
Local region-based principles and heuristics for active contour modeling, 1992. ,
<title>Deformable markers: mathematical morphology for active contour models control</title>, Image Algebra and Morphological Image Processing II, 1991. ,
DOI : 10.1117/12.49885
IntroductionàIntroductionà l'analyse numérique des ´ equations aux dérivées partielles, 1983. ,
Optimal points for numerical differentiation, Numerische Mathematik, vol.2, pp.214-227, 1960. ,
Equally-weighted formulas for numerical differentiation, Numerische Mathematik, vol.4, pp.381-392, 1963. ,
C 1 splines for interpolation of rapidly varying data, Rocky Mountain Journal of Mathematics, vol.14, issue.1, pp.239-250, 1984. ,
Spline functions and the problem of graduation, Proc. Natl ,
An interpolation curve using a spline in tension, Journal of Mathematical Physics, vol.45, issue.3, pp.312-317, 1966. ,
Fitting surfaces to scattered data, Approximation Theory II, pp.203-268, 1976. ,
Error Bounds for Interpolation and Differentiation by the Use of Spline Functions, Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, vol.2, issue.3, pp.440-447, 1965. ,
DOI : 10.1137/0702034
Surface Reconstruction in Computer Vision, 1991. ,
Discontinuity preserving surface reconstruction, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.229-234, 1989. ,
DOI : 10.1109/CVPR.1989.37854
Surface approximation using weighted splines, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.44-49, 1991. ,
DOI : 10.1109/CVPR.1991.139659
Inferring surface trace and differential structure from 3-D images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, pp.833-854, 1990. ,
Image Analysis Using Multigrid Relaxation Methods, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.2, pp.129-139, 1986. ,
DOI : 10.1109/TPAMI.1986.4767767
Regularization of Inverse Visual Problems Involving Discontinuities, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.4, pp.8413-424, 1986. ,
DOI : 10.1109/TPAMI.1986.4767807
The computation of visible-surface representations, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.10, issue.4, pp.417-438, 1988. ,
DOI : 10.1109/34.3908
On Edge Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.2, pp.147-163, 1986. ,
DOI : 10.1109/TPAMI.1986.4767769
Elastically deformable models, Proceedings of SIGGRAPH '87, pp.205-214, 1987. ,
Constraints on deformable models: recovering 3-D shape and nonrigid motion, AI Journal, vol.36, pp.91-123, 1988. ,
Relationship of several variational methods for the approximate solutions of ill-posed problems, Math. Notes, vol.7, issue.3, pp.161-166, 1970. ,
Smoothing noisy data with spline functions, Numerische Mathematik, vol.24, pp.383-393, 1975. ,
Pratical approximate solutions to linear operator equations when the data are noisy, SIAM J. Numer. Anal, vol.14, issue.4, pp.651-667, 1977. ,
Surface fitting with scattered noisy data on euclidean D-space and on the sphere, Rocky Mountain Journal of Mathematics, vol.14, issue.1, pp.281-299, 1984. ,
Estimation of activation parameters from one kinetic experiment (varytemp method). error analysis and revised computer program, Acta. Chem ,
Linear Algebra, 1971. ,
DOI : 10.1007/978-3-662-39778-7
A fast algorithm for active contours, [1990] Proceedings Third International Conference on Computer Vision, pp.592-595, 1990. ,
DOI : 10.1109/ICCV.1990.139602
Feature extraction from faces using deformable templates, IEEE Proceedings of Computer Vision and Pattern Recognition, 1989. ,
The organization of curve detection: Coarse tangent fields and fine spline coverings, 1988. ,
A Three-Dimensional Edge Operator, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.3, issue.3, pp.3324-331, 1981. ,
DOI : 10.1109/TPAMI.1981.4767105
en pointillé) et de la courbe initiale (en noir), l'attraction de la courbe par les points de contour dont la courbure est extrémale est représentée dans la figure (b) La courbe obtenue permet une ´ evaluation plus précise de la position des points de contour. L'utilisation d'une force d'attraction classique ne permet pas une reconstruction fiable des points de contour (c) ,