Segmentation d’images hyper-spectrales - Hyper-spectral images segmentation

Segmentation d’images hyper-spectrales

Hyper-spectral images segmentation

Robin Girard

Corresponding Author Email: 
robin.girard@imag.fr
Page: 
277-288
|
Received: 
19 December 2005
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

We present a new image segmentation algorithm for hyper-spectral images that are supposed to be piecewise constant. The procedure is composed by three steps. The first step (denoising) is inspired by a nonparametric adaptive weights smoothing image restoration procedure based on a growing region type algorithm; the second step uses parameters estimated during the first phase to produce an estimation of the boundaries of the image segmentation. The last step of the algorithm groups the differents areas obtained during the second phase by minimising a penalized empirical squared loss criterion. The segmentation algorithm is then applied to simulated nuclear magnetic resonance data.

Résumé

Nous présentons un algorithme de segmentation d'images hyper-spectrales supposées constantes par régions. Cet algorithme est composé de trois phases. La première est une phase de débruitage inspirée d'une méthode adaptative de lissage pondéré fondée sur une segmentation par croissance de régions, la deuxième se sert des paramètres obtenus lors du débruitage de la première phase et a pour but de produire une estimation des contours des régions connexes issues du débruitage. La dernière étape de l'algorithme consiste à fusionner les régions issues de la deuxième phase en minimisant une version pénalisée de l'erreur quadratique de reconstruction. La méthodologie est illustrée sur des données simulées d'imagerie de résonance magnétique nucléaire.

1. Introduction
2. Généralités Et Notations
3. AWS : Algorithme De Débruitage Et D’estimation Des Poids
4. Segmentation Par Estimation Des Frontières
5. Regroupement Des Zones Par Minimisation De L’erreur Quadratique Empirique Pénalisée
6. Application
7. Conclusion Et Perspectives
A. Choix Des Paramètres De AWS
B. Calcul Et Estimation De E0[M(Γ)]
  References

[1] F. ABRAMOVICH, A. ANTONIADIS, T. SAPATINAS, and B. VIDAKOVIC, Optimal testing in a fixed-effects functional analysis of variance model, International Journal of Wavelets, Multiresolution and Information Processing, 2004.

[2] F. ABRAMOVICH, Y. BENJAMINI, D. DONOHO, and I. JOHNSTONE, Adapting to unknown sparsity by controlling the false discovery rate, Annals of statistics, 34, 2006.

[3] Y. BENJAMINI and Y. HOCHEBERG, Controlling the false discovery rate : a practical and poweful, approach to multiple testing, Journal of Royal Statistical Society B, 57:289-300, 1995.

[4] Y. BENJAMINI and D. YEKUTIELI, The control of the false discovery rate in multiple testing under dependency, The Annals of Statistics, 29(4):1165-1188, 2001.

[5] L. BREIMAN, J. FRIEDMAN, OLSHEN R., and STONE C.J, Classification and regression trees, Belmond, CA: Wadsworth, 1983.

[6] D. CANET, J.C. BOUDEL, and E. CANET SOULAS, La RMN, concepts, méthodes et applications, Dunod, 2002.

[7] D. DONOHO, Cart and best-ortho-basis: A connection, Annals of Statistics, 25: 1870--1911, 1997.

[8] J. FAN, Test of significance based on wavelet thresholding and neyman’s truncation, JASA, 91:674-688, 1996.

[9] L. GUIGUES, Modèles Multi-Échelles pour la Segmentation d’Images, PhD thesis, IGN, 2003.

[10] G. HAGBERG, From magnetic resonance spectroscopy to classification of tumors, a reviewof pattern recognition methods, NMR in Biomedicine, 156: 11: 148, 1998.

[11] I.YU., INGSTER and I. SUSLINA, Nonparametric Goodness-of-Fit Testing under Gaussian Model., volume 169 of Lecture Notes in Statistics, Springer-Verlag, New-York, 2002.

[12] IAN H. JERMYN and H. ISHIKAWA, Globally optimal regions and boundaries as minimum ratio weight cycles, IEEE Transaction on pattern analysis and machine intelligence, 23(10), oct 2001.

[13] M. KOHLER, Nonparametric estimation of piecewise smooth regression functions, Technical report, Stuttgart, 2003.

[14] S. MALLAT, A Wavelet Tour of Signal Processing, Academic Press, 1999.

[15] H. PHILIPPE, N. STRANSKY, J.P. THIERY, F. RADVANYI, and E. BARILLOT, Analysis of array cgh data: from signal ratio to gain and loss of dna regions, Bioinformatics, 20(18): 3413-3422, 2004.

[16] J. POLZEHL and V. SPOKOINY, Adaptive weights smoothing with applications to image restoration, J.R Stat Soc B, 62: 335-354, 2000.

[17] J. POLZEHL and V. SPOKOINY, Vector adaptive weights smoothing with application to mri, J.R Stat Soc B, 63:335-354, 2001.

[18] V. SPOKOINY, Adaptative hypothesis testing using wavelets, Annals of Statistics, 24(6):2477--2498, december 1996.

[19] J.D. STOREY, The positive false discovery rate: A bayesian interpretation and the q-value, Annals of Statistics, 31: 2013-2035, 2003.

[20] J.D. STOREY, J.E. TAYLOR, and SIEGMUND, A direct approach to false discovery rates, Journal of the Royal Statistical Society, Series B, 64: 479-498, 2002.

[21] J.D. STOREY, J.E. TAYLOR, and SIEGMUND, Strong control, conservative point estimation, and simultaneous conservative consistency of false discovery rates: A unified approach, Journal of the Royal Statistical Society, Series B, 66:187-205, 2004.

[22] FABIEN SZABLO DE EDELENYI, Développement d’une nouvelle approche d’analyse des images spectroscopiques RMN: les images nosologiques, PhD thesis, UJF, novembre 2001.

[23] J. TAYLOR, R. TIBSHIRANI, and B. EFRON, The miss rate for the analysis of expression data, Biostatistics, 6(1): 111-117, 2005.

[24] B. WHITCHER, A.J. SCHWARZ, H. BARJAT, S. SMART, R. GRUNDY, and M. F. JAMES, Wavelet-based cluster analysis: Datadriven grouping of voxel time-courses with application to perfusionweighted and pharmacological mri of the rat brain, NeuroImage, 24(2): 281-295, 2005.

[25] C. ZHU, S. and A. YUILLE, Region competition, IEEE Trans. on Pattern Analysis and Machine Intelligence, 18(9), 1996.