Presentation - MIV

ACI’s GRID – IDHA & MDA 

Reduction Methods for Multiband 

Image Analysis 

F. Flitti 1 , C. Collet 1 and F.Bonnarel 2 

1 

LSIIT, Strasbourg Univ. 

2 

Strasbourg Astronomic Observatory 

1 

http://picabia.u-strasbg.fr/lsiit/ 

2 

http://cdsweb.u-strasbg.fr/

collet@lsiit.u-strasbg.fr 

iAstro Workshop - Nice Observatory 

16/17 October 2003 

Plan 

Pattern recognition 

* Classification task 

* Curse of dimensionality 

* Data reduction 

Multi-super-hyperspectral analysis 

* goals 

* limits 

Data reduction 

* Superspectral images in radio-astronomy context 

* 1 st method : Reduction using local projections 

* 2 nd method : Reduction using spectrum gaussian modeling 

Conclusion and Perspectives



16/17 October 2003 

Pattern recognition 

Guessing / predicting the unknown nature 

of an observation 

* discrete quantity 

* definition of pattern 

Methods 

* template matching 

* statistical classification 

* neural networks 

Recognition 

* supervised classification 

* unsupervised classification 

>> Set of features



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Classification 

Space spanned by feature vectors 

* is subdivided using decision boundaries 

* which are established by statistical decision theory 

* Bayes decision theory : average risk is minimized 

Performances of a classifier 

* sample size 

* nb of features 

* classifier complexity (criterion function) 

Classification of high dimensional vector 

* curse of dimensionality 

* main factor affecting the classification task



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Hughe phenomenon 

Inherent sparsity of high dimensional spaces 

* in the absence of simplifying assumptions, the amount of data needed 

to get reasonably low variance estimators is really high 

* N-band observations >> N times more data but in R N space 

Dimensionality reduction 

* appropriate dimensionality of the reduced feature space 

* Important structure in the data actually lies in a much smaller 

dimensional space, and will therefore try to reduce the 

dimensionality before attempting the classification. 

This approach can be successful if the dimensionality reduction/feature 

extraction method loses as little relevant information as possible in the 

transformation from high-dimensional space to the low-dimensional one.



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PCA (Karhunen-Loève expansion) and so on… 

* rotates the original feature space before projecting the feature 

vectors onto a limited number of axe 

* Energy based criterion (variance) 

* PCA seeks to minimize the mean squared reconstruction error 

* Maximization of the projection variance 

* Probabilistic PCA (PPCA, 1999) : 

gaussian a priori



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ICA principles 

* Model of source mixture (« cocktail party problem ») 

* linear transform making the data components independent 

* Mutual information measured by Kullback-Leibler distance 

* Weak mutual information between sources : Neguentropy 

(non gaussianity criterion) 

* pre-processing : centered data, spherical noise 

* loss of source order 

*lossof source power 

ICA’s methods 

* Cumulant-based approach (Comon) 

* Jade (4th order cumulant + joint diagonalization), (Carodoso, Souloumiac) 

* Infomax : Neural Network (Bell, Sejnowski) ; 

* FastICA (Oja & Hyvärinen), 

* SOBI : cross-correlation + joint diagonalization (Belouchrani)…



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Multidimensional scaling 

* multivariate data analysis techniques : any method searching 

for a low dimensional representation of objects given 

their high-dimensional representation 

Projection pursuit 

* Battacharya distance between 2 distributions 

* Subspaces max this distance 

Kohonen’s self organizing map



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Limits 

A reduction in the number of features may lead to a loss in the 

discrimination power and thereby lower the accuracy of the resulting 

recognition system. 


* feature selection : selects best subset of the input feature set 

* feature extraction : creates new features based on 

transformation or combination of the original feature 

The main issue in dimensionality reduction is the choice of a criterion 

function. 

A commonly used criterion is the classification error of a feature subset.



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Vector valued images 

Multispectral data 



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Mueller Imaging 

Mueller matrix describes interaction between 

light source and raw materials 

Segmentation : vein of the leaf are well detected 

Paper to appear : J. Zallat, Ch. Collet and Y. Takakura, “Polarization Images Clustering”, 

Applied Optics, to appear, January 2004



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MRI 

3D MARSIAA Software 

(Markovian Quadtree or Markov Chain) 

For classification tasks 

Markov Chain 

3D Markovian 

Quadtree 

Magnetic Resonance Imagery 

Multimodal imagery by using different imaging modalities



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MRI



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Vector valued images



16/17 October 2003 

Vector valued images

The images to be reduced 



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48 bands 

around CO ray 

of the GG 

tauri system 

from the 

IRAM 

interferometer



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Reduction using local projections 

(1 st technique) 

Multispectral / 

Superspectral 

cube 

Grouping 

Bottom to up clustering algorithm using 

multiscale similarity measure based on 

normalized histograms and barycenters 

Local projections on each cluster obtained by 

the grouping : 

PCA /ICA 

1 st axe of the Principal Component Analysis 

1 st axe of the fastICA with deflationary 

orthogonalization 

Segmentation 

Markov modelling on the quadtree



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Grouping 

Multispectral / 

Superspectral 

Image 

Grouping 

S 2 

S 1 

S 0 

Difference between normalized histograms & 

barycenters at each scale 

Summing over all scales and normalizing 

similarity measure 

Illustration of the 

bottom to up 

clustering algorithm: 

Grouping the closest 

two clusters at each 

iteration



16/17 October 2003 



Local projections 

On each cluster established by the grouping step, we perform one 

of the two projections: 

PCA: 

Seeks data variance maximisation. Projection matrix given by the 

eigen vectors of the covariance matrix of data. 

PCA /ICA 

ICA: 

We use the fastICA algorithm with deflationary orthogonalization 

which seeks maximisation of the nongaussianity 

Finally, one keeps only the first image corresponding to the higher 

eigenvalue (PCA) or to the higher nongaussianity criterion (ICA).



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The images reduced by the 

1 st technique with PCA



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1 st technique with PCA 

Grouping 

Hierarchical Markovian 

Segmentation (MARSIAA)



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Segmentation Results of The images 

reduced by the 1 st technique with PCA 

Map on each reduced image



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reduced by the 1 st technique with PCA 

Combined maps



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1 st technique with ICA



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1 st technique with ICA 

Grouping 





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reduced by the 1 st technique with ICA 




16/17 October 2003 


reduced by the 1 st technique with ICA 

Combined maps



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Reduction using spectrum 

gaussian modeling 

(2 nd technique) 

Superspectral 

Image (N bands) 

Spectrum in 

each pixel 

Spectrum Gaussian 

Modeling 

(a 1 ,a 2 , … ,a M ) 

The N original bands are 

reduced to M parameter 

images. In our case N = 48 

and M=6. 

Segmentation 

We choose the decomposition 

base as a set of M uniformly 

distributed gaussians on the λ 

interval. Then only 

M parameters are used to 

represent the spectrum on 

each pixel.



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The images reconstructed using 

Gaussian modeling (2 nd technique) 

The original 48 images (256 x 256) 

rearranged as 48 vectors of 256 2 

elements 

The 48 images reconstructed using 

gaussian modeling (M=6) rearranged 

as the originals



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2 nd technique, M=6



16/17 October 2003 


2 nd technique, M=6 

Gaussian 

Model 





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reduced by the 2 nd technique, M=6 




16/17 October 2003 


reduced by the 2 nd technique, M=6 

Combined maps



16/17 October 2003 

Conclusion & further works 

1 st technique with ICA 

1 st technique with PCA 

2 nd technique, M=6 

 

 

 

 

Rotation of the disk detected especially with 

Gaussian modeling 

Unsupervised algorithms 

The central zone seems interesting and need more 

investigations 

More investigations on the segmentation maps on 

each reduced image

Presentation - MIV

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