Reduction Methods for Multiband Image Analysis F. Flitti 1 , C. - - PowerPoint PPT Presentation

Reduction Methods for Multiband Image Analysis

• F. Flitti1 , C. Collet1 and F.Bonnarel2

1 LSIIT, Strasbourg Univ. 2 Strasbourg Astronomic Observatory 1 http://picabia.u-strasbg.fr/lsiit/ 2 http://cdsweb.u-strasbg.fr/

ACI’s GRID – IDHA & MDA

Plan

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Pattern recognition

* Classification task * Curse of dimensionality * Data reduction

Multi-super-hyperspectral analysis

* goals * limits

Data reduction

* Superspectral images in radio-astronomy context * 1st method : Reduction using local projections * 2nd method : Reduction using spectrum gaussian modeling

Conclusion and Perspectives

Guessing / predicting the unknown nature

• f an observation

* discrete quantity * definition of pattern

Methods

* template matching * statistical classification * neural networks

Recognition

* supervised classification

* unsupervised classification

>> Set of features

Pattern recognition

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

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

Classification

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

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 RN 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.

Hughe phenomenon

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

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

Dimensionality reduction

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

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 * loss of 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)…

Dimensionality reduction

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

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

Dimensionality reduction

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

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.

Dimensionality reduction

* 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.

Dimensionality reduction

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Vector valued images

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003 Multispectral data <10 bands H y p e r s p e c t r a l d a t a > 5 b a n d s MARSIAA Software (Markovian Quadtree or Markov Chain) For classification tasks

Gaussian Model for Superspectral data segmentation Reduction (Clustering, PCA, PPCA, ICA, Projection Pursuit…) before segmentation

Superspectral data 10<bands<50 Superspectral data 10<bands<50

Others imagery modalities : Polarimetric imagery (Stockes Imagery, Mueller Imagery) Magnetic Resonance Imagery Multimodal imagery by using different imaging modalities

J.-N Provost, Ch. Collet, P. Rostaing, P. Pérez and P. Bouthemy “Hierarchical Markovian Segmentation of Multispectral Images for the Reconstruction of Water Depth Maps'', Computer Vision and Image Understanding, to appear, December 2003.

Mueller Imaging

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Segmentation : vein of the leaf are well detected

Mueller matrix describes interaction between light source and raw materials

Paper to appear : J. Zallat, Ch. Collet and Y. Takakura, “Polarization Images Clustering”, Applied Optics, to appear, January 2004

MRI

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Magnetic Resonance Imagery Multimodal imagery by using different imaging modalities

3D MARSIAA Software (Markovian Quadtree or Markov Chain) For classification tasks Markov Chain 3D Markovian Quadtree

MRI

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Vector valued images

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Vector valued images

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

The images to be reduced

48 bands around CO ray

• f the GG

tauri system from the IRAM interferometer

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Reduction using local projections (1st technique)

Multispectral / Superspectral cube Bottom to up clustering algorithm using multiscale similarity measure based on normalized histograms and barycenters Grouping Local projections on each cluster obtained by the grouping : 1st axe of the Principal Component Analysis 1st axe of the fastICA with deflationary

• rthogonalization

PCA /ICA Segmentation Markov modelling on the quadtree

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Multispectral / Superspectral Image Grouping

Difference between normalized histograms & barycenters at each scale S0 S1 S2 Illustration of the bottom to up clustering algorithm: Grouping the closest two clusters at each iteration Summing over all scales and normalizing

similarity measure

Reduction using local projections (1st technique) Grouping

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Reduction using local projections (1st technique) Local projections

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

• f the two projections:

PCA: Seeks data variance maximisation. Projection matrix given by the eigen vectors of the covariance matrix of data. 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).

PCA /ICA

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

The images reduced by the 1st technique with PCA

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

The images reduced by the 1st technique with PCA

Grouping

Hierarchical Markovian Segmentation (MARSIAA)

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Segmentation Results of The images reduced by the 1st technique with PCA

Map on each reduced image

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Segmentation Results of The images reduced by the 1st technique with PCA

Combined maps

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

The images reduced by the 1st technique with ICA

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

The images reduced by the 1st technique with ICA

Hierarchical Markovian Segmentation (MARSIAA)

Grouping

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Segmentation Results of The images reduced by the 1st technique with ICA

Map on each reduced image

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Segmentation Results of The images reduced by the 1st technique with ICA

Combined maps

Reduction using spectrum gaussian modeling

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Superspectral Image (N bands) Spectrum in each pixel Spectrum Gaussian Modeling (a1,a2, … ,aM) The N original bands are reduced to M parameter

• images. In our case N = 48

and M=6. 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.

(2nd technique)

Segmentation

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

The images reconstructed using Gaussian modeling (2nd technique)

The original 48 images (256 x 256) rearranged as 48 vectors of 2562 elements The 48 images reconstructed using gaussian modeling (M=6) rearranged as the originals

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

The images reduced by the 2nd technique, M=6

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

The images reduced by the 2nd technique, M=6

Hierarchical Markovian Segmentation (MARSIAA)

Gaussian Model

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Segmentation Results of The images reduced by the 2nd technique, M=6

Map on each reduced image

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Segmentation Results of The images reduced by the 2nd technique, M=6

Combined maps

collet@lsiit.u-strasbg.fr iAstro Workshop - Nice Observatory 16/17 October 2003

Conclusion & further works

2nd technique, M=6 1st technique with PCA 1st technique with ICA

• 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