A New Subspace Approach for Supervised Hyperspectral Image Classification

A New Subspace Approach for Supervised

Hyperspectral Image Classification



Jun LiJun Li1,21,2,, José M. Bioucas-Dias José M. Bioucas-Dias22 and and Antonio PlazaAntonio Plaza11

11Hyperspectral Computing LaboratoryHyperspectral Computing LaboratoryUniversity of Extremadura, Cáceres, SpainUniversity of Extremadura, Cáceres, Spain

22Instituto de Telecomunicaçoes, Instituto Superior Técnico, TULisbon, PortugalInstituto de Telecomunicaçoes, Instituto Superior Técnico, TULisbon, PortugalContact e-mails: {junli, aplaza}@unex.es, [email protected] e-mails: {junli, aplaza}@unex.es, [email protected]

Talk Outline:Talk Outline:1. Challenges in hyperspectral image classification

2. Subspace projection

2.1. Subspace projection-based framework

2.2. Considered subspace projection techniques: PCA versus HySime

2.3. Integration with different classifiers (LDA, SVM, MLR)

3. Experimental results

3.1. Experiments with AVIRIS Indian Pines hyperspectral data

3.2. Experiments with ROSIS Pavia University hyperspectral

4. Conclusions and future research lines

1. Challenges in hyperspectral image classification









A New Subspace Approach for Hyperspectral Classification

IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011

Concept of hyperspectral imaging using NASA Jet Propulsion Laboratory’s Airborne Visible Infra-Red Imaging Spectrometer

1IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2011), Vancouver, Canada, July 24 – 29, 2011

Challenges in Hyperspectral Image Classification

Panchromatic Panchromatic

Hyperspectral

(100’s of bands)

Hyperspectral

(100’s of bands)

MultispectralMultispectral

(10’s of bands)

MultispectralMultispectral

(10’s of bands)


Ultraspectral

(1000’s of bands)

Ultraspectral

(1000’s of bands)


Challenges in hyperspectral image classification

• Imbalance between dimensionality and training samples, presence of mixed pixels

Challenges in hyperspectral image classification

• The special characteristics of hyperspectral data pose several processing problems:

1. The high-dimensional nature of hyperspectral data introduces important limitations in supervised classifiers, such as the limited availability of training samples or the inherently complex structure of the data

2. There is a need to address the presence of mixed pixels resulting from insufficient spatial resolution and other phenomena in order to properly model the hyperspectral data

3. There is a need to develop computationally efficient algorithms, able to provide a response in a reasonable time and thus address the computational requirements of time-critical remote sensing applications

• In this work, we evaluate the impact of using subspace projection techniques prior to supervised classification of hyperspectral image data while analyzing each of the aforementioned items



Subspace Projection-Based Framework


Subspace projection-based framework.-• Hyperspectral image data generally lives in a lower-dimensional

subspace compared with the input feature dimensionality

• This can be exploited to address ill-posed problems given by limited training samples

• The projection into such subspaces allows us to specifically avoid spectral confusion due to mixed pixels, thus reducing their impact in the subsequent classification process

J. Li, J. M. Bioucas-Dias and A. Plaza, “Spectral-spatial hyperspectral image segmentation using sub-space multinomial logistic regression and Markov random fields,” IEEE Transactions on Geoscience and Remote Sensing, in press, 2011.

Component1

Component2

Considered Subspace Projection Techniques: PCA versus HySime


Principal Component Analysis (PCA).-• High-dimensional data can be transformed effectively according to its

distribution in feature space (e.g. by finding the most important directions or axes, establishing those axes as the references of a new coordinate system which takes into account data distribution)

• Orders the resulting components in decreasing order of variance


Principal Component Analysis (PCA).-• High-dimensional data can be transformed effectively according to its

distribution in feature space (e.g. by finding the most important directions or axes, establishing those axes as the references of a new coordinate system which takes into account data distribution)

• Orders the resulting components in decreasing order of varianceBandPCA 1 BandPCA 2 BandPCA 3 BandPCA 4 BandPCA 5

BandPCA 6 BandPCA 7 BandPCA 8 BandPCA 9 BandPCA 10





Hyperspectral Signal Identification by Minimum Error (HySime).-

• A recently developed method for subspace identification in remotely sensed hyperspectral data, which offers several additional features with regards to principal component analysis and other subspace projection techniques

J. M. Bioucas-Dias and J. M. P Nascimento, “Hyperspectral subspace identification,” IEEE Transactions on Geoscience and Remote Sensing, vol. 46, no. 8, pp. 2435-2445, 2008.

Principal Component Analysis

• Seeks for the projection that best represents the original hyperspectral data in least square sense

• Reduces the original signal into subset of eigenvectors without computing any noise statistics

• The difficulty in getting reliable noise estimates from the resulting eigenvalues is that these eigenvalues still represent mixtures of signal sources and noise

HySime

• HySime finds the subset of eigenvectors and the correspondent eigenvalues by minimizing the mean square error between the original signal and its projection onto the eigenvector subspace

• Uses multiple regressions for the estimation of the noise and signal covariance matrices

• Optimally represents the original signal with minimum error


Supervised Classification Framework Tested in this Work


Test classification accuracy

PCA, HySime

Supervised Classification Framework.-• Includes subspace projection and supervised classification based on

training samples:

Subspace projection

Supervised classifier

TrainingSamples

TestSamples

Randomly selected


Integration of subspace-based framework with different classifiers.-

• Three different supervised classifiers tested in this work:

1. Linear discriminant analysis (LDA): find a linear combination of features which separate two or more classes; the resulting combination may be used as a linear classifier (only linearly separable classes will remain separable after applying LDA)

2. Support vector machine (SVM): constructs a set of hyperplanes in high-dimensional space; a good separation is achieved by the hyperplane that has the largest distance to the nearest training data points of any class

3. Multinomial logistic regression (MLR): models the posterior class distributions in a Bayesian framework, thus supplying (in addition to the boundaries between the classes) a degree of plausibility for such classes

Integration with different classifiers (LDA, SVM, MLR)



2.1. Classic techniques for subspace projection: PCA

versus HySime









2.1. Classic techniques for subspace projection: PCA

versus HySime









AVIRIS Indian Pines data set.-

• Challenging classification scenario due to spectrally similar classes

• Early growth stage of the agricultural features (only around 5% coverage of soil)

• 145x145 pixels, 202 spectral bands, 16 ground-truth classes

• 10366 labeled pixels (random training subsets evenly distributed among classes)

Experimental Results Using Real Hyperspectral Data Sets


False color composition

Ground-truth


• Classification results using 160 training samples (10 training samples per class)

• For the SVM classifier we used the Gaussian RBF kernel after testing other kernels

• The mean accuracies (after 10 Monte Carlo runs) and processing times are reported






SVM (OA=65.36%) Subspace SVM (OA=70.33%)

LDA (OA=50.74%) Subspace LDA (OA=54.90%)

Linear MLR (OA=60.38%)

Subspace MLR (OA=67.53%)

Ground-truth


ROSIS Pavia University data set.-



False color composition Ground-truth Training data

Overall classification accuracies and kappa coefficient (in the parentheses) using different training sets for the ROSIS Pavia University

Conclusions and Future Lines.-

• We have evaluated the impact of subspace projection on supervised classification of remotely sensed hyperspectral image data sets

• Two dimensionality reduction methods have been used: PCA and HySime, although many others are available and could be used: MNF, OSP, VD

• Three different supervised classifiers considered: LDA, SVM, MLR

• Experimental results indicate that different approaches for hyperspectral image classification approaches can benefit from subspace projection, particularly when very limited training samples are available

• Subspace projection can be naturally integrated with multinomial logistic regression (MLR) classifiers, which greatly benefit from dimensionality reduction

• Future work will focus on the evaluation of other subspace projection approaches and hyperspectral data sets

Conclusions and Hints at Plausible Future Research


•IEEE J-STARS Special Issue on Hyperspectral Image and Signal Processing






Jun LiJun Li1,21,2,, José M. Bioucas-Dias José M. Bioucas-Dias22 and and Antonio PlazaAntonio Plaza11

11Hyperspectral Computing LaboratoryHyperspectral Computing LaboratoryUniversity of Extremadura, Cáceres, SpainUniversity of Extremadura, Cáceres, Spain

22Instituto de Telecomunicaçoes, Instituto Superior Técnico, TULisbon, PortugalInstituto de Telecomunicaçoes, Instituto Superior Técnico, TULisbon, PortugalContact e-mails: {junli, aplaza}@unex.es, [email protected] e-mails: {junli, aplaza}@unex.es, [email protected]

A New Subspace Approach for Supervised Hyperspectral Image Classification

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