Proceedings of the Symposium on Global and Environmental Monitoring: Proceedings of the Symposium on Global and Environmental Monitoring

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Persistent identifier:: 856665355

Title:: Proceedings of the Symposium on Global and Environmental Monitoring

Sub title:: techniques and impacts ; September 17 - 21, 1990, Victoria Conference Centre, Victoria, British Columbia, Canada

Year of publication:: 1990

Place of publication:: Victoria, BC

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 856665355

Language:: English

Document type:: Multivolume work

Volume

Persistent identifier:: 856669164

Title:: Proceedings of the Symposium on Global and Environmental Monitoring

Sub title:: techniques and impacts; September 17 - 21, 1990, Victoria Conference Centre, Victoria, British Columbia, Canada

Scope:: XIV, 912 Seiten

Year of publication:: 1990

Place of publication:: Victoria, BC

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 856669164

Illustration:: Illustrationen, Diagramme, Karten

Signature of the source:: ZS 312(28,7,1)

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Editor:: International Society for Photogrammetry and Remote Sensing, Commission of Photographic and Remote Sensing Data

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Volume

Collection:: Earth sciences

Chapter

Title:: [WP-1 ADVANCED COMPUTING FOR INTERPRETATION]

Document type:: Multivolume work

Structure type:: Chapter

Chapter

Title:: COMPARISON OF SOME TEXTURE CLASSIFIERS. Einari Kilpela and Jan Heikkila

Document type:: Multivolume work

Structure type:: Chapter

After this procedure has finished the final classification happens using the resulted dataset and the 1-NN classifier. By the so called Multiediting approach, the number of samples can be further reduced by repea ting the above editing procedure until no editing occurs. In /DevKit80/ both theore tical and experimental evidence is given for proving the most favorable result, that the above procedure converges asympto tically (in the number of iterations) to the Bayes decision rule. After the multiediting algorithm, the data is nicely clustered (because all the misc- lassified samples are rejected). The 1- NN classifier creates piecewise linear decision boundary (being approximation of the Bayes boundary). This boundary is ac tually defined by a small subset of samp les belonging to the outer boarders of the clusters. It is clear that only these sample points are needed for the 1-NN clas sifier. The aim of condensing is to find such representative points. So after multiediting and condensing, a mostly powerful 1-NN classifier can be used. It has the property of approximating the Bayes decision boundary and being very fast to compute. Our k-NN classifier has been implemented by using this technique. 3.2 The Average Learning Subspace Method The subspace methods are reported in /Oja83/. A subspace in the n-dimensional pattern space is spanned by p linearly independent, orthonormal basis vectors a i . The dimension of the subspace is then p. From the point of view of classifica tion, a subspace restricts the possible directions in it, while the lengths remain undetermined. Suppose we have M classes in the classification problem, each being represented by a subspace, with dimensiona lities p^^ . Usually p i is much lower than the original dimension. The simple classi fication rule then states that: if the distance between the pattern vector x and subspace i is smaller than between the pattern vector and subspace j, then classi fy x in class i. The distance from the subspace can be computed as follows: d(x,L) = | x | 2 - Epix 1 ^ ) 2 , where u t are the orthonormal basis vec tors . Since |x| 2 is the same for each class, it can be dropped and the classification rule consists only of inner products. So, if the subspaces dimensions are small, the classifier is very fast. ■me essential question in the subspace method is how to actually construct the class subspaces to obtain optimal perfor mance. The CLAFIC method /Watana69/ forms each subspace by minimizing the mean square error of the distances of a training set. This can be shown to be equivalent of maxi mizing £ (u• T Cu. ), p v j j ’' The eigenvalue decomposition solves this problem and usually the first few eigenvec tors span the subspace. A serious drawback of the CLAFIC method is that each class subspace, although de pending on the statistics of the class, is formed independently from the other classes. So, two classes overlapping each other may be very hard to discriminate. This leads to the ALSM-method which adapts itself better to this situation by learn ing. In the ALSM-method, the autocorrela tion matrices are updated according to misclassifications. This means that, if either a sample vector of class i is misc lassif ied to another class (j), or a sample vector of another class (k) is misclassi- fied to i, the learning phase of the clas sifier updates the autocorrelation matri ces of each class by: R = R + £ a*S m <i ' j) - £ y3*S m (k ' i) ‘ m m-1 m r' m Here a and /3 are small constants, and should be small enough to avoid overshoot ing. In this learning phase, the subspa ces will be iterated sufficiently long so, that the classification of the training set becomes stable. The algorithm can be proven to converge /Oja83/. The constants a and /? were both set to values 0.005 in this project. 4. SUMMARY OF THE RESULTS The test material consists of two 1:15 000 aerial images both digitized in 4500*4500 format, one SPOT scene from rural and one SPOT scene from urban area. Two indepen dent test sites were created. The other was used as a training sample and consisted of approximately 1300 samples for each class. The other was used as an indepen dent test set and consisted of approximate ly 5000 samples for each class. The clas sification tried to separate five classes, urban or residential areas, two types of forest areas, pasture land or parks, and fields. In case of multichannel imagery, the textural descriptors were computed from channel 3 (infrared). The practical classification was performed using a window of 31*31 pixels in the ae rial images and using a window of 13*13 in the SPOT images. Subspaces vs. extracted ad hoc features Some preliminary runs were made to have an idea, if there is some difference in using the traditional feature descriptors of the cooccurrence statistics and the Fou rier power spectrum, compared to the stra tegy of using these descriptors as such. These tests were performed on the basis of the aerial images only. The dimensional reduction achieved by an orthogonal transformation was surprisingly high. The dimension of the final subspace was usually 5-10, although the original where C is the autocorrelation matrix.337

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