1. REMOTE SENSING Multispectral Image Classification
Professor Ke-Sheng Cheng
Department of Bioenvironmental Systems Engineering
National Taiwan University

2. Thematic Maps or Images
Multispectral images  Thematic images
Themes (also known as classes)
Soil
Water
Vegetation
etc.
Spectral signatures
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

3. The Classification Process
Number and Types of classes
Extraction of classification features
Classification algorithms (classifiers)
Classification accuracy assessment
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

4. 11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

5. Land-use/Land-cover (LULC) Classes
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

7. Feature Extraction Example features Original multispectral bands
Subset of bands
Derived features
Vegetation indices
Principal components
Textural features
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

8. Feature Space
Because of class variability, the “signature” is actually a statistical distribution of feature vectors.
Successful classification requires separated distributions, i.e. minimal overlap.
Image classification is essentially a work of feature space partition.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

10. Features Selection
There may be many features available to us and we need to select “good” features to achieve high classification accuracies.
Separation index can be used to measure similarity or dissimilarity among classes.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

11. Types of Image Classification Algorithm
Classification processes
Supervised classification
Unsupervised classification
Characteristics of classification features
Parametric classification
Nonparametric classification
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

12. Supervised Classification
Collecting training data for each class.
Each training pixel is associated with a feature vector.
Characterizing the feature pattern for each class from the training data.
Delineating class boundaries using mathematical or statistical methods.
Assigning pixels to corresponding classes.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

13. Supervised Classification in 2-D Feature Space
Satellite image to be classified
Feature 2
Training data collection
Delineating class boundaries
Assigning classes to non-training pixels
Feature 1
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

14. Statistical Classification Algorithms
Let X = (x1, x2,…, xn)T represent an n-dimensional feature vector and 1, 2, …, M be M classes. We now define M decision (or discriminant) functions di(X), i=1, 2,…, M with the property that, if a pixel with feature vector X belongs to class i , then di(X) > dj(X), j=1, 2,…, M, i  j .
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

15. In the feature space, the decision boundary separating classes i and j is given by values of X which satisfies
dij(X) = di(X)  dj(X) = 0
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

16. Minimum Distance Classifier
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

17. The decision boundary is
We can also choose
Thus,
The decision boundary is
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

18. It does not consider the variance of each class.
For minimum distance classifier, each class is characterized by its mean vector in the multidimensional feature space.
It does not consider the variance of each class.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

19. Maximum Likelihood Classifier
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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

20. where fi(X) is the probability density function of feature vector of the class i.
For 1-dimensional feature space and two classes case, it is equivalent to
The ML classifier does not consider the a priori probabilities of individual classes.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

21. Bayes Classifier
Let the probability that a particular pixel with feature vector X comes from class i be denoted
If the classifier decides that the pixel comes from j when it actually comes from i, it incurs a loss, denoted Lij.
However, the feature vector X may belong to any of the M classes under consideration, thus the average loss incurred in assigning X to j is :
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

22. From the conditional probability
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

23. The decision for classification is
Since p(X) is common for all j(X), we can also choose to use
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

24. Therefore, If we choose 11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

25. 11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

26. Thus, the decision criterion for Bayes classifier is
The decision function di(X) is
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

27. Bayes Classifier for Gaussian Distribution
Consider a 1-dimensional feature space (n = 1) and two classes (M = 2) case. The feature vector X has a normal distribution in each class.
For class i, Thus,
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

28. If the two classes are equally likely to occur, i. e
If the two classes are equally likely to occur, i.e ,Then, the decision boundary is Xo.
pdf
pdf of 2
pdf of 1 m1 m2 X Xo
Assigning to class 2
Assigning to class 1
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

29. For an n-dimensional feature space and M-class case,
where Ci is the covariance matrix of feature vector X for class i.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

30. For Gaussian distribution we usually use
Therefore,
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

31. We can also choose
The above decision function is a quadratic function and therefore, the decision boundaries are quadratic curves.
If the feature vector is truly multivariate Gaussian, the Bayes classifier is the optimal classifier.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

32. Decision function of the minimum distance classifier.
If all covariance matrices are equal, Ci = C for i=1,2,…, M, then
If C = I (identity matrix) and all classes are equally likely to occur, then
Decision function of the minimum distance classifier.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

33. 11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

34. Classifier Threshold
It is implicit in the above classification algorithms that pixels at every point in feature space will be classified into one of the available classes, irrespective of how small the actual probabilities of class membership are.
Such situation can be dealt with by adopting thresholds to the decision process.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

35. 11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

36. In practice, thresholds are applied to the discriminant functions and not the probability densities, i.e.,
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

37. 11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

38. Independent of the feature vectors of individual pixels.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

39. A pixel will not be classified if .
The decision
if for all , and
A pixel will not be classified if
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

40. Assessing the Classification Accuracies
The confusion matrix (also known as the error matrix)
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

41. EC: error of commission
EO: error of omission
EC: error of commission
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

42. The Kappa analysis
The expected accuracy is the accuracy expected based on chance, or the expected accuracy if we randomly assign class values to each pixel.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

43. 1  overall accuracy =1  OA = error by our classification = 
1  expected accuracy =1  EA = error by random classification = 
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

44. 11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

45. Feature Reduction (Ch. 10, Remote Sensing Digital Image Analysis, Richards, 1995)
There may be many features (including spectral and textural features) available to users for image classification.
Features that do not aid discrimination, by contributing little to the separability of different classes should be discarded.
Removal of least effective features is referred to as feature selection, this being one form of feature reduction.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

46. The other form of feature reduction is to transform the pixel vector into a new set of co-ordinates in which the features that can be removed are made more evident.
Feature reduction is performed by checking how separable various classes remain when reduced sets of features are used. For such purpose, a measure of separability of classes is required.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

47. Divergence
Divergence is a measure of the separability of a pair of distributions that has its basis in their degree of overlap. It is defined in terms of the likelihood ratio
where and are respectively the probability density of classes and at the position x.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

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Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

51. Since divergence is never negative it follows therefore that In other words, divergence never decreases as the number of features is increased.
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

52. Divergence of a pair of multivariate normal distributions
Suppose that and are normal distributions with means and covariances of mi and i and mj and j respectively. It can be shown that
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

53. 11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

54. Further studies Nonparametric classification using geostatistics
Evaluating uncertainty of classification accuracies by bootstrap resampling
Parametric bootstrap resampling (distribution-based stochastic simulation of training samples)
Nonparametric bootstrap resampling
Gaussian transformation prior to classification
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.

55. Gaussian transformation prior to classification
11/23/2018
Laboratory for Remote Sensing Hydrology and Spatial Modeling, Dept of Bioenvironmental Systems Engineering, National Taiwan Univ.