1. Image Classification: Supervised Methods
Lecture 8
Prepared by R. Lathrop 11//99
Updated 3/06
Readings:
ERDAS Field Guide 5th Ed. Ch 6:

2. Where in the World?

3. Learning objectives Remote sensing science concepts Math Concepts
Basic concept of supervised classification
Major classification algorithms
Hard vs Fuzzy Classification.
Math Concepts
Skills
--Training set selection: Digital polygon vs. seed pixel-region growing
--Training aids: plot of training data, statistical measure of separability;
--Edit/evaluate signatures
-- Applying Classification algorithms

4. Supervised vs. Unsupervised Approaches
Supervised - image analyst "supervises" the selection of spectral classes that represent patterns or land cover features that the analyst can recognize Prior Decision
Unsupervised - statistical "clustering" algorithms used to select spectral classes inherent to the data, more computer-automated Posterior Decision

5. Supervised vs. Unsupervised
Run clustering algorithm
Select Training fields
Edit/evaluate signatures
Identify classes
Edit/evaluate signatures
Classify image
Evaluate classification
Evaluate classification

6. Supervised vs. Unsupervised
Supervised Prior Decision: from Information classes in the Image to Spectral Classes in Feature Space
Red
NIR
Unsupervised Posterior Decision: from Spectral Classes in Feature Space to Information Classes in the Image

7. Training
Training: the process of defining criteria by which spectral patterns are recognized
Spectral signature: result of training that defines a training sample or cluster parametric - based on statistical parameters that assume a normal distribution (e.g., mean, covariance matrix) nonparametric - not based on statistics but on discrete objects (polygons) in feature space

8. Supervised Training Set Selection
Objective - selecting a homogenous (unimodal) area for each apparent spectral class
Digitize polygons - high degree of user control; often results in overestimate of spectral class variability
Seed pixel - region growing technique to reduce with-in class variability; works by analyst setting threshold of acceptable variance, total # of pixels, adjacency criteria (horiz/vert, diagonal)

9. ERDAS Area of Interest (AOI) tools
Seed pixel or region growing dialog

10. Region Growing: good for linear features
Spectral Distance = 7 Spectral Distance = 10

11. Region Growing: good for spectrally heterogeneous features
Spectral Distance = 5 Spectral Distance = 10

12. Supervised Training Set Selection
Whether using the digitized polygon or seed pixel technique, the analyst should select multiple training sites to identify the many possible spectral classes in each information class of interest

13. Guided Clustering: hybrid supervised/unsupervised approach
Polygonal areas of known land cover type are delineated as training sites
ISODATA unsupervised clustering performed on these training sites
Clusters evaluated and then combined into a single training set of spectral signatures

14. Training Stage Training set ---> training vector
Training vector for each spectral class- represents a sample in n-dimensional measurement space where n = # of bands
for a given spectral class j
Xj = [ X1 ] X1 = mean DN band 1
[ X2] X2 = mean DN band 2

15. Classification Training Aids
Goal: evaluate spectral class separability
1) Graphical plots of training data - histograms coincident spectral plots scatter plots
2) Statistical measures of separability - divergence Mahalanobis distance
3) Training Area Classification
4) Quick Alarm Classification paralellipiped

16. Parametric vs. Nonparametric Distance Approaches
Parametric - based on statistical parameters assuming normal distribution of the clusters e.g., mean, std dev., covariance
Nonparametric - not based on "normal" statistics, but on discrete objects and simple spectral distance in feature space

17. Parametric Assumption: each spectral class exhibits a unimodal normal distribution
255
Digital Number
# of pixels
Bimodal histogram: Mix of Class 1 & 2
Class 1
Class 2

18. Training Aids histogram (check for normality)
Graphical portrayals of training data
histogram (check for normality)
“good”
“bad”

19. Training Aids Graphical portrayals of training data
coincident spectral mean plots

20. Training Aids
Scatter plots: each training set sample constitutes an ellipse in feature space
Provides 3 pieces of information - location of ellipse: mean vector - shape of ellipse: covariance - orientation of ellipse: slope & sign of covariance
Need training vector and covariance matrix

21. Mix: grass/trees
Broadleaf
Examine ellipses for gaps and overlaps. Overlapping ellipses ok within information classes; want to limit between info classes
Conifer

22. Training Aids
Are some training sets redundant or overlap too greatly?
Statistical Measures of Separability: expressions of statistical distance that are sensitive to both mean and variance - divergence Mahalanobis distance

23. Training Aids
Training/Test Area classification: look for misclassification between information classes; training areas can be biased, better to use independent test areas
Quick alarm classification: on-screen evaluation of all pixels that fall within the training decision region (e.g. parallelipiped)

24. Classification Decision Process
Decision Rule: mathematical algorithm that, using data contained in the signature, performs the actual sorting of pixels into discrete classes
Parametric vs. nonparametric rules

25. Parallelepiped or box classifier
Decision region defined by the rectangular area defined by the highest and lowest DN’s in each band; specify by range (min/max) or std dev.
Pro: Takes variance into account but lacks sensitivity to covariance (Con)
Pro: Computationally efficient, useful as first pass
Pro: Nonparametric
Con: Decision regions may overlap; some pixels may remain unclassified

26. Parallelepiped or Box Classifier
Upper and lower limit of each box set by either range (min/max) or # of standard devs.
Note overlap in Red but not NIR band

27. Parallelepipeds have “corners”
Parallelepiped boundary
NIR
reflectance .
Signature ellipse
unir
Candidate pixel
ured
Red reflectance
Adapted from ERDAS Field Guide

28. Parallelepiped or Box Classifier: problems
Red reflectance
NIR
reflectance
Veg 1
Unclassified pixels ??
Veg3
Soil 3
Misclassified pixel
Veg 2
Overlap region
Soil 2
Soil 1
Water 2
Water 1
Adapted from Lillesand & Kiefer, 1994

29. Minimum distance to means
Compute mean of each desired class and then classify unknown pixels into class with closest mean using simple euclidean distance
Con: insensitive to variance & covariance
Pro: computationally efficient
Pro: all pixels classified, can use thresholding to eliminate pixels far from means

30. Minimum Distance to Means Classifier
Red reflectance
NIR
reflectance
Veg 1
Veg3
Soil 3
Veg 2
Soil 2
Soil 1
Water 2
Water 1
Adapted from Lillesand & Kiefer, 1994

31. Minimum Distance to Means Classifier: Euclidian Spectral DistanceY
92, 153
Distance = 111.2
Yd =
180, 85
Xd = X

32. Feature Space Classification
Image analyst draws in decision regions directly on the feature space image using AOI tools - often useful for a first-pass broad classification
Pixels that fall within a user-defined feature space class is assigned to that class
Pro: Good for classes with a non-normal distribution
Con: Potential problem with overlap and unclassified pixels

33. Feature Space Classifier
Analyst draws decision regions in feature space

34. Statistically-based classifiers
Defines a probability density (statistical) surface
Each pixel is evaluated for its statistical probability of belonging in each category, assigned to class with maximum probability
The probability density function for each spectral class can be completely described by the mean vector and covariance matrix

35. Parametric Assumption: each spectral class exhibits a unimodal normal distribution
255
Digital Number
# of pixels
Bimodal histogram: Mix of Class 1 & 2
Class 1
Class 2

36. 2d vs. 1d views of class overlapwj wi
Band 2
2d vs. 1d views of class overlap
Band 1
255
Digital Number
# of pixels
Band 1

37. Probabilities used in likelihood ratiowj
255
Digital Number
# of pixels wi }
p (x | wj) {
p (x | wi)

38. Spectral classes as probability surfaces
Ellipses defined by class mean and covariance; creates likelihood contours around each spectral class;

39. Sensitive to large covariance values
Some classes may have large variance and greatly overlap other spectral classes

40. Mahalonobis Distance Classifier
D = (X-Mc)T (COVc-1)(X-Mc)
D = Mahalanobis distance c = particular class
X = measurement vector of the candidate pixel
Mc = mean vector of class c COVc = covariance matrix
COVc-1 = inverse of covariance matrix T = transposition
Pro: takes the variability of the classes into account with info from COV matrix
Similar to maximum likelihood but without the weighting factors
Con: parametric, therefore sensitive to large variances

41. Maximum likelihood classifier
Pro: potentially the most accurate classifier as it incorporates the most information (mean vector and COV matrix)
Con: Parametric procedure that assumes the spectral classes are normally distributed
Con: sensitive to large values in the covariance matrix
Con: computationally intensive

42. Bayes Optimal approach
Designed to minimize the average (expected) cost of misclassifying in maximum likelihood approach
Uses an apriori (previous probability) term to weight decisions - weights more heavily towards common classes
Example: prior probability suggests that 60 of the pixels are forests, therefore the classifier would more heavily weight towards forest in borderline cases

43. Hybrid classification
Can easily mix various classification algorithms in a multi-step process
First pass: some non-parametric rule (feature space or paralellipiped) to handle the most obvious cases, those pixels remaining unclassified or in overlap regions fall to second pass
Second pass: some parametric rule to handle the difficult cases; the training data can be derived from unsupervised or supervised techniques

44. Thresholding
Statistically-based classifiers do poorest near the tails of the training sample data distributions
Thresholds can be used to define those pixels that have a higher probability of misclassification; these pixels can be excluded and labeled un-classified or retrained using a cluster-busting type of approach

45. Thresholding: define those pixels that have a higher probability of misclassification
255
Unclassified Regions
# of pixels
Class 1
Class 2
Threshold

46. Thresholding
Chi square distribution used to help define a one-tailed threshold
Chi Square
# of pixels
Threshold: values above will remain unclassified

47. Hard vs. Fuzzy Classification Rules
Hard - “binary” either/or situation: a pixel belongs to one & only one class
Fuzzy - soft boundaries, a pixel can have partial membership to more than one class

48. Hard vs. Fuzzy Classification
Hard Classification
Forested Wetland
Forest
Water
Fuzzy Classification
Adapted from Jensen, 2nd ed. 1996

49. Hard vs. Fuzzy Classification
NIR reflectance
MIR
reflectance
Forest
Forested Wetland
Hard decision boundaries
Water
Adapted from Jensen, 2nd ed. 1996

50. Fuzzy Classification: In ERDAS
Fuzzy Classification: in the Supervised Classification option, the analyst can use choose Fuzzy Classification and then choose the number of “best classes” per pixel.
This will create multiple output classification layers, as many as the number of best classes chosen above.

51. Fuzzy Classification: In ERDAS
Fuzzy Convolution: calculates the total weighted inverse distance of all the classes in a window of pixels and assigns the center pixel the class with the distance summed over the entire set of fuzzy classification layers.
This has the effect of creating a context-based classification.
Classes with a very small distance value will remain unchanged while classes with higher distance values may change to a neighboring value if there are a sufficient number of neighboring pixels with class values and small corresponding distance values.

52. Main points of the lecture
Training:
--Training set selection: Digital polygon vs. seed pixel-region growing
--Training aids: plot of training data, statistical measure of separability;
--Edit/evaluate signatures.
Classification algorithms:
box classifier,
minimum distance to means classifier,
feature space classifier,
statistically-based classifiers (maximum likelihood classifier, Mahalonobis distance classifier)
Hybrid classification: statistical + Threshold method;
Hard vs Fuzzy Classification.

53. Homework
1 Homework: Unsupervised classification (Hand up your excel file and figure process);
2 Reading Textbook Ch. 9: ;
3 Reading Field Guide Ch. 7: ,