1. Image Classification: Redux
Lecture 7
Prepared by R. Lathrop 11//99
Updated 11/02
Readings:
ERDAS Field Guide 5th Ed. Ch 6:

2. 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

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

4. 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

5. 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

6. 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)

7. 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

8. 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

9. 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

10. Training Aids Graphical portrayals of training data
histogram (check for normality)
ranges (coincident spectral plots)
scatter plots (2D or 3D)
Statistical Measures of Separability: expressions of statistical distance that are sensitive to both mean and variance - divergence Mahalanobis distance

11. 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

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

13. 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)

14. 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

15. 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

16. 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

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

18. 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

19. 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

20. 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

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

22. 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

23. 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

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

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

26. 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

27. 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

28. GIS Rule-based approaches
Unsupervised or supervised techniques to define spectral classes
Use of additional geo-spatial data sets to either pre-stratify image data set, for inclusion as additional band data in classification algorithm or post-processing
Develop set of boolean rules or conditional statements example: if spectral class = conifer and soil = sand, then pitch pine

29. Region-based classification approaches
As an alternative to “per-pixel” classification approaches, region-based approaches attempt to include the local spatial context
Textural channels approach: inclusion of texture (local variance) as an additional channel in classification; con: tends to blur edges
Region growing: Image segmented into spectrally homogenous, spatially contiguous regions first, then these regions are classified using a spectral classification approach; conceptually very promising but robust operational algorithms scarce

30. Object-oriented classification: eCognition example
From the eCognition website: “Image analysis with eCognition is based upon contiguous, homogeneous image regions which are generated by an initial image segmentation.Connecting all the regions, the image content is represented as a network of image objects. These image objects act as the building blocks for the subsequent image analysis. In comparison to pixels, image objects carry much more useful information. Thus, they can be characterised by far more properties than pure spectral or spectral-derivative information, such as their form,texture, neighbourhood or context.”
To download free trial version, go to:

31. Post-classification “smoothing”
Most classifications have a problem with “salt and pepper”, i.e., single or small groups of mis-classified pixels, as they are “point” operations that operate on each pixel independent of its neighbors
Majority filtering: replaces central pixel with the majority class in a specified neighborhood (3 x 3 window); con: alters edges
Eliminate: clumps “like” pixels and replaces clumps under size threshold with majority class in local neighborhood; pro: doesn’t alter edges

32. Accuracy Assessment
Various techniques to assess the “accuracy’ of the classified output by comparing the “true” identity of land cover derived from reference data (observed) vs. the classified (predicted) for a random sample of pixels
Contingency table: m x m matrix where m = # of land cover classes
Columns: usually represent the reference data
Rows: usually represent the remote sensed classification results

33. Accuracy Assessment Contingency Matrix

34. Accuracy Assessment Sampling Approaches: to reduce analyst bias
simple random sampling: every pixel has equal chance
stratified random sampling: # of points will be stratified to the distribution of thematic layer classes (larger classes more points)
equalized random sampling: each class will have equal number of random points
Sample size: at least 30 samples per land cover class

35. Accuracy Assessment Issues
What constitutes reference data? higher spatial resolution imagery (with visual interpretation) “ground truth”: GPSed field plots existing GIS maps
Problem with “mixed” pixels: possibility of sampling only homogeneous regions (e.g., 3x3 window) but introduces a subtle bias

36. Errors of Omission vs. Commission
Error of Omission: pixels in class 1 erroneously assigned to class 2; from the class 1 perspective these pixels should have been classified as class1 but were omitted
Error of Commission: pixels in class 2 erroneously assigned to class 1; from the class 1 perspective these pixels should not have been classified as class but were included

37. Errors of Omission vs. Commission: from a Class2 perspective
Omission error: pixels in Class2 erroneously assigned to Class 1
Commission error: pixels in Class1 erroneously assigned to Class 2
# of pixels
Class 1
Class 2
255
Digital Number

38. Accuracy Assessment Measures
Overall accuracy: divide total correct (sum of the major diagonal) by the total number of sampled pixels; can be misleading, should judge individual categories also
Producer’s accuracy: measure of omission error; total number of correct in a category divided by the total # in that category as derived from the reference data
User’s accuracy: measure of commission error; total number of correct in a category divided by the total # that were classified in that category

39. Accuracy Assessment Measures
Kappa coefficient: provides a difference measurement between the observed agreement of two maps and agreement that is contributed by chance alone
A Kappa coefficient of 90% may be interpreted as 90% better classification than would be expected by random assignment of classes
Allows for statistical comparisons between matrices (Z statistic); useful in comparing different classification approaches to objectively decide which gives best results

40. Kappa coefficient
Khat = (n * SUM Xii) - SUM (Xi+ * X+i) n2 - SUM (Xi+ * X+i)
where SUM = sum across all rows in matrix
Xi+ = marginal row total (row i)
X+I = marginal column total (column i)
n = # of observations
Takes into account the off-diagonal elements of the contingency matrix (errors of omission and commission)

41. Accuracy Assessment Measures