Image Classification: Supervised Methods

Image Classification: Supervised Methods

Lecture 8

Prepared by R. Lathrop 11//99

Updated 3/06

Readings:

ERDAS Field Guide 5th Ed. Ch 6:234-260

Where in the World?

Learning objectives• Remote sensing science 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

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

Supervised vs. Unsupervised

Edit/evaluate signatures

Select Training fields

Classify image

Evaluate classification

Identify classes

Run clustering algorithm

Evaluate classification

Edit/evaluate signatures

Supervised vs. Unsupervised

Red

NIR

Supervised Prior Decision: from Information classes in the Image to Spectral Classes in Feature Space

Unsupervised Posterior Decision: from Spectral Classes in Feature Space to Information Classes in the Image

Training• Training: the process of defining criteria by which

spectral patterns are recognized• Spectral signature: result of training that defines a

training sample or clusterparametric - 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

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)

ERDAS Area of Interest (AOI) tools

Seed pixel or region growing dialog

Region Growing: good for linear features

Spectral Distance = 7 Spectral Distance = 10

Region Growing: good for spectrally heterogeneous features

Spectral Distance = 5 Spectral Distance = 10

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

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

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

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

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

Parametric Assumption: each spectral class exhibits a unimodal normal

distribution

0 255Digital Number

# of pixels

Class 1 Class 2

Bimodal histogram: Mix of Class 1 & 2

Training Aids

• Graphical portrayals of training data

– histogram (check for normality)

“good”

“bad”

Training Aids

• Graphical portrayals of training data– coincident spectral

mean plots

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

Red Reflectance

NIRReflectance

Grass

Trees

water

ImperviousSurface &Bare Soil

Spectral Feature Space

Examine ellipses for gaps and overlaps. Overlapping ellipses ok within information classes; want to limit between info classes

Conifer

Broadleaf

Mix: grass/trees

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

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)

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

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

Red Reflectance

NIRReflectance

Spectral Feature Space

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

Parallelepiped or Box Classifier

Parallelepipeds have “corners”

Red reflectance

NIR

reflectance

Adapted from ERDAS Field Guide

.

Parallelepiped boundary

Signature ellipseunir

ured

Candidate pixel

Parallelepiped or Box Classifier: problems

Red reflectance

NIR

reflectance

Soil 1 Soil 2

Soil 3

Water 1

Water 2

Veg 1

Veg 2

Veg3

Adapted from Lillesand & Kiefer, 1994

Overlap region

Misclassified pixel

??Unclassified pixels

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

Minimum Distance to Means Classifier

Red reflectance

NIR

reflectance

Soil 1 Soil 2

Soil 3

Water 1

Water 2

Veg 1

Veg 2

Veg3

Adapted from Lillesand & Kiefer, 1994

Minimum Distance to Means Classifier: Euclidian Spectral Distance

X

Y 92, 153

180, 85

Xd = 180 -92

Yd = 85-153Distance = 111.2

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

Red Reflectance

NIRReflectance

Spectral Feature Space

Analyst draws decision regions in feature space

Feature Space Classifier

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

Parametric Assumption: each spectral class exhibits a unimodal normal

distribution

0 255Digital Number

# of pixels

Class 1 Class 2

Bimodal histogram: Mix of Class 1 & 2

2d vs. 1d views of class

overlap

0 255Digital Number

# of pixels

wi

wj

Band 2

Band 1

Band 1

Probabilities used in likelihood ratio

0 255Digital Number

# of pixels

p (x | wj)p (x | wi)

wi

wj

}{

Red Reflectance

NIRReflectance

Spectral Feature Space

Ellipses defined by class mean and covariance; creates likelihood contours around each spectral class;

Spectral classes as probability surfaces

Red Reflectance

NIRReflectance

Spectral Feature Space

Some classes may have large variance and greatly overlap other spectral classes

Sensitive to large covariance values

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

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

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

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

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

Thresholding: define those pixels that have a higher probability of

misclassification

0 255Unclassified Regions

# of pixels

Class 1 Class 2 Threshold

Thresholding• Chi square distribution used to help define a one-

tailed threshold

0Chi Square

# of pixels

Threshold: values above will remain unclassified

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

Hard vs. Fuzzy Classification

Water Forested Wetland

Forest

Hard Classification

Fuzzy Classification Adapted from Jensen, 2nd ed. 1996

Hard vs. Fuzzy Classification

NIR reflectance

MIR

reflectance

Water

Forested Wetland

Forest

Adapted from Jensen, 2nd ed. 1996

Hard decision boundaries

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.

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.

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.

Homework

1 Homework: Unsupervised classification (Hand up your excel file and figure process);

2 Reading Textbook Ch. 9:337-389;

3 Reading Field Guide Ch. 7:226-231, 235-253.