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Signal Theory Methods inMultispectral Remote Sensing
• Brief History of the field
• Some fundamentals of remote information
• Outline of spectral analysis methodology
David Landgrebe
Professor Emeritus of Electrical & Computer Engineering
Purdue University
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1957 - Sputnik
REMOTE SENSING OF THE EARTH
Atmosphere - Oceans - Land
Brief History
1958 - National Space Act - NASA formed
1960 - TIROS I
1960 - 1980 Some 40 Earth ObservationalSatellites Flown
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1967 NRC Summer Study on UsefulApplications of Earth-Oriented Satellites
Panels on:
• Point-to-point Communication
• Navigation & Traffic Control
• Sensors & Data Systems
• Geodesy & Cartography
• Economic Analysis
• Systems for Remote Sensing
Information and Distribution
• Agriculture, Forestry, Geography
• Geology
• Hydrology
• Meteorology
• Oceanography
• Broadcasting
• Points-to-point Communication
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The Multispectral Concept
Enlarged 10 Times
Thematic Mapper Simulated Color IR Image
Band No.
Re
lati
ve
R
es
po
ns
e
0
5 0
1 0 0
1 5 0
2 0 0
1 2 3 4 5 6 7
Green Veg.
Bare Soil
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Thematic Map Generation
Image Data Thematic Map
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Data Representations
Spectral Space
0
1000
2000
3000
0.40 0.80 1.20 1.60 2.00 2.40
Wavelength (µm)
Water Trees Soil
Feature Space
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0 500 1000 1500 2000
Band 0.60
Water
Trees
Soil
Sample
• Image Space - Geographic Orientation
• Feature Space - For Use in Pattern Analysis• Spectral Space - Relate to Physical Basis for Response
Image Space
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Example Data Presentations
Image SpaceSpectral Space
Feature Space
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Vegetation in Spectral Space
Laboratory Data: Two classes of vegetation
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Scatter Plots of Reflectance
0.720.710.700.690.680.670.660.6510
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Class 1 - 0.67 µm
Class 2 - 0.67 µmClass 1 - 0.69 µm
Class 2 - 0.69 µm
Scatter of 2-Class Data
Wavelength - µm
Re
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cta
nc
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- %
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Vegetation in Feature Space
1 51 41 31 21 11 016
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Class 1
Class 2
Samples from Two Classes
% Reflectance at 0.67 µm
%
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cta
nc
e
at
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9
µm
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Systems View
Sensor On-BoardProcessing
PreprocessingData
AnalysisInformationUtilization
Human Participationwith Ancillary Data
Ephemeris,Calibration, etc.
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Scene Effects on Pixel
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Sun Angle/View Angle Effects
12:25 PM
Soybeans - 91 cm rows
10:50 AM
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Brief History-Land Remote Sensing
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Three Generations of Sensors
Band No.
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e R
espo
nse
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1 01 52 02 53 03 54 04 55 0
1 2 3 4
Green Veg.
Bare Soil6-bit data80 m pixels4 bands
MSS1968
Band No.
Re
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R
es
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0
5 0
1 0 0
1 5 0
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Green Veg.
Bare Soil
8-bit data30 m pixels7 bandsTM
1975
Wavelength (µm)
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adia
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e
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0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Water
Emerging Crop
Trees
Soil
10-bit data20 m pixels≈ 200 bandsHyperspectral
1986
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Scatter Plot for Typical Data
90
105
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48 54 60 66 72 78
BiPlot of Channels 11 vs 9
Channel 9
Channel 11
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• 8-bit data in 2 bands = (28)2 = 65,536 cells
• About 3000 pixels in 1000 occupied cells
Agricultural Area
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Hyperspectral Data - A Simple Example
• Assume 10 bit data in a 100 dimensional space.
• That is (1024)100 ≈ 10300 discrete locations
Even for a data set of 106 pixels, the probability
of any two pixels lying in the same discrete location
is vanishingly small.
Thus, in theory, everything is separable from everything.
But how?
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SCLB LesionsInfection begins at thebottom of the plant
Southern Corn Leaf Blight
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Blight Stages
Healthy Plants Moderate Blight Severe Blight
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1971 Corn Blight Watch ExperimentFlightlines
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1971 CBWE Intensive Area Flightlines
• All segments flown & analyzedevery two weeks throughout thegrowing season with a 13 bandscanner
• Discrimination successful intothree stages of blight:
�Little or none
�Moderate
�Severe
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Hughes Effect
m=2510
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50100
200
1000
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m = ∞
1 100050020010050201052
MEASUREMENT COMPLEXITY n (Total Discrete Values)
0.50
0.55
0.60
0.65
0.70
0.75M
EA
N R
EC
OG
NIT
ION
AC
CU
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G.F. Hughes, "On the mean accuracy of statistical pattern recognizers," IEEE Trans. Inform. Theory., Vol IT-14, pp. 55-63, 1968.
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Estimation Error - A Simple Example12 Pixel Training
Class 1 Class 2
µ 183 4
25 7=
.
.µ 2
85 2
29 3=
.
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Σ11 17
0 06 0 24=
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. .Σ 2
1 66
0 73 2 97=
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. .
ρ1 = 0.11 ρ2 = 0.33
ρσ
σ σ13
13
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=
-1≤ ρρρρjk ≤ +1
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200 pixel training
Estimation Error - A Simple Example200 Pixel Training
Class 1 Class 2
Class 3 Class 4
µ 383 5
26 2=
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.µ 4
86 9
31 2=
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Σ31 86
0 13 1 00=
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. .Σ4
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ρ3 = 0.09 ρ4 = 0.63
µ 183 4
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.µ 2
85 2
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Σ11 17
0 06 0 24=
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. .Σ 2
1 66
0 73 2 97=
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. .
ρ1 = 0.11 ρ2 = 0.33
12 pixel training
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Estimation Error - A Simple ExampleSome Conclusions
• Mean Vector - A First Order Statistic
• Covariance Matrix - A Second Order Statistic
• To Perfectly Represent an Arbitrary Distribution Would RequireStatistics of All Orders.
• The Number of Samples Required for Acceptable Estimation ErrorGrows Rapidly With Order.
• With Typical (Finite) Numbers of Training Samples
- First Order Statistics Can Usually Be Estimated Satisfactorily.
- Second Order Statistics Are More Problematic But UsuallyAcceptable.
- Statistics Beyond Second Order Are Usually Unusable.
• Thus complex classes must be modeled by a (small) collection ofestimated density functions, i.e. subclasses.
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Analysis System
Direct Method
Observations from the ground
Observations of the ground
Calibration, Adjustment forthe atmosphere, the solar curve,
goniometric effects, etc.
Indirect Method
Imaging SpectroscopyPre-Gathered SpectraEnd Member Analysis
DataAdjustment7
High Dimensional Data
Class ConditionalFeature Extraction
FeatureSelection
Classifier/Analyzer
Label Training Samples
Determine Quantitative Class Descriptions
1
2 3 4
5
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Final Result
An exhaustive, separable, informational value list of classes is key.Subclasses may be necessary to adequately model all classes.
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Hyperspectral Image of DC Mall
HYDICE Airborne System1208 Scan Lines, 307 Pixels/Scan Line210 Spectral Bands in 0.4-2.4 µm Region155 Megabytes of Data(Not yet Geometrically Corrected)
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Define Desired Classes
Training areas designated by polygons outlined in white
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Thematic Map of DC Mall
Legend Operation CPU Time (sec.) Analyst TimeDisplay Image 18Define Classes < 20 min.Feature Extraction 12Reformat 67Initial Classification 34Inspect and Mod. Training ≈ 5 min.Final Classification 33
Total 164 sec = 2.7 min. ≈ 25 min.
Roofs
Streets
Grass
Trees
Paths
Water
Shadows
(No preprocessing involved)
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MultiSpec©
• Import Data (Binary or ASCII)
• Histogram & Display Images
• Cluster (Single Pass or Iterative)
• Define Classes (Rectangular, Polygonal)
• Feature Definition (Subsets, or Optimal Subspaces)
• Statistics Enhancement (Via Labeled & Unlabeled)
• Classification (Spectral or Spectral/Spatial)
• Results Display (Thematic and Tabular)
• Utility Functions (Graph Spectra, Scatter Diagrams,
Principal Components, Ratios, Add Bands, Mosaicing,
Changing Geometry, Visualization aids, etc.)
Available via WWW at: http://dynamo.ecn.purdue.edu/~biehl/MultiSpec/Additional documentation via WWW at: http://dynamo.ecn.purdue.edu/~landgreb/publications.html
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Algorithms Available
DataAdjustment
High Dimensional Data
Class ConditionalFeature Extraction
FeatureSelection
Classifier/Analyzer
Label Training Samples
Determine Quantitative Class Descriptions
1
2 3 4
5
6
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Final Result
Discriminant Analysis Feature Extraction (DAFE) 2Decision Boundary Feature Extraction (DBFE) 2Nonparametric Weighted Feature Extraction (NWFE) 2Projection Pursuit 2Feature Selection 3Maximum Likelihood Classification Algorithms 4Clustering (Unsupervised Classification) 5LOOC 6Statistics Enhancement 6
Algorithm Box
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Textbook Synopsis
Signal Theory Methods in Multispectral Remote SensingDavid Landgrebe
To be published by John Wiley and Sons, Inc, January 8, 2003
Part I. A Brief Overview
Chapter 1. Introduction and overview of the multispectral approach
Part II. The Basics for Conventional Multispectral Data
Chapter 2. Measurements and Sensor System Fundamentals
Chapter 3. Fundamental Concepts of Pattern Recognition
Part III. Additional Details
Chapters on: Training A Classifier, Hyperspectral Data Characteristics,Feature Definition, A Data Analysis Paradigm & Examples, Use of SpatialVariations, Noise in Remote Sensing Systems, Multispectral Image DataPreprocessing
Appendix: An Outline of Probability Theory
Exercises
Student Compact DiscColor Figures of text materialMultiSpec-based projects
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High Dimensional Data
Class ConditionalFeature Extraction
FeatureSelection
Classifier/Analyzer
Label Training Samples
Determine Quantitative Class Descriptions
1
2 3 4
5
6
Final Result
Extract Semi-labeledSamples & Likelihoods
8
The primary limitation is estimation error due to finite training.
Use the classified samples which have high likelihood asadditional training samples.
Analysis System
34
