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ltI (F t ,TR-220-1075APRIL 1972
UNSUPERVISED CLASSIFICATION OFREMOTE MULTISPECTRAL SENSING DATA
172-27204
Ic.AS C 1237s9e Aa)1AsXPEaISED ,
Prepared for:
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
GEORGE C. MARSHALL SPACE FLIGHT CENTERAero-Astrodynamics Laboratory
UNDER CONTRACT NAS8-27364
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NORTHROP SERVICES. INC.P. 0. BOX 1484
HUNTSVILLE, ALABAMA 35807
TELEPHONE (205)837-0580
REPRODUCED BY
NATIONAL TECHNICALINFORMATION SERVICE
U.S. DEPARTMENT OF COMMERCEI. SPRNGFJELD, VA. 2216
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https://ntrs.nasa.gov/search.jsp?R=19720019554 2018-07-08T16:18:12+00:00Z
TR-220-1075
UNSUPERVISED CLASSIFICATION OF REMOTE MULTISPECTRAL SENSING DATA
15 April 1972
by
M. Y. Su.
PREPARED FOR:
NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONGEORGE C. MARSHALL SPACE FLIGHT CENTER
AERO-ASTRODYNAMICS LABORATORY
Under Contract NAS8-27364
REVIEWED AND APPROVED BY:
A. L. Grady, anager :
Advanced Engineering Analysis
,Detail Ijiusirations intahiSs ooturnt ma'o be bethehis dcumed .o n oh0% studied on mIor
NORTHROP SERVICES, INC.HUNTSVILLE, ALABAMA
TR-1075NORTHROP SERVICES. INC.
FOREWORD
This study was undertaken by Northrop Services, Inc., for NASA/MSFC,
Huntsville, Alabama, under Contract No. NAS8-27364. This will constitute the
interim report for the period of 12 months ending on April 15, 1972. The
program was under the direction of MSFC Aero-Astrodynamics Laboratory, Flight
Data Statistics Office, with Mr. R. R. Jayroe, Jr. as the project monitor.
ACKNOWLEDGEMENTS
The author wishes to thank Dr. F. R. Krause, Mr. R. E. Cummings and Mr.
R. R. Jayroe, Jr. for their helpful discussions in completing this work. The
author wishes also to acknowledge Dr. H. W. Smedes, U. S. Geological Survey,
Denver, Colorado, for supplying the remote multispectral data over the
Yellowstone National Park, through the Flight Data Statistics Office, and for
his comparison of the unsupervised classification maps with the associated
ground truth map and to the Purdue University, Laboratory for Remote Sensing
Applications, for Supplying the Purdue C-1 Flight Line data. Assistance with
data processing from Jerry Durret, NASA Co-op student, was also appreciated.
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SUMMARY
This report presents a new automatic processing technique for unsuper-
vised classifications (or clustering) for multispectral remote sensing data.
This technique has been implemented into a digital computer program. Appli-
cations of the computer program for actual multispectral scanner data from
the aircraft survey will also be presented.
Up to the present, main approaches are based on supervised maximum
likelihood classification techniques which require reference spectral target
signatures from training areas on the ground. One of the most serious draw-
backs of the supervised classification techniques is associated with the high
variability of the spectral signatures.
The unsupervised classification technique avoids the above drawback by
not requiring the reference signatures. Essentially, the technique will group
the data sets into a number of classes based on the intrinsic similarity with-
in each class. The physical identification of each class is done by checking
a small area belonging to each class after the data processing. In this
respect, the application of unsupervised techniques is in the reverse order
of the supervised technique. The advantage of processing the data in the
former order is that the investigator shall know better where to select the
ground truth. Another advantage is for on-board data compression to minimize
the rates of data transmission from future spacecrafts to the ground receiving
stations. The third advantage is that automatic change analysis of earth
resources study can be more logically carried out by the unsupervised technique.
The new unsupervised classification technique for classifying multi-
spectral remote sensing data which can be either from the multispectral
scanner or digitized color-separation aerial photographs consists of two parts:
(a) a sequential statistical clustering which is a one-pass sequential variance
analysis and (b) a generalized K-means clustering. In this composite
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NORTHROP SERVICES. INC. TR-1075
clustering technique, the output of (a) is a set of initial clusters which
are input to (b) for further improvement by an iterative scheme.
Applications of the technique using an IBM-7094 computer on multispectral
data sets over Purdue's Flight Line C-1 and the Yellowstone National Park
test site have been accomplished. Comparisons between the classification maps
by the unsupervised technique and the supervised maximum liklihood technique
indicated that the classification accuracy is comparable to each other.
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TABLE OF CONTENTS
TitleSection
FOREWORD . . . . . . . . . . . . . . . . . . . . . . . .
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . .
SUMMARY . . . . . . . . . . . . . . . . . . . . . . . .
LIST OF ILLUSTRATIONS .................
LIST OF TABLES .....................
I INTRODUCTION ......................
II THE COMPOSITE SEQUENTIAL K-MEANS CLUSTERING TECHNIQUE
2.1 STATISTICAL SEQUENTIAL CLUSTERING . . . . . . . . .2.2 GENERALIZED K-MEANS CLUSTERING . . . . . . . . . .2.3 MERGING OF SEQUENTIAL AND K-MEANS CLUSTERING . . .
III UNSUPERVISED CLASSIFICATION OF AGRICULTURAL REMOTESENSING DATA ................. .....
3.1 DATA DESCRIPTION . . . .. . . . . . .......3.2 PRELIMINARY DATA ANALYSIS . . . . . . . . . . . . .3.3 UNSUPERVISED CLASSIFICATIONS . . . . . . . . . . .3.4 COMPARISON WITH SUPERVISED CLASSIFICATION . . . . .
IV UNSUPERVISED CLASSIFICATIONS OF NATURAL TERRAIN TYPES
4.1 DATA DESCRIPTION . . . . . . . . . . . . . . . . .4.2 PRELIMINARY DATA ANALYSIS . . . . . . . . . . . . .4.3 UNSUPERVISED CLASSIFICATION OF TERRAIN TYPES . . .4.4 COMPARISON WITH SUPERVISED CLASSIFICATION . . . . .
V CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . .
VI REFERENCES . .. . . . . . . . . . . . . . . . . . . . .
Page
. . ii
· . ii
. . iii
. . vi
. . ix
. . 1-1
. . 2-1
. . 2-1
. . 2-4
. . 2-9
. . 3-1
* . 3-1. . 3-1. . 3-3* . 3-6
. . 4-1
. . 4-1
. . 4-1
. . 4-3
. . 4-5
. . 5-1
. . 6-1
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LIST OF ILLUSTRATIONS
Title
FLOWCHART OF STATISTICAL SEQUENTIAL CLUSTERING . . . . . . .
COMPARISON OF THE PRESENT AND GENERALIZED K-MEANS ALGORITHMS.
3-1 AIR PHOTO OF PURDUE FLIGHT LINE C-1 (SCAN 587-797).
3-2 PROBABILITY HISTOGRAM OF CHANNEL 1 (0.4-0.44 im). .
3-3 PROBABILITY HISTOGRAM OF CHANNEL 6 (0.52-0.55 im)
3-4 PROBABILITY HISTOGRAM OF CHANNEL 10 (0.66-0.72 pm).
3-5 PROBABILITY HISTOGRAM OF CHANNEL 12 (0.8-1.0 im). .
3-6 GREY-LEVEL PLOT OF CHANNEL 1 (0.4-0.44 m) . . . . .
3-7 GERY-LEVEL PLOT OF CHANNEL 6 (0.52-0.55 m) ....
3-8 GREY-LEVEL PLOT OF CHANNEL 10 (0:66-0.72 m) ....
3-9 GREY-LEVEL PLOT OF CHANNEL 12 (0.8-1.0 m) . . . . .
3-10 SCATTER PLOT OF CHANNEL 1 VERSUS CHANNEL 6 . . . . .
3-11 SCATTER PLOT OF CHANNEL 1 VERSUS CHANNEL 10 . . . . .
3-12 SCATTER PLOT OF CHANNEL 6 VERSUS CHANNEL 10 . ...
3-13 INVENTORY BOUNDARIES BY THE BOUNDARY ENHANCEMENTTECHNIQUE FOR PURDUE C-1 FLIGHT LINE . . . . . . . .
3-14 CLASSIFICATION MAP BY THE STATISTICAL SEQUENTIALTECHNIQUE WITH 18 CLASSES . . . . . . . . . . . . . .
3-15 CLASSIFICATION MAP BY THE STATISTICAL SEQUENTIALTECHNIQUE WITH 17 CLASSES . . . . . . . . . . . . . .
3-16 CLASSIFICATION MAP BY THE STATISTICAL SEQUENTIALTECHNIQUE WITH 16 CLASSES . . . . . . . . . . . . . .
3-17 CLASSIFICATION MAP BY THE STATISTICAL SEQUENTIALTECHNIQUE WITH 15 CLASSES . . . . . . . . . . . . . .
3-18 CLASSIFICATION MAP BY THE STATISTICAL SEQUENTIALTECHNIQUE WITH 14 CLASSES . . . . . . . . . . . . . .
3-19 CLASSIFICATION MAP BY THE STATISTICAL SEQUENTIALTECHNIQUE WITH 12 CLASSES . . . . . . . . . . . . . .
3-20 CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 18 CLASSES AND NO ITERATION . . . . .
3-21 CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 18 CLASSES AFTER ONE ITERATION . . . .
3-22. CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 18 CLASSES AFTER 2 ITERATIONS . . . .
..... 3-8
..... 3-9
..... 3-10
..... 3-11
..... 3-12
..... 3-13
..... 3-14
..... 3-15
..... 3-16
..... 3-17
..... 3-18
..... 3-19
. .... ·3-20
..... 3-21
..... 3-22
..... 3-23
..... 3-24
..... 3-25
..... 3-26
...... 3-27
..... 3-28
. .... 3-29
vi
Figure
2-1
2-2
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LIST OF ILLUSTRATIONS (Continued)
Figure Title
3-23 CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 17 CLASSES . . . . . . . . . .
3-24 CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 16 CLASSES . . . . . . . . . .
3-25 CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 15 CLASSES . . . . . . . . . .
3-26 CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 14 CLASSES. . . . . . . . . .
3-27 CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 13 CLASSES . . . . . . . . . .
3-28 CLASSIFICATION MAP BY THE COMPOSITE CLUSTERINGWITH 13 CLASSES AND WITHOUT ITERATION. . . . .
3-29 CLASSIFICATION MAP BY THE COMPOSITE CLUSTERINGWITH 13 CLASSES AFTER ONE ITERATION . .. ..
. . . .TECHNIQUE
TECHNIQUE. . . . .
TECHNIQUE
3-30 CLASSIFICATION MAP BY THE COMPOSITE CLUSTERING TECHNIQUEWITH 13 CLASSES AFTER 2 ITERATIONS . . . . . . . . . . .
3-31 CLASSIFICATION MAP BY THE COMPOSITE CLUSTERING TECHNIQUEWITH 14 CLASSES AND WITHOUT ITERATION . . . . . . . . ...
3-32 CLASSIFICATION MAP BY THE COMPOSITE CLUSTERING TECHNIQUEWITH 14 CLASSES AFTER ONE ITERATION . .. . . . . . . . .
3-33 CLASSIFICATION MAP BY THE COMPOSITE CLUSTERING TECHNIQUEWITH 14 CLASSES AFTER TWO ITERATIONS . . . . . . . . . .
3-34 CLASSIFICATION MAP BY PURDUE UNIVERSITY LARS'S SUPERVISEDBAYES CLASSIFICATION TECHNIQUE (Ref. 10, p. 40) . . . ..
3-35 TABULATION OF CLASSIFICATION RESULTS OF TEST FIELDS(Ref. 10, p. 41) . ...... . . . . . . . . . . . . .
4-1
4-2
4-3
4-4
4-5
4-6
4-7
GRAY-SCALE VIDEO DISPLAY OF REFLECTANCE FOR CHANNEL 9 . . . . 4-7
PROBABILITY HISTOGRAM OF CHANNEL2 . . . . . . . . . . . . . . 4-8
PROBABILITY HISTOGRAM OF CHANNEL9 . . . . . . . . . . . . . . 4-9
PROBABILITY HISTOGRAM OF CHANNEL 10 .............. 4-10
PROBABILITY HISTOGRAM OF CHANNEL 12. . . . . . . . . . . . . . 4-11
DIGITAL GRAY-LEVEL PLOT OF CHANNEL 2 . . . ... . . . . . . . . 4-12
DIGITAL GRAY-LEVEL PLOT OF CHANNEL 10 . .. .. . . . . . . . 4-13
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Page
3-30
3-31
3-32
3-33
. . 3-34
· · 3-35
. . 3-36
. . 3-37
. . 3-38
. . 3-39
. . 3-40
3-41
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LIST OF ILLUSTRATIONS (Concluded)
Figure Title Page
4-8 SCATTER PLOT OF CHANNELS 2 AND 9 ................ 4-14
4-9 SCATTER PLOT OF CHANNELS 2 AND 10 . ..... . . .. . . . . . 4-15
4-10 SCATTER PLOT OF CHANNELS 2 AND 12 . . . . . . . . . . . . . . . 4-16
4-11 SCATTER PLOT OF CHANNELS 9 AND 10. . . . . . . . . . . . . . . 4-17
4-12 SCATTER PLOT OF CHANNELS 9 AND 12 . . . . . . . . . . . . . . . 4-18
4-13 SCATTER PLOT OF CHANNELS 10 AND 12 . ... . . . . . . . . . . 4-19
4-14 THE INVENTORY BOUNDARY MAP BY THE BOUNDARY ENHANCEMENTTECHNIQUE . . . ............ ........... 4-20
4-15 UNSUPERVISED CLASSIFICATION MAP AFTER ONE ITERATION WITH18 CLASSES . . .... .... . . . . . . . . . . . . . . . . 4-21
4-16 UNSUPERVISED CLASSIFICATION MAP AFTER TWO ITERATIONS WITH17 CLASSES . . . . . . . . . . . . . . . . . . . . . . . . . . 4-22
4-17 UNSUPERVISED CLASSIFICATION MAP AFTER FIRST MERGING WITH16 CLASSES . . . . . . . . . . . . . . . . . . . . . . . . . . 4-23
4-18 UNSUPERVISED CLASSIFICATION MAP AFTER THE SECOND MERGINGWITH 15 CLASSES . . . . . . . . . . . . . . . . . . . . . . . . 4-24
4-19 UNSUPERVISED CLASSIFICATION MAP AFTER THE THIRD MERGINGWITH 14 CLASSES . ...... . . ............... 4-25
4-20 UNSUPERVISED CLASSIFICATION MAP AFTER THE FOURTH MERGINGWITH 13 CLASSES .................................... 4-26
4-21 UNSUPERVISED CLASSIFICATION MAP AFTER THE FIFTH MERGINGWITH 12 CLASSES . ...... . . ... . . . . . . . . . . 4-27
4-22 UNSUPERVISED CLASSIFICATION MAP AFTER THE SIXTH MERGINGWITH 11 CLASSES . . . . . . . . . . . . . . . . . . . .. . . . 4-28
4-23 UNSUPERVISED CLASSIFICATION MAP AFTER THE SEVENTH MERGINGWITH 10 CLASSES ........................ 4-29
4-24 UNSUPERVISED CLASSIFICATION MAP AFTER THE EIGHTH MERGINGWITH 9 CLASSES . . . . . . . . . . . . . . . . . . . . . . . . 4-30
4-25 GROUND TRUTH SURVEY MAP ...................... 4-31
4-26 LARS CLASSIFICATION: YELLOWSTONE NATIONAL PARK(CH-2, 9, 10 AND 12) .. ........ . .......... . 4-34
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LIST OF TABLES
Title
SPECTRAL BANDS OF MICHIGAN MULTISPECTRAL SCANNER. . .
SUMMARY OF MEAN SPECTRAL RADIANCES OF 14 CLASSES BYTHE COMPOSITE CLUSTERING TECHNIQUE (Figure 3-33)..
SUMMARY OF UNSUPERVISED CLASSIFICATION AND MERGING OFTHE ESTABLISHED CLASSES FOR YELLOWSTONE NATIONAL PARKTEST SITE (SCAN 200-500) . . . . . . . . . . . . . .
MEAN SPECTRAL VECTORS FOR 18 CLASSES - YELLOWSTONENATIONAL PARK . . . . . . . . . . . . . . . . . . . .
Page
. . . . . 3-2
. . . . . 3-7
. . ... 4-32
. . . . . 4-33
ix
Table
3-1
3-2
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Section I
INTRODUCTION
Applications of nonsupervised clustering techniques have recently
attracted more attention for processing and analyzing multispectral data
obtained by remote sensing of the earth's resources and environment (refs. 1-7).
In the past, main approaches in dealing with these types of data were based on
supervised classification techniques which required reference spectral target
signatures from training areas (ref. 8).
One of the most serious drawbacks of the supervised classification tech-
niques is associated with the high variability of the reference spectral sig-
natures. These signatures depend not only on different physical targets of
interest, but also on the following factors (some known and some unknown in
the process of data gathering):.
* Background materials
* Atmospheric and meteorological conditions
* Different physical location and orientation
* Time of day, different reason of data collection
* Sensor scan angle and sun elevation and azimuth
* Different stages of plant growth
* Different land use practices.
With so many variable factors affecting the remote sensing data, it is
very difficult, if not impractical, to set up an operational system for estab-
lishing the reference spectral signature (or ground truth) library. So far,
the users of the supervised classification methods mainly obtain the reference
spectral signatures directly from training sets which form parts of the test
areas. Even with this practice, it still requires much human judgment and
intervention to select proper training areas for obtaining sufficient accuracy
of classification.
The nonsupervised classification, or clustering, techniques avoid most of
the above difficulties and operational impracticability. The clustering
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technique does not require the reference spectral signatures. In essence the
technique will group the sample data into a number of classes, all of which
are statistically homogeneous. Finally, the physical identification of each
class is accomplished by collecting the ground truth from a suitable size area
belonging to that particular class. In this sense, the applicationof cluster-
ing techniques to the multispectral data analysis is in the reverse order of
the supervised classification technique. The advantage of processing the data
in the order according to the clustering techniques is that it will be known
better where to select the reference ground truth.
Another advantage of the clustering technique is for data flow compres-
sion in the telemetry of data from the spacecraft to the ground data receiving
station. It is quite clear now that the data rate collected by the satellite-
borne sensors will be so large that present telemetry systems can not handle
it. However, Dr. A. Park indicated that if the data can be compressed to 1/50
or greater of the present volume, then the presently available commercial TV
receiving station can be used for space data collection. It is quite feasible
that the clustering techniques can process onboard the raw data and compress
it into the acceptable reduced volume for this purpose. It is also possible
in the hydrological applications to augment a relatively few number of ground
sensors by the remote sensing data with the clustering techniques.
Under the present contract, a new composite sequential K-means clustering
algorithm has been developed with actual applications to two sets of remote
sensing data; the Purdue agricultural field (Purdue C-1 Flightline) and the
Yellowstone National Park test site. The latter test site is actually in
natural wilderness with various terrain types, forest cover and parts of it under
cloud shadow. According to Dr. A. Park, NASA Headquarters, Earth Resources
Program, this set of remote sensing data is about the most complex data
collected under the NASA Earth Resource Program. Thus, it may offer themost
critical test to date of the capability of the unsupervised clustering
technique. If the technique can obtain an acceptably accurate classification
map, then it may be safe to apply to other remote multispectral sensing data
for earth resources and environment survey.
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The principles behind the composite clustering technique will be pre-
sented in Section II. Detailed mathematical algorithms, computer programs and
users manual will not be given in this report, but will be included in the
final contract report. Applications of the technique to the aforementioned
two sets of data together with some supporting processing by other computer
programs developed under previous contracts (ref. 9) will be given in Sections
III and IV, respectively. A comparison of the unsupervised classification
maps with Purdue LARS' results (refs. 8 and 10) will be made. Finally, some
future developments and concluding remaks will be made in Section V.
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Section II
THE COMPOSITE SEQUENTIAL K-MEANS CLUSTERING TECHNIQUE
The composite clustering technique developed essentially consists of two
independent clustering techniques. The first is called the statistical
sequential classification technique (SSC) (refs. 11 and 12) and the second is
called generalized K-means techniques (GKM) (ref. 13). Therefore, each tech-
nique will first be described, and then how they can be merged into one will
be described.
2.1 STATISTICAL SEQUENTIAL CLUSTERING
The sensor collects multispectral data from a target which forms an image.
An image can be composed of m scan lines of n resolution elements per scan
line. Each resolution element yields a K-dimensional observation vectorth
x(.i), i = 1,2,... K, where X. indicates the i h spectral band.
The purpose of the SSC program is to classify the given sequences of
multisectional data into a specified number of subclasses; each of which is
statistically homogeneous or similar in their spectral characteristics. To
accomplish this goal, the program consists of four main steps:
* Establishing new classes
* Classifying new samples into established classes
* Merging excessive classes
* Displaying classification results and statistics.
A flowchart of the main steps of the algorithm is depicted in Figure 2-1.
Step 1 - all control parameters and statistical tables are read in. Step 2 -
M (M = 6) samples are read in, which shall be tested to decide whether they
come from the same population. If they do, they will be designated as the
first population. If they do not, then the first sample will be dumped into
a null-class, which contains all the samples unidentifiable, and then read in
a new sample as shown in Steps 6 and 7. These new M samples will be tested
once again in Step 3 to see whether they constitute a new population. The
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above process will be repeated until the first population is established. The
statistical parameters of interest for this population are calculated in
Step 5.
Next, one proceeds to check whether the end of the entire sample sequence
is reached. If it is, the program will print out the final results of the
number of samples in that population; the corresponding sample mean vector,
covariance matrix, and classification map. The latter map represents a 2-
dimensional spatial location of samples from each population. After this
printout, the program will terminate itself. If there are still samples left,
the program will proceed to check whether the total number of established
homogeneous populations exceed the prescribed number. If the answer is yes,
the program will proceed to Step 11 in order to reduce the number of estab-
lished populations back to the prescribed number. This is accomplished by
combining two populations that are most similar to each other into a enlarged
population encompassing all those samplesbelonging to the two original popu-
lations. Subsequently, the program will also recalculate the corresponding
sample mean vector and covariance matrix in Step 12. If the answer is no,
then the program proceeds to Step 13, to read in a new sample. The sample
is then subjected to another test to see whether it belongs to any established
population in Step 14. If the answer is yes, the sample is added to that popu-
lation where it belongs, and the corresponding sample mean vector and covariance
matrix are updated. This process is repeated until anew sample is encountered
which does not belong to any of the established populations. This new sample
will be held in a temporary hold location until M such samples have been
accumulated. These M samples are then tested to see whether they constitute
a new population as was done for establishment of the first population. If
the test is affirmative, then a new population will be set up for them and then
continue to Step 5. If the test is negative, the sample which is held first
in the temporary hold will be dumped into the class of unidentifiable class,
then proceed to read in a new sample. This process is repeated until all the
sample sequences have been processed. The final outputs of the whole algorithm
is to print out the number of samples, the mean vector and covariance matrix
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for each population, a divergence matrix among all the populations, and
finally a 2-dimensional map of spatial locations of samples for each popu-
lation.
2.2 GENERALIZED K-MEANS CLUSTERING
The generalized K-means algorithm essentially consists of three steps
plus an additional step for displaying the 2-dimensional map of clustering
results. This algorithm is an improved version of the existing K-means
algorithms (refs. 14 through 17).
2.2.1 Step 1 - Estimation of Initial Cluster Centers
Let the sample sequence be denoted by {xi(Aj), i = 1, 2, ..., M and
j = 1, 2, 3, ..., N}. Here i denotes the sample number and j denotes its
components. The first initial cluster center C1 will be the first sample, i.e.,
C (X.) = x1(A.) (2-1)
The second initial cluster center C2 will be the sample which has the fartherest
distance from C1, i.e.,
C2(Xi) = xi(%j) with the maximum of
N 2X [xi(
j) - xl(Xj)] over all i. (2-2)
j=l
thThe (k+l) initial cluster center Ck (for k > 2) will be the sample which
has the maximum of the minimum distances among all with respect to the estab-
lished k initial cluster centers, i.e.,
Ck+(Xj) = xi(Xj) with
max inL [xi.(.) - Xk (2-3)i3)
ma mkn j=1
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The results of the above procedure is to plant evenly the initial cluster
centers whose number will be prescribed over that part of the measurement space
occupied densely by the given input sample sequence. The step of estimating
initial centers is relatively time consuming. The computer time requirement
will be proportional to
(K-i) (K-2) 1 3 2MN (K-l (K-2) =1 MNK2(1 _3 + 2) (2-4)2 2 ( K+K+K
where K is the total number of cluster centers. Clearly, the computer time
required is linearly proportional to the total sample M and number of components
per sample N, respectively, but almost to the square of the required number of
cluster centers, K. Usually, N is fixed, but in general one would expect,
without any prior knowledge, that K would increase with M.
2.2.2 Step 2 - Preliminary Improvement of Cluster Centers
This step of improving accuracy of the initial cluster centers is exactly
the same as used in the present K-means algorithm. "Preliminary" is used here
because another improvement to the cluster centers will be made after this
step as discussed in Step 3. The minimum distance criterion is employed. The
entire sample sequence is classified into K groups by calculating the distances
of each sample with respect to each cluster center and classifying the sample
into that particular center that yields the minimum distance, i.e.,
xi(Aj ) + Ck(Xj ) if
N[xi(Aj) - Ck(j)] is the minimum over all k. (2-5)
j=l k
This classification is equivalent to set up a system of hyperplane decision
boundaries to separate K clusters. Once this is done, the sample belonging to
each cluster center is used to calculate its mean measurement vector (or center-
of-gravity). These updated K centers will now be regarded as the initial
cluster centers for the next iteration- The procedure will be repeated until
the difference (or distance) between two successive iterated values of every
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cluster center is smaller than some prescribed threshold value. In general,
one would expect that smaller threshold values result in better (or more
accurate) results, but it also requires a larger number of iterations. Some
compromise is thus obviously called for and no general rule can be specified.
2.2.3 Step 3 - Final Improvement of Cluster Centers
The reason for requiring some further improvement to the cluster centers
as obtained from Step 2 can be illustrated by using Figure 2-2. In this figure
there are three natural clusterings in 2-component scattering diagrams.
Further, these three clusters are clearly linearly separable, thus it is de-
sirable to separate the samples into three clusters. Using Step 2, the best
results obtainable, after a sufficient number of iterations, is shown by the
linear minimum-distance decision boundary as indicated by the solid lines.
Parts of samples actually belonging to cluster No. 1 are mis-classified into
clusters No. 2 and 3. This resulted from the fact that inter-distance between
clusters No. 1 and 2 (similarly for cluster No. 1 and 3) is about equal to the
sum of the two intra-distances of the individual clusters of which one is much
larger than the other.
This hypothetical example is actually a very common case in the multi-
spectral observations of earth resources and environments. Investigators of
spectral signatures have pointed out this difficulty many times.
One way to deal with this difficulty and thus improve the power of the
present K-means algorithm will be proposed. To the first approximation, the
intra-distance of samples within one cluster will be the sample standard devia-
tion vector that is the square roots of the diagonal elements of the sample
covariance matrix. Except for the very elongated cluster, this sample standard
deviation vector may be characterized by a single scalar, i.e., the root mean
square of the standard deviations of the components. This characterization is
completely correct if each component has the same standard deviation. With
this basic understanding, the minimum-distance criterion used in the present
K-means algorithm can be replaced by a more general similarity criterion with
the standard deviations as weights to better locate the decision hyperplanes.
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LEGEND
- MINIMUM-DISTANCE DECISION BOUNDARIES
- GENERALIZED DECISION BOUNDARIES
MISCLASSIFIED SAMPLES BY USING MINIMIM-DISTANCEDESCISION BOUNDARIES
0
Figure 2-2. COMPARISON OF THE PRESENT AND GENERALIZED K-MEANS ALGORITHMS
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The proposed similarity criterion can be expressed as
xi(Aj ) + Ck(Aj) if
1 N2-12 ji [xi(j) - Ck(j)] 2is minimum over all k. (2-7)2 ~ x~j klj]S j=l
k
thHere, Sk is the characterized sample standard deviation for k cluster center.
The rest of the step will be the same as in Step 2.
Three important points germaine to the added step will now be discussed.
First, one might ask why not use Step 3 with the more general similarity measure
exclusively, i.e., eliminating Step 2 altogether. The answer is that the
sample standard deviations for K cluster centers may not be accurate enough
at the first few iterations in improving the cluster centers and that their
evaluations are more apt to the influence of misclassified samples than the
centers-of-gravity of clusters. Hence, there is no clear indication to
expect better performance from Step 3 than Step 2 at the first several
iterations. Therefore if Step 2 is employed to its utmost capacity, then
the best possible estimate of the sample standard deviations is obtained,
and the true power of the more general similarity will prevail.
The second point is concerned with whether Step 3 with additional evalua-
tion of sample standard deviations will be very time consuming. The answer is
no, since in Step 3, as well as Step 2, the square of the distance of each
sample with respect to each cluster center should be calculated and classify
it to the cluster center with the shorter distance. Theevaluation of sample
variance for each cluster center can make use of the above calculation by
adding a simple updating routine for accumulation. Therefore, each iteration
of Step 3 will take only slightly more time than that of Step 2.
The last point is that Step 3 will not degrade the results from Step 2.
As has been demonstrated the misclassification may occur by Step 2 only if the
intra-distance of samples in any cluster center is greater than half of the
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inter-distances between the two clusters. Further, the proposed Step 3 can
remedy this difficulty. Step 3 will do just as well as Step 2 for the cases
that Step 2 can do perfectly, i.e., the cases in which the inter-distance
between two clusters is much larger than the sum of the intra-distances for
individual clusters. This can be easily shown by noting that the intra-distance
for each cluster center should be shorter than only one-half of the inter-
distance between the associated pair of cluster centers in order to have a per-
fect (i.e., completely correct) classification. Consider the most trying but
still completely separable clustering by the minimum-distance criterion,
namely, the larger of the two intra-distances is equal to one-half of the
inter-distance between clusters and the shorter one is much smaller. For such
a case, this generalized similarity criterion will set the hyperplane decision
boundary at a distance twice the shorter intra-distance from the cluster center.
So, a perfect classification will also result.
It is worthwhile to note that the cluster centers established by Steps 1
through 3 can be joined or merged together in order to reduce the total number
of cluster centers. However, with regard to saving of computation time, it
will be better to start off using fewer clusters than merging the established
clusters.
The results of clustering by Step 3 can be displayed in a 2-dimensional
map for the multispectral observations such as the multispectral line scanner.
In addition, all the statistical parameters and sample probability density
functions can also be calculated at the last iteration of Step 3 and printed
out together with the 2-dimensional map.
2.3 MERGING OF SEQUENTIAL AND K-MEANS CLUSTERING
Before describing how the statistical sequential clustering technique and
the generalized K-means clustering technique can be combined into more power-
ful clustering techniques, the merits and drawbacks of each technique will be
discussed. This review then points out a natural way for combining these two
techniques.
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The single most significant advantage of the SSC is that it requires
only one pass of the entire data sequence to achieve fairly good clustering of
the given data. This truly sequential feature, to the author's knowledge, has
never been accomplished in any existing clustering techniques. This feature
also permits fairly fast computation. However, because of only one pass of
the data sequence, the null class of unidentifiable data samples that resulted
from establishing new classes can not be reexamined, which is the main drawback
of the SSC technique.
The most significant advantage of the GKC technique is that it possesses
the capability for repetitive correction and updating of the establishing cluster
centers. Its main-drawbacks is that the procedure for choosing the initial
cluster centers is quite arbitrary and requires as many passes of the entire
data sequence as the number of cluster centers. Furthermore, because of these
rather inaccurate initial cluster centers, many iterations of the entire data
sequence will be further required to achieve good clustering accuracy.
From the above comparison of these two techniques it is clear that they
can complement each other, since the drawbacks of each technique can be elim-
inated by properly merging the two techniques. The composite clustering
technique is then composed of two main steps:
(1) The given data sequence will be processed by the SSC technique withonly a single pass of the entire data sequence. The outputs of theprocessing will be the mean spectral vectors of clusters.
(2) The mean spectral vectors from (1) will be used as the initial clustercenters to the KGC technique. In order to allow for extra clustercenters from the null class of the SSC in (1), the original KGCprocedure for establishing extra initial cluster centers can beused as many times as desired. Next, the initial cluster centerswill be iterated about 2 to 3 times to obtain the final clustering.
In short, the above composite clustering technique can accomplish good
unsupervised classification of a given data sequence with about four passes of
the entire data set regardless of the preset number of clusters.
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Section III
UNSUPERVISED CLASSIFICATION OF AGRICULTURAL REMOTE SENSING DATA
In order to test and demonstrate the capability of the non-supervised
clustering technique, a set of computer programs has been developed. The pro-
gram to process and analyze a set of most well-known multi-spectral data which
was made available by the Purdue University's Laboratory for Applications of
Remote Sensing was employed.
3.1 DATA DESCRIPTION
The data were obtained by the University of Michigan multispectral scanner
over an agricultural experiment test site near Lafayette, Indiana, from a
flight altitude of 2600 feet on June 28, 1966. This set of data was designated
as Purdue Flight Line C-1. In particular, only the results from scans 587
through 797 are presented for the purpose of comparing our nonsupervised
classification results with LARS's supervised classification results of the
same area (ref. 18).
3.2 PRELIMINARY DATA ANALYSIS
Figure 3-1* shows the aerial photo of the target area (about 1 square
mile) with the ground truth designation superimposed. The multispectral
scanner recorded simultaneously 12 channels of spectral bands reflecting from
the earth's surface between 0.4 and 1.0 pm. These spectral bands are listed in
Table 3-1. Again for the purpose of comparison with LARS results only 4
channels were used, i.e., channels 1, 6, 10, and 12. These 4 channels have
been determined by LARS to be the optimal 4-channel feature selection (based
on the divergence measurement) for the flight line C-1 data (ref. 18).
Figures 3-2 through 3-5 show the probability histograms of each indi-
vidual channel, respectively. These histograms clearly show that the
majority of resolution elements (or target) having the spectral radiance
between 140 and 200, with the total radiance range being 0 to 256. Further,
*Figure 3-1 through 3-35 are presented folZowing the text at the end of thisSection.
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Table 3-1. SPECTRAL BANDS OF MICHIGAN MULTISPECTRAL SCANNER
CHANNEL NO. SPECTRAL BANDWIDTH CHARACTERISTIC(microns) COLOR
1 0.40 - 0.44 Violet
2 0.44 - 0.46 Blue
3 0.46 - 0.48
4 0.48 - 0.50 Blue-Green
5 0.50 - 0.52
6 0.52 - 0.55 Green Visible
7 0.55 - 0.58
8 0.58 - 0.62 Yellow
9 0.62 - 0.66 Red
10 0.66 - 0.72 Red
11 0.72 - 0.80 Reflective
12 0.80 - 1.00 near infrared
several distinct peaks were observed in each histogram which indicate the
mixing of several different populations as expected. However, these peaks are
not completely separate. This fact implies that more than one channel out of
these four would be required for discrimination between different populations.
Figures 3-6 through 3-9 show the corresponding grey-level plots of the
channels used. The road running in the flight direction in the middle of the
area is indicated by a blank. Several other rectangular agriculture fields can
also be observed from these plots. In particular, one can see the close
correspondence of the two wheat fields in Figures 3-1 and 3-8. It should be
noted that the complement of the numerical value with respect to 256 is pro-
portional to the spectral radiance received by the scanner. Hence, the larger
the numberic used in the grey-level plot, the smaller the spectra] radiance.
Figures 3-10 through 3-12 show three scatter plots between channels
1, 6, and 10, The number 1 through 8 used indicates the number of samples in
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each spectral cell, while number 9 indicates the number of samples to be 9 or
greater. Two things can be observed from these plots. First, the scatter
patterns of Figure 3-10 with Channel 1 versus Channel 6 and Figure 3-11 with
Channel 1 versus Channel 10 are alike. This indicated that Channel 6 and
Channel 10 are possibly linear related. This prediction is further confirmed
by the scatter pattern in Figure 3-11 with Channel 6 versus Channel 10. Second,
the scatter pattern in each figure does not indicate clear cut clusters, which
implies the impossibility of completely correct discrimination basing on any
two-channel pairs out of channels 1, 6, and 10. That is, three or more chan-
nels of data are needed simultaneously for discrimination between different
crops in this set of data.
Figure 3-13 shows an inventory boundary map by the boundary enhancement
technique (ref. 7) for the target area. One can see the very clear correspon-
dence of the boundaries of different crop fields between this map and the
aerial photo (Figure 3-1). One purpose of generating the boundary map is to
establish the spatial registration between the multispectral data and the
ground scene based on the aerial photo so that the training set can be selected,
if needed, as in the supervised classification by LARS. So much for the
preliminary data analysis of this particular target area. In the following,
the results from the non-supervised classification techniques will be discussed.
3.3 UNSUPERVISED CLASSIFICATIONS
In order to see more clearly the advantage of the composite clustering
technique, the results employing, separately, the SSC technique and GKC tech-
nique was presented first.
Figures 3-14 through 3-19 show the classification maps by the statistical
sequential clustering technique for the numbers of 18, 17, 16, 15, 14, and
13 classes, respectively. Actually, only Figure 3-14 with 18 classes was
processed from the data directly. The other classification maps were obtained
consecutively by merging the two most similar classes based on the minimum
distance criterion. It is interesting to examine the merging process in this
series of classification maps. The 18 classes in Figure 3-14 are designated by
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alphanumeric symbols 1, 2, ... , 8, 9, A, B, C, E, F, G, H, and I, respectively.
The class (I) appears in the last scan 797 from sample numbers 115 through 221
in Figure 3-14. This class was merged into class (1), as shown in Figure 3-15.
Next, the class (H) scattering in the rectangle defined by scans 645 and 699,
and sample numbers 1 and 45 in Figure 3-15 was merged into class (4) as shown
in Figure 3-16. Next, class (G) occupies the rectangle defined by scans 707
and 797, and sample numbers 1 and 19 in Figure 3-16 were merged into class (C)
as shown in Figure 3-17. Next, class (F) occupies the right side of scans 791
and 793 in Figure 3-17 were merged to class (1) as shown in Figure 3-18. Up
to this stage, four classes (I, H, G, and F) have been merged into other
classes. It was noted that the number of samples for each of these four classes
is relatively small compared with the total number of samples in the target
area. However, in the next merging, the very large class (2) in Figure 3-18
was merged into another large class (1). Comparing the classification maps of
Figures 3-18 and 3-19 with 14 and 13 classes, respectively, against the aerial
photo, it clearly shows that classes (1) and (2) should be two separate
classes. Thus, one may conclude that 14 classes may be the most natural
classification of this set of data. Among these 14 classes, the smallest class
containing only 19 samples is designated by symbol E in Figure 3-18 or symbol
2 in Figure 3-19.
Next, Figures 3-20 through 3-27 show the classification maps by the
generalized K-means clustering technique alone on the same set of data.
Figures 3-20 through 3-22 give the classification maps with 18 classes for
three stages of clustering, i.e., no iteration and after one and two iterations,
respectively. The rest of the classification maps were generated consecuitvely
by merging the two most similar classes based on the minimum distance criterion
down to 13 classes.
By comparison of the corresponding classification maps by the statistical
sequential technique and by the generalized K-means technique, with regard to
the ground truth map (Figure 3-1), it seems that the performances by both
techniques are about the same with about 70 to 80 percent correct classifica-
tion accuracy (or clustering). It should be noted that for the same accuracy
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of clustering it took only one pass of the data set by the statistical
sequential technique, while it took 20 passes (18 passes for establishing
initial cluster centers and 2 passes for updating these cluster centers) by
the generalized K-means technique.
The results by the composite sequential K-means clustering technique will
be discussed next. Figures 3-28 through 3-35 show the classification maps of
the same target area (Figure 3-1) by the composite technique. Figures 3-28,
3-29, and 3-30 give the classification map with 13 classes. The classification
maps were generated by using the mean vectors of the four channels l, 6, 10,
and 12 of the 13 most populous classes obtained by the statistical sequential
technique (Figure 3-18) as the initial cluster centers into the generalized
K-means technique. Figure 3-28 gives the classification without any updating
of the cluster centers, while Figures 3-29 and 3-30 give the classification,
respectively, after one and two iterations. One can see clearly that even
without any updating of the cluster centers, the simple reclassification by the
K-means technique has produced great improvement in accuracy. After only two
iterations (or updating) of the cluster centers, the classification map cor-
responds very well with the ground truth map (Figure 3-1). From Figure 3-30,
one can see that the wheat fields are classified into three classes (6, 8,
and C); corn fields into 3 classes (1, B, and D); oats into two classes (9
and 7); soybeams into 2 classes (A and 4); while hay, alfalfa, red clover,
and pasture are collectively into two classes (2 and 7). The fact that each
of the four crops - wheat, corn, oats, and soybeans are grouped into more than
one class simply implied that there existed variations within each spieces of
crop. The important point is that the three classes (6, 8, and C) representing
wheat, for example, do not mingle with the other crops. Hence, the clustering
results for these four crops should be considered correct. On the other hand,
lumping all the other crops - hay, alfalfa, red clover, etc., together into only
two classes (2 and 7) is due to their very close resemblance in the spectral
signature in the four channels used. The difficulty of distinguishing these
crops has also shown up in the supervised classification results by the LARS
program which will be discussed further later when a comparison is made with
these and LAR's results.
3-5
The road running vertically through the center of the target area will
now be discussed. In Figure 3-30,-the road is designated by class symbols 8,
B, A, D, 4, and C. Certainly, this designation is not correct. This mis-
classification of the road, however, can be easily corrected. This is accom-
plished by increasing one more class, i.e., from 13 to 14, using the K-means
technique prior to updating the initial cluster center. The results of this
processing are shown in Figures 3-31 through 3-33. Figure 3-31 is obtained
without updating, while Figure 3-32 and 3-33 are obtained, respectively, afterth
one and two iterations. This 14t h class (E) unmistakably indicates the road
as one can see in the middle part (vertically) in Figure 3-33.
Table 3-2 summarizes the quantitative results from the last classification
map (Figure 3-33). It may be noted that there are 2 small classes, i.e.,
classes (3) and (5), with samples 5 and 28, respectively. Both of them belongs
to the wheat field at the left of the map in Figure 3-33. They show much
stronger spectral radiances in channels 6 and 10 compared with other classes.
The causes for this fact is not clear, because of insufficient ground truth
information available. Note that only four passes of the data set were required
for the classification map by the composite clustering technique.
3.4 COMPARISON WITH SUPERVISED CLASSIFICATION
As mentioned earlier, the reason for choosing the particular data set for
testing our composite clustering technique is for comparison with the super-
vised classification results obtained by LARS using the maximum liklihood
classification technique. LARS's classification map is reproduced in Figure
3-34 employing the same four channels as were used for the composite clustering
discussed above (ref. 18). The training fields used in the classification
program are outlined with asterisks (*) and the test fields are outlined with
plus (+) signs. The tabulation of classification results of the test fields
is also reproduced in Figure 3-35. The test fields chosen in LARS classifi-
cation covered only about 5989/11660 = 51.5 percent of the entire field. The
overall performance of correct classification is 87.5 percent. Actually, the
entire field has been classified by the LARS program, as is evidenced by the
classification symbols covering the entire field. The so-called test fields
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Table 3-2. SUMMARY OF MEAN SPECTRAL RADIANCES OF 14 CLASSESBY THE COMPOSITE CLUSTERING TECHNIQUE (FIGURE 3-33)
CLASS CLASS NO. OF CHANNEL 1 CHANNEL 6 CHANNEL 10 CHANNEL 12CLASS CLASS NO. OFNUMBER SYMBOL SAMPLES .4-.44 rm .52-.55 pm .66-.72 vim .8-1.0 pm
1 1 1575 174.2 173.0 183.8 177.9
2 2 3103 179.5 171.3 175.0 150.0
3 3 5 162.8 114.8 88.8 160.2
4 4 1798 166.5 160.5 165.9 172.6
5 5 28 166.8 127.8 106.5 163.7
6 6 523 178.2 166.2 152.3 182.3
7 7 768 181.9 176.3 182.2 163.8
8 8 318 174.2 152.7 138.3 176.2
9 9 255 180.4 172.6 165.0 172.2
10 A 2134 159.3 154.8 159.4 181.1
11 B 852 169.0 167.3 172.4 184.9
12 C 165 168.6 140.9 127.8 170.6
13 D 1736 172.1 165.8 169.4 169.8
14 E 49 140.7 142.5 149.4 178.7
Total No. of Samples = 11,766
on the map are just the "selected" areas for computing the accuracy of correct
classification. One can see clearly that the overall performance would be less
than the cited 87.5 percent, but about 80 percent or less, if the overall
performance is based on the entire field. It is also noted from the LARS
classification results, as well as the map, that red clover, hay, and alfalfa
are fairly similar to each other, with very little discrimination among them.
Comparing the classification map by the composite clustering technique (Figure
3-33) with the LAR's results and with the ground truth aerial photo (Figure
3-1), the overall performance by the composite clustering technique over the
entire field is close to 80 percent. That is, the overall performance by the
LARS supervised classification technique and by the unsupervised composite
technique are comparable. However, it is important to recall that no training
fields or any other ground truth information has been employed in applying the
unsupervised technique.
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SAMPLE NUMBER 115
SCAN NUMBER
LEGEND:
A - A l f a l f a , S C - Corn T H - Hay W 0 - Oats DA P - Pasture RC R - Rye
Soybeans Timothy Wheat Diverted Acres Red Clover
Figure 3 -1 . AIR PHOTO OF PURDUE FLIGHT LINE C-1 (SCAN 587-797)
This page is reproduced again at the back of
this report by a different reproduction method
so as to furnish the best possible detail to the 3-8
user.
NORTHROP SERVICES. INC.
Figure 3-2. PROBABILITY HISTOGRAM OF CHANNEL 1 (0.4-0.44 Am)
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3200
2800
2400
2000
PROBABILITYDENSITYFUNCTION
1600
1200
800
400
0
60 80 100 120 140 160 180 200 220 240 260
DATA RANGE
Figure 3-3. PROBABILITY HISTOGRAM OF CHANNEL 6 (0.52-0.55 pm)
3-10
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1
1
PROBABILITYDENSITYFUNCTION
60 80 100 120 140 160 180 200 220 240 260
DATA RANGE
Figure 3-4. PROBABILITY HISTOGRAM OF CHANNEL 10 (0.66-0.72 pm)
3-11
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2800
PROBABILITYDENSITYFUNCTION
60 80 100 120 140 160 180 200 220 240 260
DATA RANGE
Figure 3-5. PROBABILITY HISTOGRAM OF CHANNEL 12 (0.8-1.0 vm)
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Figure 3-34. CLASSIFICATION MAP BY SPURDUE iUAUO.,AAAU4AUNIVESITALAR'S UPERVISED109ccscr BAYE -S C.SSLASSIFICATIONsSS TECHIQUC(Rf. 1, p 40
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LABORAIORY FUR AGRICULTURAL REMOTE SENSINGPURDUE UNIVERSIIY
*0* LARSYSAA ILLUSTRATION *e
CLASSIFICATION STUDY .. SERIAL NO. 105807300CLASSIFICATIION DAIE .. JULY 5, 1968
RUN NUMBER -----26600061
FLIGHT LINE---- CL
TAPE NUMBER---- 102
CLASSES CONSIDERED
SYMBOL CLASSS SOYBN IC CORN I0 OATSW wHEAT IR RD CL IA ALFALFAv RYEA BR SOIL
W WHEAT II
THRESHOLDS14.90014.90014.90014.90014.90014.90014.90014.90014.900
GATE ------ 6/28/66
TIME ------ 1229
ALTIIUDE-- 2600 FEET
FEATURES CONSIDERED
CHANNEL NO.I6
1012
SPECTRAL BAND0.40 0.440.52 0.550.66 0.720.80 1.00
CLASSIFICATION SUMMARY BY TEST FIELDS
CLASS
7-27 SOYB
1Z-7 SOYB
IZ-2 SOYU
12-3 SOYB
7-23 SOYB
12-9 CUORN
7-1 OATS
7-2 WHEA
12-10 wHEA
12-6 RED
1-29 RED
7-28 RED
RED
7-24 ALFA
7-24 . ALFA
TOTAL
NO OFSAMP S
401
513
ISU152
546
58c
310
260
546
713
12a
£ b5
385
19U
266
5s'uY
PCT.CORCI
63.4
19.3b8.2
91.3
94.0
84.9
93.5
90.1
80.2
96.9
98.9
86.8
93.2
83.d
NO UF SAMPLES CLASSIFIED INTO
SOYB
258
456
119
671
531
25
0
0
0
2
0
0
0
0
0
2062
CORN
12
4
11lL
8
4
553
0
0
0
3
0
0
17
0
4
OATS
84
31
18
0
0
l
314
17
0
27
4
2
S
2
19
wHEA RED ALFA RYE
O 0 0 0
O 0 0 O
0 0 0 0
O 0 0 0
I 0 O O
0 1 0 0
0 56 0 0
243 0 .0 0
492 0 0 48
0 572 109 0
u 124 0 0
0 173 0 0
O 334 24 0
O .11 177 0
0 18 223 0
616 524 736 1289 533
SOIL
0
0
0
0
10
0
0
0
0
0
0
0
O
0
0
O
0
0
0
0
THRS
53
22
2
73
0
8
0
0
6
0
0
0
5
0
2
48 10 171
OVERALL PERFORMANCE z 87.5
Figure 3-35. TABULATION OF CLASSIFICATION RESULTS OF TEST FIELDS(Ref. 10, p. 41)
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Section IV
UNSUPERVISED CLASSIFICATIONS OF NATURAL TERRAIN TYPES
To give a more critical test and establish the capability of the un-
supervised clustering technique, the most complex remote sensing data ever
collected by the University of Michigan Multispectral scanner under NASA's
sponsorship was chosen - the aircraft survey data over the Yellowstone
National Park test site. These data have been kindly made available by
Dr. W. H. Smedes, U. S. Geological Survey, Denver, Colorado.
4.1 DATA DESCRIPTION
These particular data were collected by the multispectral 12-channel
scanner onboard an aircraft at the altitude of about 6,000 feet (ref. 7). The
scanner resolution is 3 milliradians. Each scan line contains 220 ground
resolution cells about 20 feet square. The multispectral scanner recorded
simultaneously 12 channels of spectral bands reflecting from the earth's
surface between 0.4 and 1.0 pm. These spectral bands are listed in Table 3-1.
For the purpose of comparison with Purdue LARS's supervised classification
results, only four channels were used, i.e., channels 2, 9, 10 and 12. These
4 channels have been determined by LARS' feature selection program to be the
optional channels (based on the divergence criterion) for this particular set
of data (ref. 10).
4.2 PRELIMINARY DATA ANALYSIS
Figure 4-1* shows a gray-scale video display of reflectance for channel 9
(0.62-0.66 pm) over the area. Also shown in the figure is the ground truth
survey. Containing water, bedrock, forest, kame, till, talus and cloud shadow
over forest. Detailed physical descriptions of these terrain types are given
in reference 10. It is clear that the terrain feature is very complex, and
that many parts of the test site do not have clear-cut boundaries between
F'igures 4-1 through 4-26 and Tables 4-1 and 4-2 are presented foZZllowing thetext at the end of this section.
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different terrain types. This is quite different from the Purdue C-1 Flight
Line in which the boundaries between different crop types are very clear (see
Section III).
Figures 4-2 through 4-5 show the univariate probability histograms for
these four channels for the data set from scan 200 through 500. Very few
distinct modes show in each histogram, which indicates that the spectral signa-
tures from different terrain types overlap each other, and that more than one
channel would be needed for discrimination among different terrain types.
Figures 4-6 and 4-7 show the corresponding digital gray-scale plots of
the test area in channels 2 and 10, respectively. Comparing these gray-scale
plots with the gray-level video display, one can see clear correspondences for
several main areas with large contrast. It should be noted that the complement
of the numerical value with respect to 256 is proportional to the spectral
radiance collected by the scanner. Hence, the larger the numerical number as
indicated by the interval, the smaller the spectral radiance. Figures 4-8
through 4-13 show the scatter plots between channels 2, 9, 10 and 12. The
numeric 1 indicates the number of samples in each spectral cell to be between
1 and 9; numeric 2 is between 10 and 19 and so forth. From these scatter
plots, one can note that channels 2, 9 and 10 are linearly correlated, while
channel 12 is not correlated with the other three channels. This implies that
the terrain types possess quite different reflectance characteristics in the
visible and reflected IR ranges. It is also noted that no distinct cluster
is visible in these scatter plots, which, in turn, indicates the overlapping
of spectral signatures of different terrain types as observed from the
invariate probability histograms.
Figure 4-14 shows a boundary map of the test area obtained by using the
boundary enhancement principle (ref. 8). In this map, the symbol (-) indi-
cates that the enhanced spectral difference among adjacent resolution elements
lies between the mean enhanced value over the entire target area plus one
standard deviation and the mean plus two standard deviations. The symbol (+)
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indicates that the enhanced difference lies between the mean plus two standard
deviations and the mean plus three standard deviations. The symbol (x) in-
dicates that the enhanced difference is greater than the mean plus three
standard deviations. Finally, the area with the enhanced difference smaller
than the mean plus one standard deviation is left blank. In other words, the
blank area implies a relatively homogenous region, while the area indicated
by the symbol (x) has the largest spectral contract between adjacent resolu-
tion elements. These boundaries are found to be in good correspondence with
the gray-level video display in Figure 4-1.
4.3 UNSUPERVISED CLASSIFICATION OF TERRAIN TYPES
Figures 4-15 through 4-24 show the intermediate and final unsupervised
classification maps of the test area by the composite statistical and K-mean
technique. The purpose of presenting the intermediate results is to show
how the composite technique performs at its various stages so that some types
of automatic decision logic may be formulated and built into the present com-
puter program to achieve a more autonomous unsupervised classification scheme.
For processing the set of data, a maximum of 18 classes was initially
specified for the statistical sequential clustering. The output from this
processing after only one pass of the entire data set is a set of mean spec-
tral signatures for 18 initial classes. (Note: If the K-mean clustering had
been used, 17 passes of the entire data set would have been required to
estimate the 18 initial cluster centers. Further, these initial cluster
centers would not be as accurate as those obtained by the statistical sequen-
tial technique). The choice of a maximum of 18 classes for the data was based
on a rough examination of the video display of the test area (Figure 4-1),
and 18 classes were believed to be sufficient. Actually, the number is twice
as large as the main terrain types indicated by the ground truth survey map
(Figure 4-25) supplied by Dr. W. H. Smedes, U. S. Geological Survey. The
study is presently underway on how to decide on a suitable number of initial
classes for any given data set. This study will be presented in the final
contract report.
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The above mean spectral signatures of the 18 initial classes were input
to the K-mean clustering program for further improvement. Figures 4-15 and
4-16 show the classification maps after one and two iterations, respectively,
of these initial classes. A comparison of these two maps shows that the
majority of class 7 is grouped into class M in the second iteration. Other-
wise, no noticeable change has occurred in the second iteration. From the
ground truth map, one finds that classes M and 7 both belong to the same class
forest. The very few changes between the first and second iteration classifi-
cation results indicates that the cluster centers have very rapidly converged
to their true locations in the color space. In turn, this may imply that the
initial cluster centers obtained by the statistical sequential clustering
using only one pass of the data are quite good indeed. Hence, by only three
passes of the data sets, i.e., one for the statistical sequential clustering
and two for the K-mean clustering, good classification of the data set has
been accomplished. By the K-mean clustering, more than 20 passes of the data
set would have been required and the clustering results would not be as
accurate as those obtained by the composite technique.
The ground truth map (Figure 4-25) does not give a resolution element-
by-resolution element terrain type specification. Instead, it shows only the
average percentage descriptions of terrain types. For example, one area at
the upper left-hand corner shows 80 percent rubble and 30 percent forest (i.e.,
.7 R, .3 F). Thus, it is not possible to make an exact assessment of the
classification accuracy. Furthermore, the ground truth map gives only nine
terrain types. For the easier comparisons, the 17 classes resulting from the
K-mean program were further reduced one class at a time to nine classes. The
criterion used for merging classes is the simple Enclidean distance in the
color space. In other words, first the pairwise distances of all the 17
classes are calculated, and then the two classes which have the shortest
distance among all possible pairs are combined. This process is repeated on
the resulting 16 classes and so on. The classification maps for each of these
merging processes are shown in Figures 4-17. through 4-24. The actual merging
processes are summarized in Table 4-1. Two meeting arrows denotes the merging
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of two classes at that particular stage of merging with the new symbol for the
merged class given above the arrows. The single arrow denotes the change of
class symbol, for example, from class 2 to class = at the 3rd stage of merging.
The latter change of class symbol is due to the computer program coding and is
of no significance.
The physical identities of each of the nine classes are determined for
this case by comparing the unsupervised classification map (Figure 4-24) with
the ground truth survey map (Figure 4-25). The result is shown also in Table
4-1. In actual operation, the physical identities will be established by
checking a small percentage of each class on site. As mentioned earlier, it
is not possible for this set of data to make an exact assessment of classifi-
cation accuracy. The overall accuracy is about 80 percent. This comparison
was made by Dr. W. H. Smedes who has the detailed knowledge on this test site
(ref. 4). The main misclassification came from mingling two terrain types -
water and talus even prior to merging classes. The mean spectral signatures
of water and talus are given below, as obtained from small areas in the test
site,
Ch-2 Ch-9 Ch-10 Ch-12
Water 85.3 84.2 81.7 67.2
Talus 77.3 75.5 82.1 50.1
which are quite similar to each other for comparing with the mean spectral
signatures of the other 16 classes before merging of classes (Table 4-2).
4.4 COMPARISON WITH SUPERVISED CLASSIFICATION
For a better appraisal of the performance of the composite clustering
technique, the unsupervised classification map (Figure 4-24) is compared with
the supervised classification map obtained by Purdue University's LARS using
the maximum likelihood method over the same test area (refs. 4 and 10). The
supervised classification map is shown in Figure 4-26. The accuracy of the
classification is found to be about 86 percent as also reported by Dr. Smedes.
This accuracy is higher than the 80 percentby the composite clustering tech-
nique. However, to obtain this higher accuracy, much human intervention and
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manipulation were needed by (a) knowing where to pick the typical training
areas for every type of terrain of interest, (b) classifying the entire set
of data and calculating the classification accuracy, and (c) new training
areas were selected when the accuracy was found to not be good enough. In
contrast to this iterative processing with close human supervision, the unsu-
pervised classification map (Figure 4-14 or Figure 4-24) were obtained with
very little human intervention, only specifying the maximum number of initial
classes to begin with the processing. The computation time required for both
the LARS supervised and unsupervised composite classification methods are
about the same.
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This page is reproduced again at the back of this report by a different reproduction method so as to furnish the best possible detail to the user. 4-7
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4-17
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Table 4-2. MEAN SPECTRAL VECTORS FOR 18 CLASSES - YELLOWSTONE NATIONAL PARK
MEAN SPECTRAL VECTORCLASS CLASS NUMBER OF MEAN SPECTRAL VECTORNUMBER SYMBOL SAMPLES CH-2 CH-9 CH-1O CH-12
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
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$
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4
M
+
H
z
2
3
TOTAL = 16,650 Samples
1120
823
836
1625
923
1043
905
1326
433
975
1518
866
1272
319
779
1059
828
-I
110.32
91.45
84.19
62.49
93.29
76.32
116.27
71.94
86.99
121.65
67.15
103.71
57.26
136.69
80.16
53.86
78.89
135.89
107.25
96.25
58.83
115.51
83.36
145.62
75.05
86.66
155.46
67.50
125.70
51.61
175.95
101.62
45.50
89.27
150.51
115.83
103.65
58.65
128.92
88.19
163.33
77.68
89.57
175.72
68.46
138.82
50.94
204.94
116.34
44.74
93.61
83.4
81.89
76.18
58.80
82.11
73.18
86.24
69.70
56.18
88.62
67.66
82.40
53.01
93.73
77.46
42.20
85.93
4-33
TR-1075
NORTHROP SERVICES. INC.
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(CH-2, 9, 10 AND 12)
4-34
TR-1075
NORTHROP SERVICES, INC.
Section V
CONCLUSIONS
In this study, a new composite statistical sequential K-means clustering
technique has been developed. It was applied for automatic unsupervised
classification of remote multispectral sensing data over the Yellowstone
National Park test site and Purdue C-1 Flight line. It was found that the
classification technique is about 80 percent correct on both data sets, com-
pared to 86 and 85 percent classification accuracy, respectively, obtained by
the Purdue LARS supervised maximum likelihood classification method. In view
of the very little human intervention required for the application of the
unsupervised classification, the slightly lower accuracy seems still rather
good. With these two demonstrations on actual data, it seems fair to assert
that the new composite technique may be useful for processing various earth
resources survey data. From the operational viewpoint, it is also believed
that the unsupervised technique is more feasible than the supervised techniques.
There is still some automatic decision logic needed to be developed in
the present unsupervised technique such as (a) to decide the number of classes
merging optimally suited for any given data set, and (b) to examine the homo-
geneity of every class established. These two decision logics are closely
related and are important for establishing a completely autonomous nonsuper-
vised classification system. The investigating of such decision logics and
implementing them into the computer programs is presently underway. Effort is
also underway to integrate the statistical sequential clustering and general-
ized K-means clustering computer programs into a single, more efficient pro-
gram for operation type data processing. The above developments will be
reported in the future.
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Section VI
REFERENCES
1. Nagy, G., Shelton, G. and Talaba, J., "Procedural Questions in SignatureAnalysis", Proc. 7 International Symposium on Remote Sensing of En-vironment, May 17-21, 1971.
2, Haralick, R. M. and Kelly, G. L., "Pattern Recognition with MeasurementSpace and Spatial Clustering for Multiple Images", Proc. IEEE, Vol. 57,No. 4, April 1969.
3. Smedes, H. W., Linnerud, H. J., Hawks, S. G., and Woolaver, L. B.,"Digital Computer Mapping of Terrain by Clustering Techniques Using ColorFilm as a Three-Band Sensor", Proc. 7 International Symposium on RemoteSensing of Environment, May 17-21, 1971.
4. Smedes, H. W., Su, M. Y., Jayroe, R. R. et al., "Mapping of Terrain byComputer Clustering Techniques Using Multispectral Scanner Data andUsing Color Films", Proceedings of NASA 4 th Earth Resources ProgramReview, January 17-21, 1972.
5. Schell, J. A., "A Comparison of two Approaches for Category Identificationand Classification Analysis From an Agricultural Scene", paper presentedat the Conference on Earth Resources Observation and Information AnalysisSystem, the University of Tennessee Space Institute, Tullahoma, Tennessee,March 13-14, 1972.
6. Turner, B. J., "Cluster Analysis of MSS Remote Sensor Data", paper pre-sented at the same conference as ref. 5.
7. Su, M. Y., Jayroe, R. R., and Cummings, R. E., "Unsupervised Classifi-cation of Earth Recources Data", paper presented at the same conferencesas reference 5.
8. Fu, K. S., Landgrebe, D. A., and Phillips, T. L., "Information Processingof Remotely Sensed Agricultural Data", Proc. IEEE, Vol. 57, No. 4,April 1969.
9. Su, M. Y., Pooley, J., and Hand, C., "Statistical Algorithms and Com-puter Programs for Multispectral Observations", NASA CR-103182, December1970.
10. Smedes, H. W., Pierce, K. L., Tanguary, M. G., and Hoffer, R. M., "DigitalComputer Terrain Mapping from Multispectral Data, and Evaluation ofProposed Earth Resources Technology Satellite (ERTS) Data Channels,Yellowstone National Park: Preliminary Report", AIAA Paper No. 70-309,March 1970.
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11. Su, M. Y., "Algorithms for Sequential Classification of MultispectralObservations into Homogeneous Populations", Northrop-Huntsville Memoran-dum M-794-808, October 1970.
12. Su, M. Y. and Krause, F. R., "Automatic Processing of MultispectralObservations", AIAA Paper No. 71-234, AIAA Integrated Information SystemConference, February 17-19, 1971.
13. Su, M. Y., "A Generalized K-means Algorithm for Clustering MultispectralObservations", Northrop-Huntsville Memorandum M-794-964, June 1971.
14. Gasey, R. C. and Nagy, G., "Advances in Pattern Recognition", ScientificAmerican, Vol. 224, No. 4, April 1971, pp. 56-71.
15. Gasey, R. C. and Nagy, G., "An Autonomous Reading Machine", IEEE Trans.Computers, Vol. C-17, No. 5, May 1968.
16. MacQueen, J., "Some Methods for Classification and Analysis of Multi-spectral Observations", Proc. Fifth Berkeley Symposium Math. Statisticsand Probability, Vol. 1, pp. 281-297, 1967.
17. Ball, G. H., "Data Analysis in the Social Sciences: What about thedetails?", Proc. Fall Joint Computer Conf. pp. 533-559, December 1965.
18. Purdue University, "Remote Multispectral Sensing in Agriculture", LARSVol. 1, No. 4, October 1968.
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