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UNSUPERVISED CLASSIFICATION OFREMOTE MULTISPECTRAL SENSING DATA

172-27204

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Prepared for:

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

GEORGE C. MARSHALL SPACE FLIGHT CENTERAero-Astrodynamics Laboratory

UNDER CONTRACT NAS8-27364

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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.

ii

NORTHROP SERVICES. INC. TR-75

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

iii


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.

iv

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NORTHROP SERVICES. INC.

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

v

TR-1075


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 . . . . . . . . . . . . . .






3-20 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

Page

. 2-2

. 2-7


LIST OF ILLUSTRATIONS (Continued)

Figure Title

3-23 CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 17 CLASSES . . . . . . . . . .



3-26 CLASSIFICATION MAP BY THE GENERALIZED K-MEANSTECHNIQUE WITH 14 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

vii

TR-1075

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

3-42


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

viii


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

4-1

4-2

NORTHROP SERVICES, INC. TR-1075

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

1-1


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.

1-2

TR-107?5NORTHROP SERVICES. INC. TR-1075

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.

1-3

TR-1075NORTHROP SERVICES. INC. TR-1075

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

2-1


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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

2-3

TR-1075


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

2-4


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

2-5


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.

2-6

NORTHROP SERVICES. INC. _

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.

2-9


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.

2-10


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.

3-1


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

3-6



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.

3-7


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.


Figure 3-2. PROBABILITY HISTOGRAM OF CHANNEL 1 (0.4-0.44 Am)

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NORTHROP SERVICES. INC. -

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

: f

TR-1075


1

1


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

i

TR-1075


2800


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)

3-12

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Figure 3-34. CLASSIFICATION MAP BY SPURDUE iUAUO.,AAAU4AUNIVESITALAR'S UPERVISED109ccscr BAYE -S C.SSLASSIFICATIONsSS TECHIQUC(Rf. 1, p 40

3-41


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)

3-42

_ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

'/


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.

4-1


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 (+)

4-2


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.

4-3


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

4-4


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

4-5


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.

4-6


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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4-25


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4-26

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Figure 4-24.UNSUPERVISED CLASSIFICATION MAP AFTER THE EIGHTH MERGING WITH 9 CLASSES

4-30


YELLOWSTONE NATIONAL PARK

.59' .$F

.AT

LEGEND,B- BOG

F -FOREST

K-GLACIAL KAME

R-VEGETATED ROCK RUBBLE

S - SHADOWT- GLACIAL TILL

Ta- TALUS

W-WATER

Figure 4-25. GROUND TRUTH SURVEY MAP

4-31

X-SBEDROCK

~~~~~~NORTHROP SERVICES. INC. .TR-1075NORTHROP SERVICES. INC.

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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

)I

W

V

$

/

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


. - BEDROCK EXPOSURE$ - VEGETATED ROCK RUBBL

- - GLACIAL TILL

W - WATER

BLANK - THRESHOLD

1 . 1

H - SHADOWS

.E 8 - TALUS

= - GLACIAL KAME

/ - FOREST

110 . 220

. i . I! ji iiliT i.., ...................

.:. ... .: : ':. .. , . . ....':'!" .... ,.! ;i::F'''" !'lliii!ii. ,, ____________:: i

~... ...... ........ .....

480 ................. Figure 4-26. LARS CLASSIFICATION: YELLOWSTONE NATIONAL PARK

(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.

5-1

TR-1075


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.

6-1


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.

6-2

unsupervised classification of remote multispectral ... · i (f t , lt tr-220-1075 april 1972...

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