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ombining Panchromatic and Multispeetral

Imagery from Dual Resolution Satel l i te Instruments

J O H N C . P R I C E

US DA -AR S Rem ote Sensing Research Laboratory ASR I Bel tsvil le Maryland 2070 5.

A proc edure is develo ped for combining h igh spatial resolu tion panchromatic data with low er resolution mult ispectral

data in order to produce h igh spatial resolu tion d ig i tal data in mult ispectral |onn . Data s imulat ing the French SPOT

satel l i te were processe d to resemble h igh al t i tude aerial photography, but image ar tifacts can ham per p hoto in terpreta-

t ive m ethods .

ntroduct ion

(USDA, 1982) . At p resen t pho to in t e rp re-

t a t i o n o f ae r ia l p h o t o g r ap h y i s b e i n g co n -

S i n ce t h e l au n ch o f Lan d s a t 4 i n 1 98 2 s i d e r ed f o r a s s es s in g l an d u s e an d l an d

t h e s c i en t if i c co m m u n i t y h a s b een p r o - co n d i t i o n . A p p l i ca t i o n o f au t o m a t ed t ech -

v i d e d w i t h h i g h q u a l i t y d i g it a l i mag es o f n i q u es t o d i g i ta l sa t e ll it e d a t a m ay b e an

t h e ea r t h s s u r face . I n t h e m i d an d l a te e f f ec t i v e t o o l a t s o me f u t u r e t i me ,

1980s da t a o f 10 m spa t i a l r eso lu t ion wi l l de pe nd in g on the qua l i t y a nd cos t o f

b e acq u i r ed f r o m t h e S a t el li te P o u r l O b - s a t e ll it e d a t a , an d t h e av a il ab il it y o f p r o -

s e r v a t i o n d e la Te r r e ( S P O T) , an d f u t u r e ced u r e s f o r ex t r ac t in g t h e d e s i red as se ss -

La nd sa t sa t e l l i tes wi l l add a 15 m pa n- m en t o f l a rge a reas .

ch r o m a t i c b a n d t o th e c u r r en t 3 0 m I n t h is p ap e r a t e ch n i q u e is d ev e l o p ed

Th em a t i c M ap p e r ch an n e ls . S u ch d a t a f o r co m b i n i n g d u a l r e s ol u ti o n d i g it a l d a t a ,

p r o v i d e o p p o r t u n it i e s f o r d e t a il e d o b - a s f r o m S P O T a n d t h e p l a n n e d T h e m a t i c

s e r v a t i o n o f p r o cess e s a t t h e ea r t h s M ap p e r s , t o p r o d u ce h i g h s p a ti a l r e so l u -

s u r f ace , an d f o r m ap p i n g o f u r b an a r ea s t i o n mu l t i s p ec t r a l d a ta . Th e g o a l o f t hi s

an d de scr ip t ion o f l and use. As po in t ed w ork i s essen t i a l l y equ iva l en t t o t ha t o f

ou t i n a r ec en t pa per by C l i che e t a l. C l i c he e t a l. (1985) , exce p t t ha t t he ana l -

(1985) , t he SPO T da ta m ay be p rocesse d ys i s is based on s t a t is t ica l p roper t i es i n

b y i m a g e e n h a n c e m e n t a lg o ri th m s t o y i e ld t h e d a t a , r a t h e r t h a n a n a d h o c a p p r o a c h

v i s ua l p r o d u c t s r e s emb l i n g co lo r ae r ia l w h i c h s eek s an o p t i mu m i mag e d i sp l ay .

p h o t o g r ap h y . I n p a r t i cu l a r , t h e an a l y t ic ap p r o ach m ay

A l t h o u g h m an y ap p l ica t io n s o f s u ch s e r v e a s a b a s is f o r d e s i g n o f f u t u r e ea r t h

d a t a w i l l i n v o l v e m ap p i n g o f u r b an an d o b s e r v i n g s y s tems , an d t h e r e s u l tan t

s u b u r b an a r ea s, t h e r e a r e p o s s ib l e u s e s p r o d u c t s , r ep r e s en t i n g a r eco n s t r u c t i o n o f

requ i r ing bo th h igh spa t i a l r eso lu t ion and h igh sp a t i a l r eso lu t ion mu l t ispec t ra l da t a

l a r g e a r ea co v e r ag e . F o r ex amp l e , e ach 5 f r o m a s amp l ed d a t a s et , a r e s ui tab l e f o r

y ea r s t h e S o il C o n s e r v a t i o n S e r v ice o f t h e f u r t h e r n u m er i ca l s tu d ie s , s u ch a s co m -

U . S . D ep a r t m en t o f A g r i cu l t u r e ca r ri e s p u t e r c l a ss if ic a ti o n . Th e b asi s f o r t h e

o u t an i n v e n t o r y o f t h e co n d i t i o n o f n o n - t e ch n i q u e d ep e n d s o n t h e s u b s tan t ia l re -

f ed e r a l r u r a l l an d s i n t h e U n i t ed S t a te s d u n d an cy ex i s ti n g i n mo s t h i g h r e s ol u ti o n

0 0 3 4 4 2 5 7 / 8 7 / 0 . 0 0

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2/10

120 I C PRICE

m t d t i s p e c t r a l s a te l li te d a t a . T h i s r e - I n t h is p a p e r i n f o r m a t i o n i s u s e d i n

d u n d a n c y i m p l i e s t h a t p r o p e r l y c h o s e n t h e o ri g i n al s e n s e o f S h a n n o n ( 19 4 8) , i .e .,

d a t a s u b s e t s , a s f r o m S P O T , m a y b e a s a s t a t is t i c al r e p r e s e n t a t i o n o f t h e v a i l -

p r o c e s s e d t o y i e l d d a t a s i m u l a t i n g t h a t a b i l i t y i n a d a t a se t. A s h a s b e e n p o i n t e d

f r o m a l es s s o p h i s t i c a t e d b u t m o r e p o w e r - o u t ( T e r H a r r , 1 96 1; P r i ce , 1 9 8 4 b ) , t h e

f u l ( a n d e x p e n s i v e) o b s e r v i n g i n s t r u m e n t , t e r m e n t r o p y is o f t e n u s e d i n t h e e n -

D e s p i t e t h e a t t r a c t iv e n e s s o f t h i s a p - g i n e e r i n g l i t e r a t u r e a s a s y n o n y m f o r t h e

p r o a c h s o m e s ac r if ic e s a r e e x p e c t e d w h e n w o r d i n f o r m a t i o n , desp i t e the pos s ib i l -

t h e d a t a a c q u i r e d b y a r e m o t e i n s t ru m e n t i ty o f c o n f u s io n w i t h th e t h e r m o d y n a m i c

r e p r e s e n t a s a m p l e r a t h e r t h a n a c o rn - d e f i n i t i o n o f e n t r o p y . I n t h is p a p e r i n fo r -

p l e t e c o v e r a g e h i g h r e s o l u t io n m u l t i s p e c - m a t i o n r e fe r s t o t h e v ar i a b il it y o f a s e t o f

t r a l d a t a s e t. V a r i a b i li t y a s s o c i a te d w i t h a o b s e r v a t i o n s h a v i n g a p r o b a b i l i t y d i s t i l-

n u m b e r o f u n k n o w n c au se s c a n n o t b e b u t i o n p /,

f u l l y r e m o v e d , s o t h a t r e s u l t a n t d a t a

p r o d u c t s h a v e a r e s i d u a l n o i s e c o m p o - DN,,~

n e n t . T h e c o n s t r u c t i o n o f h i g h s p a ti al H = - Y'~ p i l o g 2 p i ,

r e s o l u t i o n d a t a s e ts f r o m c o m b i n e d p a n - ~= 0

c h r o m a t i c a n d m u l t i s p e c t ra l d a t a i s di s-

c u s s e d i n t h e n e x t s ec ti o n. I n t h e t h i r d w h e r e t h e P i r e p r e s e n t t h e p r o b a b i l it y o f

s e c t i o n t h e l i m i ta t io n s o f t h e p l a n n e d a g i v e n m e a s u r e m e n t v a lu e , o f t e n c a ll ed

t e c h n o l o g y f o r i m a g e a n a ly s is a r e i l- d i g i ta l n u m b e r o r

D N .

F o r e x a m p l e , a

l u s t r a t e d t h r o u g h a n e x a m p l e d r a w n f r o m s e ri es o f o b s e r v a ti o n s c o r r e s p o n d i n g t o

r a n d o m n u m b e r s i n t h e r a n ge o f 0 - 2 5 5 ,

T h e m a t i c M a p p e r d a t a . I n s o m e c a s e s

w i t h e a c h v a l u e h a v i n g a p r o b a b i l i t y o f

i m a g e a r t i f a c t s m a y b e p r e s e n t w h i c h a r e

1 / 2 5 6 , h a s a n i n f o r m a t i o n v a l u e o fd i s t r a c t i n g a t b e s t a n d w h i c h m a y c o n -

f u s e p h o t o i n t e r p r e t a t i o n . 255

H = - Y~ ( 1 / 2 5 6 ) I o g 2 ( 1 / 2 5 6 ) = 8 bi t s .

E s t i m a t i o n o f 1 0 m M u l t i sp e c tr a l D a t a / = 0

I n s e v e r a l r e c e n t p a p e r s ( P r ic e , A s d i s c u s s e d b y P r i c e ( 1 9 8 4 a) ,

1 9 8 4a , b ) t h e s u b s ta n t ia l r e d u n d a n c y o f T h e m a t i c M a p p e r d a t a f r o m a g r ic u l tu r a l

L a n d s a t a n d S P O T s i m u l a ti o n d a t a h a s a r e as g e n e r a ll y a re r a t h e r r es t r ic t e d in

b e e n i l lu s t r a te d b y c o m p u t a t i o n o f t h e r a n g e , a n d t e n d t o g r o u p a b o u t a m e a n

i n f o r m a t i o n c o n t e n t o f a c t u a l d a t a, a s v a l u e , y i e l d i n g a n i n f o r m a t i o n c o n t e n t o f

c o m p a r e d w i t h t h e i n f o r m a t io n w h i c h 4 - 5 b i ts p e r p ix e l p e r s p ec tr a l c h a n n e l

c o u l d , i n p r i n c i p l e , b e a c q u i r e d b y t h e i n s t e a d o f t h e t h e o r e t i c a ll y p o s s i b le 8 b i ts .

r e m o t e se n s o r. I t a p p e a r s t h a t i n a t y p i c al C o r r e l a t i o n a m o n g s p e c t r a l c h a n n e l s fu r -

a g r i c u l tu r a l s c e n e t h e i n f o r m a t i o n c o n - t h e r r e d u c e s t h e i n f o r m a t i o n c o n t e n t o f

t e n t r e p r e s e n t s a b o u t 4 0% o f t h e d a t a m u l t i s p e c t r a l d a t a. T h e c h o i ce o f s p e c tr a l

l e n g t h o f s t a n d a r d f o r m a t d i g it a l d a ta . c h a n n e l s f o r t h e S P O T i n s t r u m e n t r e su lt s

T h u s , i n p r i n c i p le , s u c h d a t a c o u l d b e i n a v e r y h i g h c o r r e la t io n a m o n g c h a n n e l

e n c o d e d a n d c o m p r e s s e d b y a p p r o x i- 1 ( 0 . 5 0 - 0 . 5 9 /L m ), c h a n n e l 2 ( 0 . 6 1 - 0 . 6 8

m a t e l y 6 0 % w i t h o u t r e d u c i n g t h e u t i li ty / zm ) , a n d c h a n n e l 4 , th e p a n c h r o m a t i c

o f t h e d a t a. c h a n n e l ( 0 . 5 1 - 0 . 7 3 / z m ) . T h u s t h e c o u n t

8/10/2019 Price 1987

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C O M B I N I N G D U A L R E S O L U T I O N S A T E L L I T E I M A G E R Y 1 21

v a l u es f r o m each p ix e l i n o n e o f t h e s e s ma l l e r. I n f ac t, t h e 10 m S P O T d a t a can

c h a n n e l s m a y b e u s e d t o p r e d i c t t h e c o u n t b e e n c o d e d i n t h e s p a c e cr a ft i n a n

v a l u e o f t h is p i x e l i n t h e o th e r s , t o w i t h i n 8 - 5 - 5 - 8 f o r m a t f o r f o u r s u ccess i ve p ix els ,

a s ma l l p r o b a b l e e r ro r . A j o in t p r o b ab i li ty w i t h t h e 5 - b it d a t a w o r d s r ep r e s en t i n g

f u n c t i o n m a y b e c o m p u t e d f ro m w h i c h i t t h e d i f f e r e n c e b e t w e e n t h e a c t u a l c o u n t

is p o s s ib l e t o e s t i ma t e t h e r ed u c t i o n o f v a l u e an d th e i n te r p o l a t ed v a l u e d e r i v ed

i n f o r m a t i o n co n t en t a s s o c ia t ed w i t h t h e f r o m t h e e n d - p o i n t 8 -b it w o r d s . O b v i -

r e d u n d an t s p ec t r a l ch an n e l s M a l i la , o u s ly , t h e 5 - b it w o r d s can n o t , i n g en e r a l,

1985). I t i s t h i s r edu nd an cy whic h per - r e t a in t he f lf ll acc ura cy o f t he 8 -b it va l-

mi t s t h e e s t ima t i o n o r r eco n s t r u c t i o n o f u e s , b u t a l o o k u p tab l e w i t h ex p an d ed

h igh spa t i a l r eso lu t i on m ul t i spec t r a l da t a . r ang es fo r t he l a rge and improb ab le) d i f -

B ecau s e t h e s ca le o f 1 0 an d 2 0 m r e s o - f e r en ce v a l u es is u s ed t o r e t a i n th e m a j o r

lu t i on da t a is m uc h smal l e r t han t he t yp i - pa r t o f t he i n fo rm at ion o f t he fu ll 8-b it

ca l sca l e o f spa ti a l var i ab i li t y fo r m os t da t a .

l and a reas t h ere i s a p rono un ce d t end - As i l l u s t r a t ed i n F ig . 1 , t he dua l r eso lu -

e n c y fo r s p a ti a l r e d u n d a n c y i n t h e i m a g e t io n i m a g e d a t a f r o m S P O T a n d t h e f u -

d a t a , i .e ., e ac h p i xe l t en d s t o b e s imi l a r t o t u r e Th em a t i c M ap p e r s co m b i n es t h e

t h e s u r r o u n d i n g o n es. Th i s s u g g est s t h e s p ec t r a l r ed u n d a n c y d u e t o t h e o v e r lap o f

use o f a su i t ab l e t r ans fo rm at ion , e .g ., a t he sp ec t r a l in t e rva l s i n t he v i sib le , wi th

d e l t a o r d i f f e r en ce t r an sf o r ma t i o n , i n t h e s p a t ia l r ed u n d an c y o f t h e p an c h r o -

w hic h ea ch p ixe l va lue exce p t t he f ir s t is m at i c cha nne l , as fou r 10-m p ixe ls l ie

rep l ac ed by i ts d i f f e renc e wi th i ts ne igh - w i th in a s i ng l e mul t i spec t r a l p ixel . B e-

b o r i n t h e d a t a s t r eam. Th is h a s th e e f fec t c au s e t h e 1 0-m d a t a a r e v e r y h i g h l y co r r e -

o f r ep l ac i n g l a r g e r n u m b er s r ep r e s en t i n g l a t ed w i t h ch an n e l s 1 an d 2 , b u t m u ch

t h e s a te f li te o b s e r v ed r ad i an ces, w i t h t h e l es s co r r e l a t ed w i t h ch an n e l 3, t h e t w o

d i f f e r en ces , w h i ch a r e g en e r a l l y mu ch ca s e s w i l l b e d i s cu ss ed s ep a r a te l y . Th e

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m e t h o d o l o g y t o b e d e v e l o p e d r e se m b l es I f b , , 4 i s z e ro , t hen th i s r e su l t i s t he same

t h e p r o c e d u r e u s e d i n t h e t r e a t m e n t o f a s t h a t u s e d i n t h e S P O T s i m u l a ti o n p r o -

t h e S P O T s i m u l a t io n d a t a ( S P O T I m a g e g r a m ( S P O T I m a g e C o r p . , 1 98 3, p . 2 5 ),

Co rp . , 1983) . i . e. ,

C o m b i n a t io n o f c h a n n el s / 4 j / [ i l

1 and 2 and panchromat ic data x i~ j = X ~ x 0 . 2 5 ~ x .

F ro m s t a t i s t i c a l ana lys i s o f the SP O T L j 1 .1

d a t a o n e f i n d s t h a t d a t a f r o m c h a n n e l s 1

a n d 2 , a n d t h e p a n c h r o m a t i c c h a n n e l , t o H o w e v e r , b i s g e n e r al ly n o n z e r o .

b e n u m b e r e d 4 , a r e a ll h i g h ly c o r r el a te d . T h e v a l i d it y o f t h is p r o c e d u r e w a s

t e s t e d u s i n g S P O T s i m u l a t i o n d a t a f r o m

T h u s

W a s h i n g t o n , D C . S i n c e 1 0 - m f o u r - c h a n -

X ~ = a , , , , X ' ~

+ b . . . . m :~ n = 1 , 2 , 4 n e l d a t a w e r e n o t a v a il ab l e, t h e v e r if i ca -

t i o n w a s c a r r i e d o u t b y a v e r a g i n g t h e

w h e r e t h e s u p e r s c r i p t r e p r e s e n t s t h e t h r e e c h a n n e l s o f 2 0 -m d a t a a n d t h e s i ng l e

c h a n n e l n u m b e r , t h e s u b s c r i p t i t h e p i xe l c h a n n e l 1 0 -m d a t a t o 4 0 a n d 2 0 m , re -

n u m b e r , i .e ., o n a n i m a g e li n e, a n d a , , , , s p e c t i v e l y . A p p l i c a t i o n o f t h e a b o v e p r o -

a n d b ,, ,, a r e d e t e r m i n e d b y a b e s t- f it c e d u r e t o t h e a v e ra g e d d a t a p r o d u c e d

p r o c e d u r e t o a s a m p l e o f t h e d a t a. T h i s 2 0 m v a lu e s f o r c h a n n e l s 1 a n d 2 , w h i c h

r e l a t i o n s h i p i s s u f f i ci e n t to e s t i m a t e t h e w e r e c o m p a r e d w i t h t h e o r ig i na l t r u e v a l-

1 0 - m m u l t i s p e c t r a l v a l u e s f r o m t h e c h a n - u e s a t 2 0 - m r e s o lu t i o n . R e s i d u a l e rr o r s

w e r e o f t h e o r d e r o f 2 c o u n t s a s c o m -

n e l 4 d a t a w i t h a h i g h d e g r e e o f ac c u r a c y .

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u s i n g t h e k n o w n v a l u e o f t h e 2 0 - m p i x el s 2 0 c o t m t s i n t h e o r i g in a l d a t a , i . e. , t h e

f o r c h a n n e l s 1 a n d 2 , a s f o ll ow s : L e t t h e 2 0 - m c h a n n e l 4 d a t a d e s c r i b e d 9 9 % o f t h e

v a r i a n c e o f 4 0 - m d a t a i n c h a n n e l s 1 a n d

s m a l l e r (1 0 m ) p i x el s b e i d e n t i f i e d b y x i , ,

j = 1 - 4 . T h e n u s i n g t h e c h a n n e l 4 v a lu e s 2 . T h i s s u g g e s t s t h a t t h e p a n c h r o m a t i c

t o e s t i m a t e 1 a n d 2 , d a t a c a n p r o v i d e a n e x c el le n t e s t i m a t e o f

t h e 1 0 m v a l u e s in c h a n n e l s 1 a n d 2 .

X I ~ -

a m 4 x 4 j + b , , 4

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Combinat ion of

Channel 3 and panchrom at ic data

w h e r e 8 i j i s t h e e r r o r i n t h e e s t i m a t e d

va lue x i'~. H o w e v e r , t h e a v e r a g e o f t h e T h e p r o c e d u r e d e s c r i b e d i n t h e p r e v i -

f o u r s u b p i x e l v a l u e s m u s t e q u a l t h e m e a - p u s s u b s e c t i o n i s u n s a t i s f a c t o r y fo r t h e

s u r e d v a l u e X~ o f t h e 2 0 - m p i xe l. T h u s c h a n n e l 3 d a t a b e c a u s e t h e v i si b le a n d

o n e m a y c o m p u t e a c o r r e c t io n f a c to r f = n e a r i n f r a r e d s p e c tr a l c h a n n e l s a r e n o t

X m

, , h

/ [ 0 . 2 5 F ~ j = l x ~ , ] s u e t h a t t h e c o r r e c t l i n e a r l y r e l a t e d . I n t h e S P O T S i m u l a t i o n

s u m i s o b t a i n e d f o r t h e fo u r 10 -m p ix el s, P r o g r a m c u b i c c o n v o l u t io n i n t e rp o l a t i o n

i .e ., w a s u s e d t o c r e a t e 1 0 -m p i xe l s f r o m t h e

2 0 - m d a t a . T h i s m e t h o d d i s c a r d s e n t i r e ly

x ;'j = X m ( a . , 4 x 4 + b m 4 ) /

t h e i n f o r m a t i o n p r o v id e d b y t h e p a n c h r o -

m a t i c c h a n n e l o f d at a . I n a d d i t i o n , it d o e s

[ 0 . 2 5 ~ _ _ ( a m 4 x 4 + b m 4 ) ] .

n o t s a t i s f y t h e i n t e g r a l p r o p e r t y t h a t t h e

1 f o u r 1 0 -m p i x e ls m u s t a v e r a g e t o t h e 2 0 - m

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COMBINING DUAL RESOLUTION SATELLITE IMAGERY 23

v a l u e . A s c a l e d o n e - d i m e n s i o n a l e x a m p l e w h e r e ~ 3 ( x 4 ) is t h e m e a n v a l u e o f x 3 f o r

is a p p r o p r i a t e ; i f a m e a s u r e m e n t S is a ll p i c t u r e e le m e n t s i n t h e i m a g e w h i c h

o b t a i n e d a t x = 0 , r e p r e s e n t i n g t h e i n t e r - h a v e t h e g i v e n v a lu e x 4. T h e s e 2 5 6 v a l u e s

v a l ( - 1 / 2 , 1 / 2 ) , t h e n i n t e r p o l a t e d f o r

x 3 I )

f o r I = 0 - 2 5 5 a r e o b t a i n e d w h i l e

v a lu e s S ~ 1 a t

- 1 / 4 ,

r e p r e s e n t i n g t h e t h e

a , , n

a n d

b r a n

v a l u e s a r e b e i n g d e -

i n t e r v a l ( - 1 / 2 , 0 ) a n d S ~2 , a t +

1 / 4 ,

r i v e d f o r c h a n n e l s 1 a n d 2 . D e r i v a t i o n o f

r e p r e s e n t i n g t h e i n t e r v a l ( 0, + 1 / 2 ) , m u s t 1 0 - m d a t a f o r c h a n n e l 3 i s t h u s a s i m p l e

a v e r a g e t o t h e o r i g in a l v a l u e S . H o w - l o o k u p o f t h e p r e d i c t e d v a l u e, g i v e n f r o m

e v e r , f r o m c u b i c c o n v o l u t i o n t h e v a l u e s t h e k n o w n v a l u e o f x 4. T h e r e s u l t in g f o u r

a r e g i v e n b y S ~1 = 0 . 07 0 S i _ 2 + 0 . 2 2 7 S i _ 1 n e s t e d p i x e ls a r e t h e n c o r r e c t e d a s in B

+ 0 .8 6 7 S ~ - 0 . 0 23 S ~ + 1 a n d S i2 = - f o r t h e f a c t t h a t t h e i n i ti a l e s t i m a t e o f t h e

0 . 0 2 3 S i_ 1 + 0 . 8 6 7 S i + 0 . 2 2 7 S ~ 1 - 0 .0 7 0 S i 2 ,

s u m d o e s n o t g e n e r a l l y a g r e e w i t h t h e

w i t h t h e a v e r a g e e q u a l t o - 0 .0 35 (S ~ 2 + m e a s u r e d v a l u e .

S ~ 2 ) + 0 . 1 0 2 ( S ~ _ 1 + S i 1 ) + 0 . 8 6 7 S ~. W e T h i s t e c h n i q u e w a s a p p l i e d to a v e r -

n o t e i n p a s s i n g t h a t c u b i c c o n v o l u t i o n a g e d 1 0- a n d 2 0 - m d a t a a s d e s c r i b e d i n

i s n o l o n g e r u n i q u e l y d e f i n e d , a s t h e c o e f - t h e p r e v i o u s s u b s e c t i o n . T h i s p r o c e d u r e is

f i c i e n t s u s e d f o r i n t e r p o l a t i o n o f L a n d s a t o n l y m o d e r a t e l y s u c c es s fu l , w i t h t h e p r e -

M S S d a t a w e r e m o d i f i e d a t s o m e p o i n t i n d i c t e d v a l u e s f o r c h a n n e l 3 a c c o u n t i n g fo r

t i m e d u r i n g a p p l i c a ti o n t o T h e m a t i c a b o u t 7 5 % o f t h e v a r i an c e o f t h e o r ig i n al

M a p p e r d a t a ( F i sc h e l , 1 9 84 ) T h e s e d a t a . S e v e r al a l te r n a t iv e a l g o r it h m s w e r e

w e i g h t i n g c o e f f i c i e n ts a r e g i v e n b y t e s t e d , w i t h n e a r l y i d e n t i c a l c o n c l u s io n s ;

i . e . , t h e r e d o e s n o t s e e m t o e x i s t a g e n e r a l

p r o c e d u r e w h i c h c a n d e r i v e h i g h l y a c c u -

w 1 = a d 1 - d ) 2 ,

r a t e v a l u e s f o r 1 0 - m p i x e l s o f c h a n n e l 3 .

w 2 = a + 2 ) d 3 - a + 3 ) d 2 + 1 , T h e r e a s o n i s r e a d i ly e s t a b l i sh e d f r o m

i n s p e c t i o n o f t h e tw o - d i m e n s i o n a l h i s to -

w 3 = - a + 2 ) d ~ + 2 a + 3 ) d Z - a d ,

g r a m o f c h a n n e l 3 d a t a v s . c h a n n e l 4

w 4 = a d 2 1 - d ) ,

d a t a , a s i l lu s t r a t e d i n F i g . 2.

E v i d e n t l y l o w v a l u e s o f r e f l e c t i v i t y i n

c h a n n e l 4 m a y b e a s s o c i a t e d e i t h e r w i t h

w i t h a = - 1 f o r M S S d a t a a n d o l d e r l o w v a l u e s o f r e f le c t i v it y i n c h a n n e l 3 , a s

T h e m a t i c M a p p e r d a t a , a n d a = - 1 / 2 f r o m s h a d o w s o r w a t e r , o r w i t h h i g h v a l-

f o r n e w e r T h e m a t i c M a p p e r d a t a . H e r e d u e s o f r e f le c t iv i t y in c h a n n e l 3 d u e t o

is t h e d i s t a n c e ( 0 ,1 ) f r o m p o i n t x 2 a n d x 3 v e g e t a t i o n . L o w c o r r e la t io n b e t w e e n

i n t h e s e r i e s o f f o u r p o i n t s ,

x 1 , x 2 , x 3 , x 4 .

s p e c t r a l c h a n n e l s i s f a v o r a b l e f o r s p e c t r a l

A m o r e g e n e r a l r e l a t io n s h i p t h a n t h e d i f f e r e n t i a t i o n a n d c l as s if ic a ti o n , b u t u n -

l i n e a r f i t o f t h e p r e v i o u s s u b s e c t i o n b e - f a v o r a b l e f o r i n f e r e n c e o f h i g h s p a ti a l r e s-

t w e e n t h e 1 0 -m d a t a a n d c o re g i s t er e d o l u t i o n m u l t i s p e e t ra l v a lu e s f r o m d u a l

2 0 - m d a t a is o b t a i n e d b y c o m p u t i n g t h e s p a t ia l r e s o lu t i o n d a ta . T h e c h a n n e l 3 a m -

e x p e c t e d ( m e a n ) v a l u e f o r c h a n n e l 3 f o r b i g u i t y is e s p e c i a l l y s e v e r e i n t h e

e a c h g i v e n v a l u e i n c h a n n e l 4 , a f t er t h e W a s h i n g t o n , D C s c e n e w h i c h w a s u s e d

1 0 - m d a t a h a v e b e e n a v e r a g e d t o 2 0 m . f o r t h i s s t u d y , a s m a n y c i t y p i xe l s c o n t a i n

T h u s b o t h s h a d o w s o f b u i ld i n g s a n d t re e s. T h e

p r o b l e m i s e x p e c t e d t o b e l e s s s e v e r e f o r

x ~ i x 4 )

= ~ 3 ( x 4 ) , a g r i c u l tu r a l s c e ne s , b u t t h e a c c u r a c y o f

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124 J. C. PRICE

VEGETATION

SHADOWS

COUNTS

255

255

0 CFt AI~NEL 4

FIGURE 2. Two-dimensional histogram of SPOT channels 4 and 3

illustrating that a value in channel 4 does not specify adequately the

value in channel 3 especially for low values in channel 4.

t h e p r o ced u r e d ep e n d s o n t h e n a t u r e o f s ec t i o n . C o n s i d e r ab l e d e t a i l is ev i d en t ,

t h e s cen e , i n g en e r a l , s u g g es t i n g t h a t t h e i n c r ea s ed s p a ti a l r e s o-

A l t h o u g h d e r i v a t i o n o f t h e f i tt i n g l u t i o n ( 1 0 m) o f S P O T d a t a w i ll b e o f

p a r a m e t e r s f o r t h e s p a ti a l i n t e rp o l a t io n g r ea t v a l u e f o r s t ud i e s o f u r b an l an d u s e

ap p e a r s t o r eq u i r e an ad d i t io n a l s t ep o f an d f o r p h o t o i n t e r p r e t a t i o n g en e r a ll y .

co m p u t a t i o n , s u ch s ta t is ti c a l p r o p e r t ie s F i g u r e 4 s h o w s t h a t ev en v e r y s ma ll f ea -

m ay b e r ead i l y o b t a i n ed d u r i n g ca l ib r a - t u r e s m ay b e in f e r r ed f r o m t h e 10 -m d a t a

t i o n a n d p r o d u c t i o n p r o c e s s in g o f th e u n d e r o p t i m u m c o n di ti on s .

s a t e l li t e d a t a b e f o r e d i s tr i b u ti o n t o d a t a U n f o r t u n a t e l y , ev en t h e h ig h s pa t ia l

user s ( e .g . , NAS A, 1978). r eso lu t ion da t a a re suscep t ib l e t o sam -

p l ing l imi t a t i ons due to wi th in p ixe l aver -

A r t if a c ts a n d S p a ti al I n t e r p o l a ti o n a g i n g . T h i s a v e r a g i n g c a n p r o d u c e

p ec u l i a r e f fec t s w h en ev a l u a t ed b y p h o t o -

W i t h t h e ad v en t o f h i g h e r s p a ti a l r e s o - i n t e r p r e t a t i o n . F r o m can a ls o n M ar s t o

lu t ion d ig i t a l da t a i t is poss ib l e t o reso lve l i near s as m ap pe d b y geo log i st s, l i ne seg -

n o t o n ly e v i d e n c e o f m a n s i n fl u e n c e o n m e n t s p r o d u c e a s tr o n g r e s p o ns e f r o m

t h e ea r t h s s u r f ace , s u ch a s ag r i cu lt u r a l t h e h u m an v i s u a l s y s tem. C au t i o n mu s t

f ie l d s , d am s , s t r ee t an d r o ad p a t t e r n s , b e ex e r c i s ed w h en h ig h co n t r a s t l in ea r

e t c . , b u t a l so co n s i d e r ab l e s p a ti a l d e t a i l i n f ea t u r e s a r e p r e s en t i n i mag e d a t a . T h e

thes e f ea tu res . F igu re 3 i l l u st r a tes co m - fo l lowing exa m ple and i ts quan t i t a t ive ex -

b i n ed p an ch r o m a t i c an d mu l t i s p ec t ra l p l an a t i o n i ll u s tr a t e t h e p o t en t i a l p r o b l ems

i m ag e r y o f t h e n a t i o n s c ap i t o l i n t h e a s s o c i a t ed w i t h n a r r o w l i n ea r f ea t u re s a s

Di s t r i c t o f Co lum bia , as der iv ed f rom the w el l as a poss ib le so lu tion fo r ima ge

m e t h o d o l o g y d es c r i b ed i n t h e p r ev i o u s r e s t o r a t io n . H o w ev e r , t h e r e ap p ea r s t o b e

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COMBINING DUAL RESOLUTION SATELLITE IMAGERY 125

FIGURE 3. Washington, DC: the Capitol building is at the cente r of the 2.5 km square area.

n o g e n e r a l p r o c e d u r e f o r e li m i n a ti n g r e c o r d e d b y t h e L a n d sa t 4 T h e m a t i c

a r t if ac t s ex ce p t o v e r s amp l i n g , i .e ., i mag - M ap p e r o n 1 2 D ece m b er 1 98 2 ( S cen e I D

i n g eac h p o i n t mo r e th an o n ce . O f co u r s e , 4 0 1 49 - 17 4 4 4 ). Th e p ecu l i a r l ad d e r li k e ap -

o v e r s a m p l i n g p r o v i d es v e r y l it tl e ad - p ea r an ce r e su l ts f r o m t h e s ca le o f t h e

d i t i o n a l i n f o r m a t i o n ab o u t t h e l an d d i s p l ay , w h e r e mag n i f i ca t io n p e r mi t s d i s-

s u r f ace , s e r v i n g mo s t l y t o s mo o t h o u t t h e c r i m i n a t i o n o f i n d iv i d u a l d e t ec t o r r e -

i ma g e d e f ec t s w h i ch o ccas io n a l ly r e s u lt s p o n s es a s t h ey c r os s o v e r t h e r o ad

f rom the 1 - 1 sam pl ing o f i n s t rum en t s su r faces . F ig ure 6 i ll u s tr a tes an i dea l i zed

s u c h a s S P O T a n d t h e L a n d s a t T h e m a t i c n a d i r v i e w o f a n a r r o w d a r k l in e a r f e a tu r e

M ap p e r s . i n F i g . 6 ( a ), t h e av e r ag i n g e f f ec t o f t h e

F i g u r e 5 i ll u st ra t e s t h e ap p ea r an ce o f l a r g e p i x e l s i z e an d t h e r e s u lt an t d e t ec t o r

dark , na r ro w s t ri ps , i .e . , para l le l roads r espons es fo r t h ree ad j ace n t de t ec to r s i n

s ep a r a t e d b y s ev e ra l h u n d r e d m e t e r s, a s F i g . 6 ( b ), an d an an a l y ti c s o lu t io n i n F i g.

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1 26 J . C . P R I C E

F I G U R E 4 . U n d e r o p t i m u m c o n d it i o ns f e a tu r e s a s s m a l l

a s a u t o m o b i l e s m a y b e r e c o g n i z e d in t h e S P O T 1 0 m

d a t a . C a r s a r e n o t r e s o l v e d i n t h e m a t c h i n g a e r ia l p h o -

t o g r a p h y b u t t h e i r p l a c e m e n t w i t h r e sp e c t to l a n e

m a r k e r s i s s u f f i c i e n t f o r p o s i t i v e i d e n t i f i c a t i o n .

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C O M B I N I N G D U A L R E S O L U T I O N S A T E L L I T E I M A G E R Y 12 7

F I G U R E 5 . T h e m a t i c M a p p e r i m a g e o f a d i v i d e d h i g h w a y 1 5 k m w e s t o f B l y t he , C A . T h e

s t r i p i n g r e p r e s e n t s

r e s p o n s e s o f i n d i v i d u a l d e t e c t o r s .

O rr 3 I S C A N - /

I - l L ~ '~ '~R 0 A D

I -

N A D I R V I E W

S

/

n.. -.~j,~.~ f l /

Lkll-- ~ I

I -- :3 ~ ~ A'~-.~ . . . .

U.I 0 ~ '~

,,.,,

S C A N ' -

a . W = d s in 0

01-3

f ~ ~ t / == ; a r = a + f - a ) L I W ) c o s O

I I

F I G U R E 6 .

S c h e m a t i c r e p r e s e n t a t i o n

o f a s i n g l e n a r r o w l i n e r o a d )

a s v i e w e d f r o m a b o v e a ) , t h e

c o r r e s p o n d i n g o u t p u t s f o r a d j a c e n t

d e t e c t o r s b ) , a n d t h e s o l u t i o n fo r t h e r e l a t iv e d e t e c t o r / r o a d a n g l e , t h e

w i d t h o f t h e r o a d , a n d t h e r e f l e c t i v i t y o f t h e r o a d , g i v e n

i d e a l i z e d

m e a s u r e m e n t s

c ) . N o te t ha t t he r e su l t

i s n o t

p r o d u c e d b y

s c a n

d i r e c t i o n ;

i . e . , t h e s a m e i m a g e w o u l d b e p r o d u c e d

b y s c a n m o t i o n i n

t h e p e r p e n d i c u l a r d i r e c t i o n .

6 c ) , a s s u m i n g a b a c k g r o u n d r e f l e c t i v i ty g r o u n d , e t c . , s t r o n g l y s u g g e s t u s i n g a v e r -

a , a n d a r o a d r e f l e c t iv i t y g i v e n b y a r. a g e s f r o m a n u m b e r o f a p p r o p r i a t e ly

A l t h o u g h s o l u t i o n f o r 0 , w , a n d a r i s s h i f t e d i m a g e l i n e s . I f t h e c o n f i g u r a t i o n i s

p o s s i b l e in t h i s i d e a l i ze d c a s e , g i v e n t h e r e c o g n i z a b l e b y a n i m a g e a n a l y s t, t h e n

c o n t i n u o u s t r a c e f r o m o n l y t h e o n e d e t e c - m a g n i f i c a t i o n a n d i n t er p o l a ti o n m a y b e

t o r , i n p r a c t i c e t h e u n c e r t a i n t y i n e s t i m a t - u s e d t o r e s t o r e t h e l i n e a r f e a t u r e s t o

i n g t h e r o u n d i n g w i d t h d ) , t h e c h a n g e t h e i r a c c u s t o m e d a p p e ar a n ce . W h i le a n

i n d e t e c t o r o u t p u t a s c o m p a r e d t o b a c k - i m a g e a n a l y s t m a y r e a d il y id e n t i f y t h is

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128 J C PRICE

p a r t i cu l a r t y p e o f i mag e a r t if ac t , t h e R e f e r en ces

s i t u a t io n i n g eo me t r i ca l l y co m p l ex u r b a n

area s , g ive n di f fe r ing s izes an d shap es of Cl iche, G. , Bonn, F. , and Tei llet , P . 1985),

bu i ld in gs an d road s, e tc . , i s no t favorable. In tegrat ion of the SPOT panchromat ic

Sim ple in te rpo lat io n of the im ag e does chann el in to i ts mul ti spectral mode for

no t im pro ve the d i sp l ay o f f ea tu res such image sharpness enhancement , Photo-

as t ha t i n f i gu re 5 . gram m . Eng . Rem ot e Sens. 3:311-316.

Fischel, D. 1984), Validation of the Them atic

Mapper radiometric and geometric correla-

Co nc lus ion an d Ou t look t ion a lgori thms , IEE E Trans . Geosci . R e-

m o t e Sens. GE-22:237-242.

In th is p ap er the tech niq ue s for pro- Mal ila, W. A. 1985) , Compar ison of the in-

du ci ng eq uiv ale nt h igh reso lut ion mul t i - formation contents of Landsat TM and MSS

s p ec t r a l d a t a h av e b ee n d i s cu ss ed i n t h e D a t a, Photogramm. Eng. Re mo te Sens.

9:1449-1457.

co n t ex t o f t h e i n f o r ma t i o n co n t en t o f t h e

i m a g e d a t a . T o t h e e x t e n t t h a t s u ch N A S A 1 9 78 ), Heat Capaci ty Mapping Mis-

s ion U ser s G uide J. Price, Ed.), Goddard

me t h o d s a r e f ea s i b l e t h e r e ex i s t a n u mb er

of pro m isin g de velo pm en ts: Space Fl ight Center , Greenbelt , MD, 120

pp., revised 1980.

1 . The des ign o f be t t e r sensors , wi th

th e c ho ice of spect ral in tervals , spa- Pr ice, J . C. 1984a) , Compar ison of the infor-

mation content of data from the Landsat-4

t ial reso lut ion , an d prec is ion sele cted The ma t ic M apper and the Mul ti spectral

on the bas i s o f t he i n fo rm at ion con- Scanner , IEEE Trans. Geosci . Remote Sens.

t e nt of th e da ta vs . the cost of in- GE-22:272-281.

s t ru m en tat ion an d da ta han dl ing . Pr ice, J . C. 1984b) , Stati st ical analysis of

2 . T he use of co din g tech niqu es, bo th SPOT simulation data and comparison wi th

in th e spa cec raf t an d in g rou nd Landsat-4 Them at ic Mapper data , In SPOT

proc essin g, to red uc e da ta volum es Simulation Applications Handbook, Am.

an d s im pl i fy the task of im ag e ana l - Soc. of Photogrammetry , Fal l s Church, VA.

ysis an d in ter pre tat ion , pp . 157-164.

3 . T he de ve lop m en t of spec ial ized in- Shannon, C. E. 1948) , A mathemat ical the-

t e rpo la t ion an d d i sp l ay t echn iques o ry o f communica tion , Bell Syst. Tech. I .

t o b r in g ou t t he m ax im um deta i l i n 27 :379-423 and 623-656 .

d ig i t a l da t a , u s ing hu m an gu id anc e SPOT Image Corp . 1983), 1983 U.S . SPOT

if nec essa ry . T he pho to en ha nc e- Simulation Campaign, Auxi l iary Informa-

m en t t ec hn iq ues o f C l i che e t al . t ion Package , 90 pp .

1985) are in th is dom ain . Ter Haar , D. 1954) , Elements of Statistical

C l ea r l y , t h e n ew g en e r a t i o n o f s a t e l l i t e Mechanics , Reinhart, N ew York, p. 161.

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Received 25 February 1986; revised 19 September 1986