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2 1
R e l a t i o n a l
D e s c r i p t i o n s
i n
P i c t u r e
P r o c e s s i n g
H.
G. Barrow
and R. .
Popplestone
Department
of
Machine
I n t e l l i g e n c e and
P e r c e p t i o n
U n i v e r s i t y
o f Edinburgh
Abstract
In
t h i s
paper
we
d e s c r i b e
work
o n
t h e
r e c o g n i t i o n
b y
computer of
o b j e c t s
viewed b y
a
TV
camera. We ave w r i t t e n a
program which w i l l
r e c o g n i z e a
range
of
b j e c t s i n c l u d i n g
a
cup, a
wedge,
a hamm er , a
p e n c i l , and a p a i r of
s p e c t a c l e s .
A i s u a l
image,
r e p r e s e n t e d
b y
a 64.x
6 4 a r r a y of l i g h t
l e v e l s ,
i s r s t
p a r t i t i o n e d
i n t o
connected
r e g i o n s .
These
r e g i o n s
a r e
chosen
t o
have
w e l l -
d e f i n e d e d g e s .
Having
chosen t h e
r e g i o n s , t h e
program
then computes
p r o p e r t i e s of and
r e l a t i o n s
between r e g i o n s .
P r o p e r t i e s
i n c l u d e shape as
d e f i n e d
b y F o u r i e r
a n a l y s i s of h e
s
t f r
e q u a t i o n of h e
bounding
u r v e . A y p i c a l r e l a t i o n
between
r e g i o n s i s t h e
d e g r e e of d j a c e n c y .
F i n a l l y ,
t h e
program matches
t h e
a c t u a l
r e l a t i o n a l
s t r u c t u r e of
h e r e g i o n s
of
t h e
p i c t u r e
w i t h
i d e a l
r e l a t i o n a l
s t r u c t u r e s
r e p r e s e n t i n g v a r i o u s o b j e c t s ,
u s i n g a
h e u r i s t i c
s e a r c h
p r o c e d u r e , and s e l e c t s t h a t
o b j e c t
whose r e l a t i o n a l
s t r u c t u r e
b e s t
matches
t h e
a c t u a l
p i c t u r e .
INTRODU TION
In
No vem ber
1 9 6 9 ,
a M a r k
i
robot
d e v i c e Barrow
and S a l t e r 1970) was
connected
o n - l i n e
t o t h e
I C I ,
4130 computer of h e
Department of
Machine
I n t e l l i g e n c e
and P e r c e p t i o n ,
U n i v e r s i t y of
Edinburgh.
The primary
s e n s o r
of h e d e v i c e i s a TV camera, and t h e
computer m a y
sample
t h e
p i c t u r e a t
4096
p o i n t s
i n a 6 4 x 6 4 a r r a y , and r e a d
t h e
p i c t u r e
b r i g h t n e s s a s one
o f 16 e v e l s .
T h e
d e v i c e
i s
a v a i l a b l e
under
t h e
Multi
-P o e
t i m e - s h a r i n g
implementation
of
h e
P
- 2 language
B u r s t a l l ,
C o l l i n s , and o p p l e s t o n e 1 9 7 1 ) . T h e
program
l i b r a r y
c o n t a i n s
f u n c t i o n s f o r
o p e r a t i n g t h e
d e v i c e :
f o r example, h e f u n c t i o n
c a l l
PICINT X,
) e t u r n s t h e
b r i g h t n e s s
l e v e l of
i c t u r e p o i n t x , y).
377
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PPRO CHES
FOR PICTURE ANALYSIS
History
In t h e
f i e l d of o b j e c t
r e c o g n i t i o n , t h e r e seems
t o have
been
much
p r e -
o c c u p a t i o n w i t h p l a n e- s u r f a c e d
o b j e c t s ,
presumably
b e c a u s e t h e y p r o j e c t
onto
a
e t i n a
i n
a
e l l - d e f i n e d
and
s i m p l e
manner;
n t e r n a l
r e p r e s e n t a t i o n s
of
t h e s e s o l i d s
a r e e a s i l y c o n s t r u c t e d ;
and t i s e a s y t o deduce s t r u c t u r e of
t h e
s o l i d from a p i c t u r e . For
t h e s e r e a s o n s
t h r e e r o b o t p r o j e c t s
i n t h e
United
S t a t e s , a t S t a n f o r d
Research
I n s t i t u t e , S t a n f o r d
U n i v e r s i t y ,
and MIT,
p r e s e n t l y
r e s t r i c t
t h e
environment
of h e i r
d e v i c e s t o t h a t
of
u b e s , wedges,
and t h e l i k e .
P i c t u r e s of
l a n e
- s u r f a c e d o b j e c t s
a r e
u s u a l l y
i n t e r p r e t e d
b y i t t i n g s t r a i g h t
l i n e s t o
edges n
t h e
p i c t u r e ,
and then d e n t i f y i n g
p a r a l l e l o g r a m s and t r i a n g l e s
as a c e s
of
o l i d s , and hence t h e
s o l i d s t h e m s e l v e s .
Guzman s program SEE
Guzman
968), which
decomposes
a
i n e
drawing
of
a
s c e n e i n t o s e t s
of
e n c l o s e d
a r e a s , each
s e t c o r r e s p o n d i n g
t o a
s i n g l e
body,
erforms
x t r e m e l y
w e l l , and
produces a n a n a l y s i s
which s
remarkably
s i m i l a r to
t h a t of a
h u m a n
o b s e r v e r .
I t
depends,
however, upon t h e assump-
t i o n
t h a t
a l l
o b j e c t s
i n view
a r e p l a n e
s u r f a c e d .
R o b e r t s
program
(Roberts
1965), which r e c o g n i z e s p l a n e- s u r f a c e d
o b j e c t s ,
does
so
by
having a n i n t e r n a l 3-D
model of
a n
o b j e c t ,
computing
p r o j e c t i o n s from
i t
and
m a n i p u l a t i n g them
u n t i l a i t
i s o b t a i n e d
w i t h
t h e
p i c t u r e .
E x t e n s i o n t o
i r r e g u l a r
o b j e c t s i s
b y s y n t h e s i z i n g t h e
model
from a
l a r g e
number of
i m p l e o n e s .
We
ad
d i r e c t
e x p e r i e n c e of t h e
problems of t h e l i n e f i n d i n g
and f i t t i n g .
Murphy
( 1 9 6 9 )
had
i n v e s t i g a t e d
a p p l i c a t i o n
of h e u r i s t i c
s e a r c h
t o p i c t u r e
i n t e r p r e t a t i o n , t o
economize on t h e
amount of computation
r e q u i r e d . His
program d i d not
p r o c e s s
t h e
e n t i r e p i c t u r e
i n pseudo- p a r a l l e l , but
was
g u i d e d
t o
look a t
p a r t s
of t
on
t h e
b a s i s
of v i d e n c e
g a t h e r e d so f a r .
In
t h i s w a y
he
could
f i n d
t h e l i n e s of a
cube,
only
r e q u i r i n g
t o
sample
1 0
p e r
c e n t of t h e
a v a i l a b l e
p i c t u r e
p o i n t s .
Working
w i t h
Dr .M.
u r s t a l l , R a s t a l l
( 1 9 6 9 )
ook
a
e c h n i q u e of Unger,
which
d e t e r m i n e d
whether
two
graphs
were
i s o m o r p h i c ,
and
e x t e n d e d
i t t o
d e t e r m i n i n g
monomorphism
of
two
f a m i l i e s of
g r a p h s ,
t h a t i s
f i n d i n g
whether
one
f a m i l y
was
a s e t of c o r r e s p o n d i n g subgraphs of t h e
o t h e r .
B u r s t a l l
s u g g e s t e d
t h i s
might be a p p l i e d t o
p i c t u r e
i n t e r p r e t a t i o n .
A i n e
drawing
can
be
d e s c r i b e d b y r e l a t i o n s between t h e
l i n e s ,
such a s MEET,
PARALLEL, nd
so
on.
Each r e l a t i o n
d e f i n e s
a graph whose
nodes
a r e
t h e
l i n e s
of
h e
p i c t u r e ;
a n
a r c between two nodes means
t h a t
t h a t r e l a t i o n h o l d s
between
t h e
c o r r e s p o n d i n g
two
i n e s . The
s e t
of
e l a t i o n
graphs e s c r i b e s t h e
p i c t u r e ,
and
s i m i l a r l y w e
m a y
d e s c r i b e p i c t u r e s of
i n g l e
o b j e c t s .
Thus, w e
can
check
f o r
t h e
e x i s t e n c e of
a
g i v e n
o b j e c t by t r y i n g t o f i n d t h e o b j e c t
graph
- f a m i l y
a s subgraphs
of
t h e
p i c t u r e
graph
- f a m i l y ,
u s i n g
R a s ta l l s
program.
R a s t a l l
h i m s e l f t r i e d
t h i s and was
i n d e e d a b l e t o f i n d o b j e c t s
in
p i c t u r e s .
I t
seemed
t h a t a
working
o b j e c t
r e c o g n i t i o n
program
could
be
c o n s t r u c t e d
3 78
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BARROW
AND
POPPLESTONE
by
combining
t h e
programs
of
Murphy
and of Rasta1 1 but
t would
not be
a b l e t o
handle i r r e g u l a r
o b j e c t s .
At h i s time
w e
l e a r n e d of h e
work o f
r i c e
and F e n n e m a
1970)
t SRI o n
r e g i o n
a n a l y s i s . In
t h i s ,
t h e
fundamental
components of
t h e
a n a l y s i s
a r e
a r e a s
and
not
l i n e s ,
e n a b l i n g
i n f o r m a t i o n
which
i s
somewhat m o r e
g l o b a l
t o be
used i n
t h e
p r o c e s s i n g .
The
n a l y s i s
e s s e n t i a l l y
f i n d s t h e
major
a r e a s of
t h e
p i c t u r e .
I t appeared
t h a t a
d e s c r i p t i o n of t h e p i c t u r e
i n terms
of
p r o p e r t i e s of
r e g i o n s for
example,
CIRCULAR n d
r e l a t i o n s between them for
example,
ADJACENT
ould be
b e t t e r
input f o r
R a s t a l l s
program.
There
would
be
fewer
r e g i o n s
than
l i n e s ,
but
a
i c h e r
v o c a b u l a r y
of
r o p e r t i e s
and
r e l a t i o n s .
OUTLINE
OF THE
PROGRAM
The
p r o c e s s i n g
o f
a
p i c t u r e
p r o c e e d s a s
f o l l o w s :
1)
he
p i c t u r e i s f i r s t
c o m p l e t e l y
d i g i t i z e d
and s t o r e d i n
t h e
computer c o r e
s t o r e
as
an r r a y
of
64
x
64 l e m e n t s , each o f4
i t s of
r i g h t n e s s
i n f o r m a t i o n .
A l l
s u c c e e d i n g p r o c e s s i n g i s
performed
upon t h e
s t o r e d
p i c t u r e ,
b e c a u s e
s u c c e s s i v e
samples
a t a p o i n t
i n
t h e p i c t u r e
m a y
not
y i e l d t h e s a me v a l u e s
of
b r i g h t n e s s due t o
n o i s e i n t h e camera and s a m p l e r ,
or t h e s c e n e might change
w h i l e p r o c e s s i n g i s i n
p r o g r e s s .
2) he
p i c t u r e
i s
then
a n a l y z e d
i n t o important
r e g i o n s ,
i n
t w o
s t a g e s :
a) i r s t t h e
p i c t u r e
i s d i v i d e d i n t o m a n y m a l l
e l e m e n t a r y
r e g i o n s
of
p p r o x i -
mately
uniform
b r i g h t n e s s ; b) h e
e l e m e n t a r y
r e g i o n s
a r e then
merged
t o g e t h e r ,
f o l l o w i n g
a
g i v e n
h e u r i s t i c , t o produce
a
m a l l e r s e t of
a r g e r ,
and
h o p e f u l l y
s i g n i f i c a n t ,
r e g i o n s .
3)
he
e t
of
e g i o n s i s
then d e s c r i b e d
i n terms
of
r o p e r t i e s
of and
e l a t i o n s
between
t h e
r e g i o n s
that s
a s a
o l o u r e d
graph).
The
purpose
of
h i s i s
to
a b s t r a c t and
g e n e r a l i z e over
a
number
o f
i c t u r e s ,
t o
s i f t
out h e
i n f o r m a t i o n
r e l e v a n t
t o
i d e n t i f i c a t i o n
of o b j e c t s
and
d i s p o s e
of h e r e s t .
The
p r o p e r t i e s
d e s c r i b e
s h a p e s of
e g i o n s ,
t h e
r e l a t i o n s
d e s c r i b e t h e i r
s p a t i a l and t o p o l o g i c a l
r e l a t i o n s h i p s
for
example,
ADJACENT,
ABOVE,
nd
so
on).
4)
he
d e s c r i p t i o n i s then
matched a g a i n s t
a
s e t
of
t o r e d d e s c r i p t i o n s of
v i e w s
o f
o b j e c t s .
The b e s t
match
no t n e c e s s a r i l y
p e r f e c t )
i d e n t i f i e s
t h e
o b j e c t ,
by
s e t t i n g up
a
c o r r e s p o n d e n c e
between r e g i o n s
of t h e
p i c t u r e an d
r e g i o n s
of
t h e view of h e o b j e c t .
The Unger a s t a l l
graph
-matching
t e c h -
nique was found
t o
be i n a p p r o p r i a t e
h e r e , and
so
a
d i f f e r e n t
method,
a s e d
upon
a
combination
of
t h e
Graph
T r a v e r s e r , and Branch
-and
-Bound
t e c h -
n i q u e s was d e v i s e d .
I t
w i l l
be
noted
t h a t
w e
r e
s t o r i n g
a e t
o f
odels
o r r e s p o n d i n g
t o
o b j e c t s ,
and w e f i n d t h e
model
which
b e s t
a c c o u n t s f o r
t h e p i c t u r e .
However,
t h e
models
in
t h i s c a s e
a r e
of
h e
s e n s o r y
i n p u t , and not of
h e
o b j e c t
i t s e l f
as
i n
R o b e r t s
c a s e ) .
Onc e t h e i d e n t i f i c a t i o n
has
been m a d e
from
t h e
p i c t u r e ,
w e
m a y
then
r e t r i e v e
i n f o r m a t i o n
from
a
data bank
c o n c e r n i n g
t h e
o b j e c t ,
and
t h i s m a y
n c l u d e
i t s t h r e e - d i m e n s i o n a l
s t r u c t u r e .
379
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APPROACHES FOR
PICTURE ANALYSIS
Figure
1. Teacup
as seen
by
t h e TV camera,
i s p l a y e d on a monitor.
1
01254,
7W4W04567m4
312i4,n714oli149(5789417345676
4d1;:A4
4
7
4
-
..1t..4
3
.
.....
.
4,1.-4,, /T....
m
g...1411=15g.
tt
•,.Y4
5
.
4%45
1
4445454z2 X54o
:Ot.X...e4k4'44
4“•4445; 4fl.M.4 ,:tX -
4
1444
0'000.0
4 4
.44,1g4k•AIXO,X,•*:
•
•
• 4.;•
4
4,44
4 4XX5
+i
,,• ••
44A .4'4
1
.044'4k4
..-:5
•'-::• •
:
4..m4
4../
.
0
•
4
1
012347671v51234567c4
i13345o71
4
ut.134t,s7o531/3..567
6wule7
4
55/mq3123
'S4,02,4
.1
I
10
Figure
2 .
D i g i t i z e d
r e t i n a l
image'of
he input
from
t h e
TV
amera.
The
16
d i s c r i m i n a b l e b r i g h t n e s s
l e v e l s a r e r e p r e s e n t e d by
d i f f e r e n t
l i n e - p r i n t e r c h a r a c t e r s .
380
-
8/16/2019 ai computervision.pdf
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BARROW
ANDPOPPLESTONE
91234797490173456709j12S456764912345678491714567490123456784012$
1
9
7
A A
AAAAAAAAAAAAAAAAAAAAA
1
AAAAAAAAAAAAAAAAA AAAA
AAAA
9
AAAAAAAAAAAAAAAAAAAAAAAAAAAAA
7
AAAAA684488898AAAAAAA0400AAAAAA
A668088000
A4AAA6AA4AA604AAA666
BOHPHP
A8AAAAAA404AA940AAAAAAAA
AAAAAA
BP4CCRO
1
99
AAA6404404A9AAA4AAAA9AAAAA
4YCCCCC47
9
90444
AAAA94AA604444A4AAAA
mqHCCCCC1194 7
AAAAAA4AAAA6APH448H44CCC44O6
7
H41
,mP,
0044
0440dRHHHH4P4R0RHP4p444w
9
1411,
.4 19,4
dP4Hm44PH
9
4
4,4,
1
0144
1
H,
4.14444
4P.PAHRH,
40.44444P
.
6
444l4PHH4
0
44444HHRH74
9
104
7
k9H[1,OL191.4914na99914d140,
7
940401111
1
9.4406444H4y4
PO4,00
,44.14414 Hk4Hpj4
9
%.
46444949.440
,
4500
. 7
PRPH1
4
HP4
7
5
1
91239,5789
01234‘4,79961W3950709912345089012395679991234997996123
Figure 3 .
Region
a n a l y s i s of h e
r e t i n a l image i n t o s i g n i f i c a n t
r e g i o n s . Note
t h e
h o l e
i n
t h e h a n d l e ,
r e p r e s e n t e d by r e g i o n c and
t h e
shadow, e p r e s e n t e d by
t h e
r e g i o n
marked
w i t h
t h e
symbol
.
Figure
4.
Computer- s y n t h e s i z e d d e s c r i p t i o n
of
h e
r e g i o n s i n terms of
p r o p e r t y
and
r e l a t i o n a l
measures. The numbers
a s s o c i a t e d
w i t h t h e
a r c s a r e
t h e
measures,
h e
names
r e
t h e
names of
h e
r e l a t i o n s .
COMP
compactness )
s
a
hape
p r o p e r t y ,
and i s 4 r c t i m e s
t h e
a r e a d i v i d e d
by t h e
square of
h e
p e r i m e t e r . ADI a d j a c e n c y )
i s
t h e
p r o p o r t i o n
of
h e
boundary
of
h e
f i r s t r e g i o n
which
i s
a l s o a
boundary of
h e
second. Not
l l
t h e
p r o p e r t i e s and
r e l a t i o n s d e s c r i b e d
i n
t h e
t e x t a r e shown in t h i s
f i g u r e .
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PPRO CHES
FOR
PICTURE
N LYSIS
The
program
w i l l now be
d e s c r i b e d
i n more
d e t a i l .
DESCRIPTION OF THE
PROGR M
Region Finding
The
i r s t
s t a g e
of
h e
p r o c e s s
i s
t o
f i n d
t h e
i m p o r t a n t
r e g i o n s
of
h e
p i c t u r e .
A
e g i o n
i s
r e p r e s e n t e d b y a Pop
-2
e c o r d
which
n c l u d e s a
e s c r i p t i o n of t s
boundary n terms
of l e m e n t a r y
v e c t o r s , t h e
p o s i t i o n of
t s c e n t r e of
r e a ,
i t s
a r e a and
p e r i m e t e r ,
and a
membership
f u n c t i o n .
This
f u n c t i o n ,
when
a p p l i e d t o any
p o i n t of
h e
p i c t u r e , w i l l
y i e l d
a r u t h v a l u e ,
which
i n d i c a t e s
whether
h e
p o i n t l i e s w i t h i n
t h e
r e g i o n .
The
i m p l y
- c o n n e c t e d n e s s m a y
eem t i r s t
s i g h t t o
g i v e
r i s e
t o
d i f f i c u l t i e s
—
what
happens
f a
r e g i o n has a
` h o l e
i n
i t ?
In
t h i s
c a s e
t h e h o l e
i s
a l s o
a
r e g i o n , but
one
which
i e s
w i t h i n t h e
boundary of
h e l a r g e r
r e g i o n .
P o i n t s
of
t h e
i n n e r r e g i o n a r e
a l s o
members
of
h e
o u t e r
r e g i o n .
The
m a l l e s t
minimum
area)
e g i o n
t o
which
a o i n t
b e l o n g s
i s of
a r t i c u l a r i n t e r e s t ;
t i s
what
one
would
i n t u i t i v e l y
c a l l
t h e
r e g i o n
of
h a t
p o i n t . I f
one
wished t o
d e a l w i t h
m u l t i p l y- c o n n e c t e d
r e g i o n s , i t
would
be
an
e a s y
m a t t e r
t o
d e s c r i b e them i n
terms
of h e simply
- c o n n e c t e d o n e s .
The
p r o c e s s of
i n d i n g t h e
r e g i o n s i s i t s e l f
composed
of two
p h a s e s .
The
f i r s t i s
f i n d i n g a
number of
l e m e n t a r y
r e g i o n s of
h e
p i c t u r e , t h e
second
i s
merging
t o g e t h e r
r e g i o n s
which
s a t i s f y
some
c r i t e r i o n ,
u n t i l
no
f u r t h e r
merge i s
p e r m i s s i b l e
and we
a r e
l e f t w i t h
a s m a l l
number of
s i g n i f i c a n t
r e g i o n s .
B r i c e
and
Fennema
1970) s e
an
a l g o r i t h m
which
p a r t i t i o n s
t h e
p i c t u r e
c o m p l e t e l y
i n t o
e l e m e n t a r y
r e g i o n s ,
t h e d e f i n i t i o n
of
an
e l e m e n t a r y
r e g i o n
b e i n g a
connected s e t of
p o i n t s ,
which
l l
have
t h e
same
b r i g h t n e s s
l e v e l .
This
e c e s s a r i l y f i n d s
a
a r g e number
of e g i o n s .
We r i e d t h i s
a l g o r i t h m
upon
a
i c t u r e of a
cup,
i t h 64 x
64 o i n t s
and 16
e v e l s .
The number
of e g i o n s
found was
2 2 0 .
C l e a r l y
t h i s
p r o c e s s
y i e l d s
a
l o t of d a t a
f o r
f u r t h e r
pro-
c e s s i n g .
Our
t e c h n i q u e
i s not
complete but
m u ch
f a s t e r and
more
economical.
The
d e f i n i t i o n
of
an
e l e m e n t a r y r e g i o n
i s r e l a x e d
t o i n c l u d e
p o i n t s
w i t h i n
a
s m a l l
range of
b r i g h t n e s s
l e v e l s .
We
ave found
a
s u i t a b l e
range t o
be 3
l e v e l s .
Note t h a t
t h i s
r e l a x a t i o n makes
t h e
e l e m e n t a r y r e g i o n s
l a r g e r ,
t h e r e
a r e
c o r r e s p o n d i n g l y fewer
of them,
but h e y m a y
now
o v e r l a p .
I n s t e a d
of i n d i n g
an
e l e m e n t a r y
r e g i o n
f o r
each
p o i n t
on t h e
r e t i n a , we
s e l e c t a
u b s e t of
h e
r e t i n a l
p o i n t s
and i n d
t h e e l e m e n t a r y
r e g i o n s
c o n t a i n i n g
t h e s e .
In
our c a s e 256
p o i n t s
s p r e a d over t h e
p i c t u r e i n a
16 x 16
a r r a y
a r e
s u f f i c i e n t t o f i n d
s i g n i f i c a n t
r e g i o n s
i n most a s e s .
The
mechanics
of h e r e g i o n f i n d i n g
a r e
a s
f o l l o w s .
S e l e c t t h e
n e x t
s t a r t i n g
p o i n t
and
d e t e r m i n e i t s
b r i g h t n e s s .
Step
p o i n t by
p o i n t
towards
t h e
n e a r e s t
edge
of
h e
p i c t u r e u n t i l
e i t h e r
t h e
edge s
e n c o u n t e r e d , or
a
p o i n t
i s
found
which has
b r i g h t n e s s
o u t s i d e
t h e
range
of
±
rom
h e
s t a r t i n g
v a l u e . I f
t h e
edge s e n c o u n t e r e d ,
t h e
r e g i o n
we
r e
t r y i n g
t o
f i n d
e x t e n d s
o f f
t h e
p i c t u r e .
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B RROW
ND
POPPLESTONE
We
r e c u r r e n t l y
i n t e r e s t e d
only
i n
o b j e c t s
f u l l y
w i t h i n t h e f i e l d
o f
v i e w , so
t h e
r e g i o n must
be
p a r t
o f h e
background.
We
h e r e f o r e a b a n d o n t h i s r e g i o n
a n d
proceed
t o
t h e n e x t s t a r t i n g
p o i n t .
I f
a
p o i n t
not
i n
t h e r e g i o n
i s
e n c o u n t e r e d ,
we
a r e a t t h e
boundary
o f
h e
r e g i o n . Remember h i s p o i n t ,
u r n l e f t
a n d
o l l o w t h e
boundary.
The boundary
w i l l
e i t h e r
g o o f f t h e
edge
o f
h e
p i c t u r e , n
which
c a s e
we
g i v e
up a n d
proceed
t o t h e n e x t s t a r t i n g p o i n t , or w i l l r e t u r n
t o
t h e
f i r s t boundary
p o i n t .
At
t h i s
p o i n t
i t
should
be
s t a t e d
t h a t t h e
bound a r y o f
a
r e g i o n
p a s s e s
b e t w e e n
t h e
p i c t u r e p o i n t s . Each p i c t u r e p o i n t
i s
thus surrounded by four p o s s i b l e
e l e m e n t a r y bound a r y v e c t o r s . During t h e walk r ound t h e boundary n o t e i s
kept o f h e
d i r e c t i o n s o f
h e i n d i v i d u a l
s t e p s , so a
e c o r d can
be o n s t r u c t e d
o f
t h e boundary
c u r v e
i n
terms
o f h e
e l e m e n t a r y v e c t o r s . We t e p r ound i n such
a
i r e c t i o n
t h a t t h e r e g i o n
e n c l o s i n g t h e s t a r t i n g p o i n t i e s o n t h e
l e f t
Having found h e boundary u r v e , a
n u m b e r
o f r o p e r t i e s
m a y be
computed
f o r
t h e r e g i o n by
s i m p l e
n u m e r i c a l i n t e g r a t i o n
o f
v a r i o u s f u n c t i o n s
r ound
t h e
c u r v e . In
t h i s m a n n e r t h e a r e a ,
c o o r d i n a t e s
o f h e
c e n t r o i d ,
a n d a v e r a g e
b r i g h t n e s s d i f f e r e n c e ( c o n t r a s t ) a c r o s s t h e boundary a r e
c a l c u l a t e d .
I f t h e
c u r v e has been f o l l o w e d
i n
a n
a n t i- c l o c k w i s e
d i r e c t i o n , i t w i l l
b ou nd
t h e
r e g i o n
e x t e r n a l l y
a n d e n c l o s e t h e s t a r t i n g p o i n t , a n d
t s a r e a w i l l be c a l c u l a t e d
to
be p o s i t i v e . I f
t h e
c u r v e c l o s e s i n
a
c l o c k w i s e
d i r e c t i o n ,
then we
have been
f o l l o w i n g
a n n t e r n a l boundary r ound a
h o l e :
t
does
not n c l o s e t h e s t a r t i n g
p o i n t , a n d i t s a r e a w i l l be found t o be n e g a t i v e .
Regions
w i t h n e g a t i v e a r e a
a r e r e j e c t e d .
I f
t h e y a r e o f
s i g n i f i c a n t
s i z e
t h e y
w i l l be
found from s t a r t i n g
p o i n t s w i t h i n .
When
c l o s e d
c u r v e w i t h p o s i t i v e a r e a has been
found a
r e g i o n r e c o r d
i s
c o n s t r u c t e d ,
c o n t a i n i n g t h e
c u r v e
a n d
c a l c u l a t e d
p r o p e r t i e s .
heck i s
m a d e
t o
s e e
whether
t h i s r e g i o n
has a l r e a d y been n o t e d ,
by
comparing
t h e
c a l c u l a t e d
p r o p e r t i e s w i t h t h o s e o f k n o w n r e g i o n s . Two e g i o n
r e c o r d s
w i t h
t h e
s ame
c e n t r o i d ,
a r e a , p e r i m e t e r , a n d c o n t r a s t
v e r y
probably
r e f e r t o
t h e
s ame
r e g i o n . I f
h e
r e g i o n
i s u n k n ow n t i s added
t o
t h e i s t
o fk n o w n
r e g i o n s ,
a n d
a
membership f u n c t i o n
i s c o n s t r u c t e d f o r i t The membership
f u n c t i o n
c a r r i e s a n
a r r a y
o f o n e
- b i t components u s t b i g enough
t o
e n c l o s e
t h e
r e g i o n :
each
c om p o n e nt s a y s
whether
or not
t h e
c o r r e s p o n d i n g p o i n t l i e s i n s i d e
t h e
r e g i o n .
When
r e s e n t e d
w i t h t h e
c o o r d i n a t e s
o f i c t u r e p o i n t ,
h e
membership
f u n c t i o n
f i r s t
checks t o
s e e i f t l i e s w i t h i n t h e
a r r a y , a n d i f
so t looks t
up n
t h e
a r r a y .
Re g i o n
M e r g i n g
When h e
f i r s t
phase has been co mpleted a l i s t o f
r e g i o n
r e c o r d s
has been
c o n s t r u c t e d . The
number o f e l e m e n t a r y r e g i o n s found
v a r i e s
w i t h t h e
q u a l i t y a n d
c o n t e n t o f h e
p i c t u r e ,
a n d
may
e from o ne
o r
two
up t o
perhaps
f i f t y On
v e r a g e
about
twenty
e l e m e n t a r y
r e g i o n s a r e found.
The n e x t
phase
o f t h e
r e g i o n
a n a l y s i s i s p i e c i n g
t o g e t h e r
t h e
e l e m e n t a r y
r e g i o n s
t o
y i e l d a
s m a l l n u m b e r
o f
a r g e r ,
m o r e
s i g n i f i c a n t
r e g i o n s .
B r i c e a n d
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PPRO CHES
FOR
PICTURE
N LYSIS
Fennema 1970)
se two h e u r i s t i c s ,
a p p l i e d
s u c c e s s i v e l y , t h e aim
of which
i s t o prod uce convex
r e g i o n s w i t h s t r o n g
b o u n d a r i e s .
Ou r
r e s e n t
program s e s
t h e s i m p l e
h e u r i s t i c : merge two
d j a c e n t
r e g i o n s
i f
t h e
a v e r a g e
c o n t r a s t
a c r o s s
t h e
common
boundary i s
l e s s
than some
t h r e s h o l d
about . 1 l e v e l s was
found t o
g i v e
good
r e s u l t s .
Because
r e g i o n s
o v e r l a p t h e
n o t i o n of
common
boundary i s
s l i g h t l y
g e n e r a l i z e d
t o
be t h a t
p a r t of
h e
boundary of
one
r e g i o n
which has a p o i n t
of h e
o t h e r
r e g i o n
a d j a c e n t
t o
i t
and
o u t s i d e
i t
i m p l e
continuous
shading of a
u r f a c e
w i l l g i v e r i s e to
a
e r i e s of
t e p s
i n
b r i g h t n e s s l e v e l
of only one u n i t
when
h e
p i c t u r e i s
d i g i t i z e d .
T h u s
when
e l e m e n t a r y
r e g i o n s
a r e found
t h e r e w i l l be a
number of
them
o v e r l a p p i n g
each
o t h e r t o
correspond
t o
t h e
s u r f a c e . The
merging
p r o c e s s
w i l l
merge
them
a l l
t o g e t h e r b e c a u s e
of
h e
low
c o n t r a s t on
a v e r a g e ,
only
one
u n i t
a c r o s s common
o u n d a r i e s .
We
hould t h u s be
l e f t w i t h
a
i n g l e
r e g i o n
f o r
t h i s
s u r f a c e .
On h e
o t h e r
hand,
t
an
edge h e r e
w i l l u s u a l l y be
a
t e p
change
n
b r i g h t -
n e s s of two
or more
n i t s
so
h e a d j a c e n t
r e g i o n s
w i l l
not
be
merged. f
such
a a r g e
change
s
not
r e s e n t , an edge s
not
i s t i n g u i s h a b l e
from
a
r i g h t n e s s
contour
by
a l o w - l e v e l
p r o c e s s . I t
r e q u i r e s
judgements
of
c o n t e x t
from
a
h i g h e r l e v e l ,
p a r t i c u l a r l y
i f t h e r e i s no
b r i g h t n e s s
l e v e l
change
a t
an edge,
s
may c c a s i o n a l l y
happen.
In t h e
program, h e merging
p r o c e s s
i s c a r r i e d out
by
t a k i n g an a v a i l a b l e
r e g i o n
and
t e s t i n g
i t
a g a i n s t
a l l
t h e
o t h e r s
to
s e e
which
s a t i s f y
t h e
c r i t e r i o n .
Those
which may be merged
w i t h
i t
a r e merged
s i m u l t a n e o u s l y
and
a
new
r e g i o n
r e c o r d
i s c r e a t e d .
A l l
t h e merged r e g i o n s
a r e
d e l e t e d
from t h e
r e g i o n
l i s t
and
t h e
new one added
i f i t
has
not
a l r e a d y
been found.
This
p r o c e s s i s
i t e r a t e d u n t i l no f u r t h e r
merges a r e p o s s i b l e .
When h i s
s t a t e i s
a c h i e v e d ,
t h e
a v e r a g e
c o n t r a s t
a c r o s s
each
common
boundary i s g r e a t e r
than two
b r i g h t n e s s
l e v e l s .
The n e t
r e s u l t
of
t h e
r e g i o n a n a l y s i s i s
t h e d i v i s i o n
of t h e
p i c t u r e
i n t o
r e g i o n s , each r e g i o n
h o p e f u l l y
c o r r e s p o n d i n g t o
some s u r f a c e
of
h e
o b j e c t ,
and
each
boundary
t o
some
d g e .
F i n a l l y a weeding
- o u t
p r o c e d u r e i s e n t e r e d . This d i s c a r d s
r e g i o n s which
a r e
v e r y
s m a l l
only a few p i c t u r e
p o i n t s
and
hence pr obably s p u r i o u s ,
and
r e g i o n s which have
weak
b o u n d a r i e s , and
a r e t h e r e f o r e probably p a r t
of h e
background
which i s not
e x p l i c i t l y r e p r e s e n t e d
and
has
a l r e a d y been
p a r t i a l l y
d i s c a r d e d
b e c a u s e
i t
e x t e n d s
o f f t h e
p i c t u r e .
Making
Descriptions
Having
found
t h e
important
r e g i o n s of t h e
p i c t u r e , t h e
n e x t
s t a g e
of h e
p r o c e s s
i s
t o
d e s c r i b e
t h e
p i c t u r e
i n terms
of
r o p e r t i e s
of
and
r e l a t i o n s
b e -
tween
t h e r e g i o n s .
The purpose
of
t h e
d e s c r i b i n g
p r o c e s s i s
t o
g e n e r a l i z e .
In
p a r t i c u l a r
i t
should g e n e r a l i z e
over
t r a n s l a t i o ns , s c a l e
c h a n g e s ,
and
r o t a t i o n s .
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BARROW
AND
POPPLESTONE
The
p i c t u r e
d e s c r i p t i o n
c o n t a i n s
a s
subgraphs d e s c r i p t i o n s of
o b j e c t s
c o n t a i n e d w i t h i n
t h e
f i e l d
of i e w .
Any s e f u l s e t of
e l a t i o n s must
l l o w
such
a
subgraph
t o be
independent of
h e
r e s t
of h e
p i c t u r e ;
t h e d e s c r i p t o r s
m u st
not
be
too
g l o b a l i n
n a t u r e .
Each
d e s c r i p t i o n
subgraph
which
c o r r e s p o n d s
t o
a
view
of
a n
o b j e c t
c an
be so
formed t h a t
i t i s
i n v a r i a n t
f o r a i m i t e d
r a n g e
a n d c l a s s of movements
of h e
o b j e c t i n t h e
f i e l d
of
v i e w .
For each
o b j e c t ,
however, h e r e
may b e
s e v e r a l
q u i t e
d i f f e r e n t v i e w s . )
The
t a s k of h e
f i n a l phase of
h i s
p rog r am
i s
t o
f i n d
t h e
subgraphs of h e
p i c t u r e
d e s c r i p t i o n which
c o r r e s p o n d
t o
v i e w s
of b j e c t s ,
a n d hence
t o i d e n t i f y
t h e
o b j e c t s
t h e m s e l v e s .
What
orm r e
t h e
r e l a t i o n s a n d
r o p e r t i e s
t o
take? r e d i c a t e s
w i t h Boolean
r e s u l t s a r e obvious
c a n d i d a t e s :
t h e y
would
be
s u i t a b l e
f o r
m a n i p u l a t i o n b y
r e s o l u t i o n
theorem
- p r o v e r s .
They
have
h e
d i s a d v a n t a g e of a y i n g
v e r y
l i t t l e .
For
example,
t o
say
t h a t
one
r e g i o n
i s
b i g g e r
than a n o t h e r does
not
say
whether b y 0 . 1 or 95
p e r c e n t . One
could
e l a b o r a t e
by d e f i n i n g a
range of
p r e d i c a t e s , each
of which
c o r r e s p o n d s
t o a range of
v a l u e s of
e l a t i v e s i z e .
This l e a d s t o
r a t h e r v e r b o s e
d e s c r i p t i o n s , a n d
e x t e n s i v e
time
a n d s p a c e
r e q u i r e m e n t s .
We
s e n u m e r i c a l
measures
computed
from
t h e
p i c t u r e
f o r
each
p r o p e r t y
a n d r e l a t i o n .
B r i g h t n e s s
of
a
r e g i o n
depends u p o n
l i g h t i n g ,
c o l o u r of
s u r f a c e ,
a n d
o r i e n t a t i o n ,
a n d
i s
t h e r e f o r e
not a g o o d b a s i c
measure. t may
be n e c e s s a r y
f o r
d i s t i n g u i s h i n g
between
b l a c k
a n d
w h i t e
c a t s ,
but
t h i s
i s
of
s e c o n d a r y
importance.
T e x t u r e of h e
r e g i o n
might be
more
v a l u a b l e ,
but s
not m p l e -
mented
i n
t h e p r e s e n t
program.
Shape i s m u c h
more
u s e f u l .
I t must
be
remembered
t h a t
t h e
shape of an
image
o n t h e r e t i n a
c an
v a r y c o n s i d e r a b l y
a s t h e
o b j e c t mo ves a n d
t u r n s .
However, f w e
r e s t r i c t o u r s e l v e s t o
i d e n t i f y i n g
v i e w s
of
o b j e c t s
that i s
s e v e r a l d e s c r i p t i o n s
correspond t o
a
s i n g l e
o b j e c t ) ,
then
each
view
c an be
d e f i n e d such h a t
shape
a r i e s
o n l y
s l i g h t l y
over h e
p i c t u r e s
which correspond
t o t h a t
v i e w .
The
p r o p e r t i e s
of
e g i o n s
which
a r e
c a l c u l a t e d
a r e :
COMPACTNESS.
his i s 4n
rea
P e r i m e t e r
2
.
This
measure v a r i e s from 1
c i r c u l a r )
t o
0
very
u n c i r c u l a r ) .
SHAPEn
There
a r e
s i x
shape components.
These
a r e
d e r i v e d from a F o u r i e r
a n a l y s i s
of h e s 1 / / e q u a t i o n of h e
r e g i o n
boundary.
See Appendix.)
The o l l o w i n g
r e l a t i o n s a r e c a l c u l a t e d :
BIGGER
This
s a
measure
of
e l a t i v e s i z e
of
e g i o n s a n d
i s Area of A
Area
ofA
rea
of n),
a r y i n g between
0
n d
1 .
Because
t i s
a
r e l a t i v e
measure
i t i s
independent of c a l e .
ADJACENT.
A
measure
which
r e f l e c t s
t h e
topology
of
h e
p i c t u r e . I t
i s
t h e
f r a c t i o n of
h e boundary
of
e g i o n
A
which
has a
o i n t of e g i o n
B
d j a c e n t ,
or w i t h i n one
p o i n t
of t . The
l a t i t u d e
has been i n t r o d u c e d b e c a u s e v e r y
o f t e n a few i s o l a t e d p o i n t s o n
t h e common
boundary of two
s u r f a c e s g i v e
CC
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APPROACHES FOR PICTURE
ANALYSIS
r i s e
t o i n s i g n i f i c a n t
r e g i o n s ,
t h u s i n t e r p o s i n g
a
gap between
t h e two
major
r e g i o n s . )
I t w i l l
be noted
t h a t t h i s
measure
s not
y m m e t r i c a l .
In
a r t i c u l a r , f r e g i o n
A s i n s i d e
r e g i o n B
hen
ADJACENT A, 3)=
,
b e c a u s e a l l
p o i n t s
j u s t
o u t s i d e
t h e
boundary
of A
i e
i n B,
ut
ADJACENT B,A =0,
e c a u s e
a l l
p o i n t s
j u s t
o u t s i d e
t h e boundary of
B d o
not i e
i n A.
The
e r o
or n on
- z e r o i n f o r m a t i o n
c o n t a i n e d i n t h e
measure
can t h u s p r o v i d e
a t o p o l o g i c a l
d e s c r i p t i o n of h e
p i c t u r e , and t h e
n u m e r i c a l
v a l u e
p r o v i d e s e x t r a i n f o r m a t i o n .
DISTANCE. This measures p r o v i d e s
g e o m e t r i c a l i n f o r m a t i o n about
t h e
r e l a t i v e p o s i t i o n s of
t h e
r e g i o n s . I t i s d e f i n e d
a s t h e
d i s t a n c e between t h e
c e n t r e s of r e a of h e two
e g i o n s
i n v o l v e d
d i v i d e d by h e
g e o m e t r i c
mean of
t h e
a v e r a g e r a d i u s
of h e
r e g i o n s .
The
d i s t a n c e so
c a l c u l a t e d
w i l l
be
e e n t o
be
independent of s c a l e r o t a t i o n ,
t r a n s l a t i o n
and r e f l e c t i o n . The
a v e r a g e
r a d i u s of
a e g i o n
i s
d e f i n e d
a s
2.
rea
P e r i m e t e r .
CONVEX. his
i s
c a l c u l a t e d
by f i t t i n g an a r c of a
c i r c l e
t o t h e common
boundary of A
and
B a c t u a l l y f i t t i n g
a s t r a i g h t l i n e
t o
t h e t
(s) u r v e ) .
The
n u m b e r
c a l c u l a t e d
i s
t h e c u r v a t u r e of h e
common oundary r e l a t i v e
t o t h a t of t h e
c i r c l e f i t ti n g t h e wh ole bound ary.
(So
t h e measure
i s
not
symmetri c or
a n t i s y m m e t r i c . )
That
s a e s u l t of 1
i n d i c a t e s t h e
boundary
t o
be convex
e l a t i v e
t o
A
and t o p o s s e s s t h e
same u r v a t u r e a s t h e whole of
t h e
boundary.
A e s u l t g r e a t e r
than 1 i n d i c a t e s g r e a t e r
c u r v a t u r e .
A
e s u l t of
0
n d i c a t e s
t h a t a t r a i g h t l i n e
i s
t h e
b e s t
f i t . A
e g a t i v e
r e s u l t means h a t t h e
boundary
s
concave
i t h
r e s p e c t
t o
A.
part
rom
b e i n g
j u s t
a n o t h e r
r e l a t i o n
between r e g i o n s
which h e l p s
t o
s p e c i f y t h e
p i c t u r e ,
CONVEX
can p r o v i d e
depth
n f o r m a t i o n i n
a i m i t e d
s e n s e . f
t h e s u r f a c e
c o r r e s p o n d i n g t o
one
e g i o n
A
c c l u d e s
a n o t h e r
c o r r e s p o n d i n g t o
r e g i o n B,
hen t i s
h i g h l y
l i k e l y t h a t t h e
common
oundary
of
A
and
B i l l
be convex
i t h r e s p e c t
t o
A,
or
t
l e a s t
not
c o n c a v e . Some of
Guzman s
h e u r i s t i c s f o r
decomposing
a c e n e i n t o
b o d i e s
can
be i n t e r p r e t e d
a s u s i n g c o n v e x i t y
of b o u n d a r i e s t o
p r o v i d e s t a t i s t i c a l
i n f o r m a t i o n
about
e p t h .
In a d d i t i o n
t o
t h e
above
r e l a t i o n s , which
a r e adequate
t o
d e s c r i b e t h e
r e g i o n s
of t h e
p i c t u r e
w h i l e
r e t a i n i n g independence
of
s c a l e , t r a n s l a t i o n ,
r o t a t i o n , and
e f l e c t i o n , t h e r e a r e a few
u r t h e r r e l a t i o n
measures:
ABOVE.
his
measure
i s
s i m i l a r
t o
DISTANCE and
i s
t h e v e r t i c a l
d i s t a n c e
between
t h e
c e n t r o i d s
of
t h e
r e g i o n s i n v o l v e d ,
n o r m a l i z e d b y
d i v i d i n g b y
t h e a v e r a g e
r a d i u s .
I f p o s i t i v e , A
s above
B,
f
n e g a t i v e ,
B
s above
A.
Th e
i n c l u s i o n of ABOVE
mmediately removes
independence of
o t a t i o n i n
t h e
p l a n e
of h e
p i c t u r e .
O b j e c t s a r e
u s u a l l y e n c o u n t e r e d
i n
a
r e f e r r e d
o r i e n t a -
t i o n , so
i n c l u s i o n
w i l l
a i d
i d e n t i f i c a t i o n
i n
t h e normal c a s e .
As i l l be
e x p l a i n e d
l a t e r , i f
o b j e c t s
a r e p r e s e n t e d
d u r i n g
t r a i n i n g
i n
m a n y
r i e n t a t i o n s
e q u a l l y
o f t e n ,
t h e
w e i g h t
a t t a c h e d
t o
t h i s
measure
i l l
be
e d u c e d ,
so
t
does
not
h u r t
t o
i n c l u d e
i t . )
BESIDE. This i s
s i m i l a r
t o
ABOVE.
t i s t h e
h o r i z o n t a l d i s t a n c e between
c e n t r o i d s , n o r m a l i z e d .
However,
h e s i g n
of
h e r e s u l t
i s
always p o s i t i v e ,
so
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BARROW
AND
POPPLESTONE
t h a t
BESIDE A,
3)=BESIDE B,
A
and
t h e
measure
i s
independent
of
r e f l e c t i o n . The
i n c l u s i o n of
h i s
r e l a t i o n
a g a i n r e d u c e s t h e
independence
of
r o t a t i o n but
s s i s t s
when
o b j e c t s
a r e
u s u a l l y
s e e n i n a
p a r t i c u l a r
o r i e n t a t i o n .
The
r e f l e c t i o n
independence
has bee n
r e t a i n e d
b e c a u s e
t h e r e a r e o f t e n
t wo
v i e w s of an
o b j e c t
which a r e
almost
m i r r o r
images, o r
example,
e f t and i g h t
p r o f i l e s
of a
f a c e
a
c u p
w i t h
handle on e f t
or
on r i g h t . Whereas,
u p
-down
symmetry s r a r e .
Turning
an o b j e c t u p s i d e
down
does
not
s i m p l y
i n v e r t
t h e
p i c t u r e
u n l e s s
i t i s
viewed
e x a c t l y
from
t h e s i d e .
The
e t
of
r o p e r t i e s and
r e l a t i o n s above
seems
t o
be u s e f u l
and
p o w e r f u l .
I t
could be
e x t e n d e d
g r e a t l y
but
a t t h e
expense
of
r o c e s s i n g
s p a c e
and time
r e q u i r e m e n t s .
The
d e s c r i p t i o n
i s
g e n e r a t e d
e x h a u s t i v e l y
f o r e x p e r i m e n t a l c o n v e n i e n c e .
A
or e
p r a c t i c a l
v e r s i o n
of
h e program
would
o n l y
c o m p u t e t h e
p r o p e r t i e s
and
measures
i t
r e q u i r e d
when
t h e y were
r e q u i r e d .
[Using
t h e
m e m o -
f u n c t i o n
i d e a — e e
Michie 1968).]
Fro m
t h e p o i n t of
view of h e
n e x t
s t a g e
of h e
p r o c e s s i n g
i t
would
n e v e r t h e l e s s
appear
t h a t a complete
d e s c r i p t i o n
was a v a i l a b l e .
THE
DESCRIPTION
-MATCHING
PROCESS
Having
produced
a d e s c r i p t i o n
of h e
p i c t u r e t h e
n e x t
s t a g e
of
h e
p r o c e s s
i s t o
i n t e r p r e t t .
For h e
p u r p o s e s
of h e
p r e s e n t
r e s e a r c h e r t a i n assumptions
were
made. The
p i c t u r e i s
assumed
to- c o n t a i n a
view
of a
s i n g l e
o b j e c t
which
i s
wholly
c o n t a i n e d
w i t h i n t h e
f i e l d
of
v i e w .
The
a i m
of
t h e
p r o c e s s
i s t o d e c i d e which of a
p r e d e t e r m i n e d
s e t
of
v i e w s
of
b j e c t s
most
e s e m b l e s
t h e p i c t u r e
and hence
t o i d e n t i f y
t h e o b j e c t
i n t h e
p i c t u r e .
The
i c t u r e
w i l l
c o n t a i n a n u m b e r of
e g i o n s which a r e
not
a r t
of h e
t a r g e t
o b j e c t .
The e p r e s e n t a t i o n
of
h e
o b j e c t n t h e p i c t u r e
m a y
be
degraded
from
h e
i d e a l
by h e
a d d i t i o n or d e l e t i o n of
e g i o n s :
o r example,
h i g h l i g h t
on
a
u r -
f a c e m a y
appear
a s an
e x t r a r e g i o n a h o l e i n a
u r f a c e
m a y
not be
d e t e c t e d .
There
a r e
a
n u m b e r of
i t u a t i o n s w i t h which t h e
e x i s t i n g
program
cannot
cope
a d e q u a t e l y . I f
a
s u r f a c e
has a hard
shadow
a c r o s s i t i t m a y r e s u l t
i n
two
r e g i o n s .
An
bvious
met hod of
overcoming
t h i s
s i t u a t i o n
i s
t o
merge
t h e o f f e n d i n g
two
e g i o n s i n t o one and
c a r r y
on.
i n c e m a n y
such
merges
a r e
p o s s i b l e t h i s
approach
has
not
y e t
been
i n v e s t i g a t e d .
I t
i s p o s s i b l e
f o r two s u r f a c e s m e e t i n g
a t an edge t o
be i t so
t h a t t h e
edge
i s p r a c t i c a l l y
i n v i s i b l e .
The
e g i o n a n a l y s i s
w i l l
f i n d one
e g i o n
i n s t e a d
of wo.
A i m p l e way
of
oping
w i t h t h i s i s t o s t o r e t h e
d e s c r i p t i o n s
of
i k e l y d e g r a d a -
t i o n s
of v i e w s
a m o n g t h e t a r g e t s e t . Again
t h i s i s not v e r y economical, and
has
not been
n v e s t i g a t e d .
The
e f f e c t s of
o c c l u s i o n of
o b j e c t s
a r e v a r i e d . I f t h e
o c c l u s i o n i s s l i g h t
performance
i s
not
a f f e c t e d .
A s
t h e
o c c l u s i o n
i n c r e a s e s
t h e p r o p e r t y
and
r e l a t i o n
measures
w i l l
change.
The
matching p r o c e s s
can
s t i l l
f u n c t i o n
c o r r e c t l y
when
a
match i s
i m p e r f e c t and so
m a y
be
a b l e
t o
i d e n t i f y
t h e
o b j e c t
c o r r e c t l y .
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AP
PROA
CHE
S FO
R
PI
TUR
E ANA
LYS
IS
Str
ateg
y
T
he
d e s c
r i p t i
o n
of
h
e p i c
t u r e
b e
i n g
a n a
l y z e
d , a
nd t h e
d e s c
r i p t i
o n s of
i e w s
o
f
b j
e c t s
a r e
s i m i
l a r l y
r e p
r e s e n
t e d .
Fo
r eac
h a
r
e c o r
d of
t
wo c o
mpon
ent
s
e x i s t s .
One
c omponent
s
i n
e s s e
n c e
a
i s t
of
orma
l p a
r a m e
t e r s
. The
e
g i o n s
o
f h
e p i
c t u r
e a r
e r e p r
e s e n t
e d
by
n
umbe
rs
1 , 2 ,
3
t c .
,
t
h o s e
of
a vi
ew by
l e
t t e r s
A
B
,
..
.
The
sec
ond c
ompo
nent
s a
i s
t
o
f
e l a t
i o n s ( p r
o p e r
t i e s
of
r
e g i o
n s a r
e t
r e a t
e d
a s
tw
o-ar
gume
nt e
l a t i o
n s , of
wh
ich t
h e s
ec on
d arg
umen
t
i s
i d
e n t i c
a l
t
o t
h e f
i r s t
.
Fo
r eac
h vie
w
t
h e r e
a r e
man
y way
s n
w
hich
h
e r
e g i o n
s
of
h e
p i c t
u r e
ma
y
be
put n
t o c o
r r e s
p o n d
e n c e
w i t h
t h o
s e of
h e v i e
w .
We an
e f i n e
a o r r e
s p o n
-
denc
e to be
c o m p
l e t e
i f
f o
r
e v
e r y
r e g
i o n
of
h e vi
ew
a
c o r
r e s p
o n d i
n g r
e g i o
n
o
f
h e
p i
c t u r e
has
been
a s s i
g n e d
. Oth
erwi
se
a o r r e
s p o n
d e n c
e c a
n be
s a i
d t o
be
a r
t i a l .
Fo
r a
e l a t
i o n ,
RE
L A
,B
f
h
e v i
e w , i f
t h e
p i c t
u r e
r e g i o
n s
c
o r r e
s p o n
d i n g
t
o A
and
B r
e
d e
f i n e d
, we can
f i n d
t h
e
c o r
r e s p
o n d i
n g
p i c t u
r e
r e l a
t i o n .
Th
e
vie
w
r e
l a t i o
n s ha
ve mea
n a
nd s t a n
d a r d
d
e v i a
t i o n
s t o
r e d .
Th
e o r r
e s p o
n d i n
g
p
i c t u
r e
r e l a
t i o n i s s
a i d t o
a
g r e e
w
ith
t h e
view
r
e l a t i
o n i f t
s mea
sur
ed v a l u e
l
i e s w i
t h i n
t h r e
e s t a n
d a r d
d e v
i a t i o
n s
of
h
e m
ean
. hus
o
r any
o r
r e s p o
n d e n
c e
betw
een r
e g i o
n
s e t s
i t i
s
p o s s i
b l e t o
d e t e
r m i n
e
how
m
any
p i c t u
r e
r e l a t
i o n s
c
an b
e e s
t e d
a
g a i n
s t
view
r e l a t
i o n s ,
h
ow
ma
ny of
h e s
e a g
r e e
and
how m
any
do n
ot
kn
own a s
T r i
e s , S u
c c e s
s e s ,
and
F a i l
u r e s )
. I
t i s
then
p o s
s i b l e
t o
e v a
l u a t
e a
p a r
t i c u
l a r
c
o r r e
s p o n
d e n c e
an
d
a s s i
g n
a c o r e
t o
i t
i n
d i c a t
i n g i t s
m e r i
t . The
ai
m of
h i s s
t a g e
of
t h e
pro
gram
i
s
t
o
f i n
d
t h e
mos
t v
a l u a
b l e
c o
r r e s
p o n d
e n c e
o
f
l l
p o s s
i b l e c o r r
e s p o
n d e n
c e s ,
bo
th
com
plet
e
an
d p a r
t i a l .
No
te t
h a t i f
t h e r
e g i o n
- f
i n d i n
g
p r o c
e s s
ha
s met
w i t h
d i f f
i u l t
i e s a
nd
ha
s l o s t
a
s
i g n i
f i c a n
t r e
g i o n
or s p l
i t
i t
i n t o
two
t ma
y
be
b e t t e
r
t o
a c
c e p t
a p
a r t i a
l
c
o r r e
s p o n
d e n c
e r a t
h e r
th
an
o r c e a
n
n c o
r r e c t
as
sign
ment
of
a i
c t u r e
r e
g i o n
t
o
a
vie
w
r
e g i o
n .
T
he
pro
blem
c an be
r e s t
a t e d
a s
f i n
d i n g
t
h e b e s
t
mat
c h of
a
s
u b s e t
of
h e
p i c t
u r e
r e
g i o n
s
w
i t h
a
u
b s e t o
f
h e v
iew
r e g i
o n s . U n g e
r s
gra
ph
i s
omor
phi
sm
f
i n d i
n g
p r o
c e d u r
e
an
d R a
s t a l
l s
g e n
e r a l
i z a t i
o n s
of
i t
a r
e no
t
a d e
q u a t
e .
R a s t
a l l s
pro c
edur
e h a n d
l e s
onl
y
t
h e m
atch
ing of
a com
plet
e gra
ph w i t h
a
s u b
s e t of
n o t h
e r .
Eval
uati
on
fu
ncti
on
B
e f o r
e c
o n t i
n u i n
g , i
t i s
wort
hwhi
le t
o c o n
s i d e r
t h e
c h o
i c e
of
a
s u
i t a b l
e
f u
n c t i
o n
f o r
e v a
l u a t
i n g c
o r r e
s p o n d
e n c e
s .
T
he nu
mber
of
e l a
t i o n s
f
o r a
1
- r e g
i o n o b
j e c t
d e
s c r i
p t i o
n
i s 7
o r
2 e g i o
n s
28
o r
e g
i o n s
6
3. S
uppo
se
w
e a k e
t
h e n
umb
er
o
f
u c
c e s s
e s
t
o be
h e v
a l u e
of a
o r r e s p o n d e n c e .
I t
i s
c l e a r
t h a t
a
e r f e c t
match
w i t h
a
1
- r e g i o n
view
w i l l
b
e
r e
j e c t e
d
i n
fa
vour
of a bad
m a
tc h
wit
h a
- r e g
i o n
o b j
e c t ,
whi
ch i s un
-
s a t i
s f a c t
o r y .
T
he
s i t u a
t i o n
i s
b e t t
e r i f f r
a c t i
o n a l
s u c c
e s s i s
use
d t o
e v
a l u a t
e .
W
e ave
n t
r o d u
c e d
a
m
easu
re
o
f
h e d e g
r e e
of
a i l u
r e . I
f c om
pute
d
p i c t
u r e
3 8
8
-
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B RROW ND
POPPLESTONE
measure l i e s
w i t h i n
3sd of
t h e
mean, h e f a i l u r e i s 0, f
between
3 nd 6 s d
f a i l u r e i s 1
between 6
nd 9, a i l u r e i s 2 and so on.
T r i e s
— a i l s i s
t h u s
a m o r e s e n s i t i v e
measure than S u c c e s s e s .
There i s
s t i l l a dilemma
a p p a r e n t . At
w h a t p o i n t
does
one r e j e c t a good
match w i t h a
s i m p l e
o b j e c t f o r
a
not- s o-good
match w i t h a
complex
o b j e c t ?
I n t u i t i v e l y one f e e l s
t h a t
a match w i t h a
complex o b j e c t
i s p r e f e r a b l e t o
a n
e q u a l l y
s u c c e s s f u l
one
w i t h a s i m p l e r o b j e c t . I t
i s u n f o r t u n a t e l y
r a t h e r
e a s y
t o
f i n d
s i m p l e
o b j e c t s a s
p a r t s
of complex
o n e s .
T h e
e v a l u a t i o n
f u n c t i o n chosen works r e a s o n a b l y
w e l l
though t h e r e
i s
r o o m
f o r
improvement. T h e program
endeavours
t o
minimize
t h e
f u n c t i o n
so
i t
has
t h e
f o l l o w i n g
form:
1
T r i e s — a i l s
No.
of
e l a t i o n s
No.
of
Regions
where
No.
of
R e l a t i o n s
and No. of Regions r e f e r t o
t h e view d e s c r i p t i o n
i n v o l v e d .
A u i t a b l e
v a l u e f o r K
ppears
t o be
0 . 5 .
Tactics
A
a t h e r
n a i v e method f o r
f i n d i n g
t h e
b e s t match
would
be
t o g e n e r a t e
and
e v a l u a t e a l l
p o s s i b l e c o r r e s p o n d e n c e s . We
an, however,
improve on t h i s .
Beginning
w i t h a p a r t i a l
c o r r e s p o n d e n c e
say w i t h
n
a s s i g n m e n t s
of i c t u r e
r e g i o n s t o view
r e g i o n s
t i s a
t r a i g h t f o r w a r d m a t t e r
t o g e n e r a t e
a o r r e s p o n -
dence
of n+1)
s s i g n m e n t s
from
i t
b y
choosing
an
u n a s s i g n e d
p i c t u r e
r e g i o n and
p a i r i n g
i t w i t h a n u n a s s i g n e d view r e g i o n . In g e n e r a l a s e t of
c o r r e s p o n d e n c e s w i t h n+1)
s s i g n m e n t s
m a y
be so d e r i v e d . Let us d e f i n e
t h i s
p r o c e s s
t o
be
t h e d e v e l o p m e n t
of a c o r r e s p o n d e n c e . T h e development
can p r o c e e d
s t e p
b y s t e p i f
w e
g e n e r a t e ne w
c o r r e s p o n d e n c e s
one a t
a t i m e .
A o r r e s p o n d e n c e
which
has not
y e t
had a l l
immediate s u c c e s s o r s
d e v e l o p e d
from
t i s
d e f i n e d
t o be a r t i a l l y
d e v e l o p e d .
To v a l u a t e a n e w
c o r r e s p o n d e n c e
w e can
u s e
t h e
i n f o r m a t i o n
computed
about
i t s p a r e n t and
need
c o n s i d e r
only t h e consequences of
adding
t h e
e x t r a
p a i r
of
e g i o n s .
At
h e s t a r t
of
h e
p r o c e s s
w e
have
o n l y t h e n u l l
c o r r e s p o n d e n c e .
Fro m
t h i s
w e can
g e n e r a t e
a l l
f i r s t - o r d e r
c o r r e s p o n d e n c e s t h o s e w i t h only one p a i r of
r e g i o n s
and
from t h o s e t h e second
- o r d e r
c o r r e s p o n d e n c e s
and
so
on.
I t
m ak e s
e n s e
no w
t o
d e v e l o p
only t h e
most
promising
c o r r e s p o n d e n c e
a nd
f u r t h e r t o
g e n e r a t e only
one
s u c c e s s o r
a t
a t i m e .
So
a r
t h e p r o c e s s i s analogous t o
t h a t
of h e Gr a p h
T r a v e r s e r
Doran
a nd
Michie,
1966;
Ma r s h, 1970).
At
a g i v e n
i n s t a n t
t h e r e a r e a n u m b e r of obs
t o be
done, each
c o r r e s p o n d i n g
t o a p a r t i a l l y- d e v e l o p e d c o r r e s p o n d e n c e
a nd
a l l
a t
v a r i o u s s t a g e s
and
d e g r e e s .
B y
working
only on
t h e
b e s t
a v a i l a b l e
job
w e
can
economize
i n
e f f o r t .
There i s a d i f f e r e n c e
between
t h i s
and
c l a s s i c a l
graph t r a v e r s i n g —
i n t h i s
c a s e
w e
d o not
n e c e s s a r i l y k no w t h e
g o a l
s t a t e
w h e n
w e encounter
t
b e c a u s e w e a r e l o o k i n g f o r
t h e
b e s t .
389
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PPRO CHES FOR
PICTURE ANALYSIS
. At
h i s
p o i n t , t
appears
h a t
d e v e l o p i n g
t h e b e s t
a v a i l a b l e
c o r r e s p o n d e n c e
wa s a n i l l u s o r y
a d v a n t a g e ,
s i n c e i t
s e em s
we must
s e a r c h t h e
whole
s p a c e
anyway.
Not o .
Given a
c o r r e s p o n d e n c e ,
not
only
can
we
e v a l u a t e i t
we
can l s o
d e t e r m i n e
upper and lower
bounds o r
t h e
v a l u e s of
l l i t s
s u c c e s s o r s ,
b e c a u s e
no
u c c e s s o r
can
have fewer
s u c c e s s e s
or
fewer
a i l u r e s than
t
h a s .
Thus we can
i n c o r p o r a t e
d o n t
d e v e l o p
a
c o r r e s p o n d e n c e
i f i t s
s u c c e s s o r s
cannot g i v e
b e t t e r v a l u e s
than
t h e most
u c c e s s f u l
s o
f a r
f o u n d .
This
u s e s
t h e s a m e
pruning t e c h n i q u e
as h e Branch
-and
-Bound
method
—
e e
B u r s t a l l
1 9 6 7 . )
We
need
t o
r e m e m b e r only t h e
b e s t
c o r r e s p o n d e n c e so f a r
en-
c o u n t e r e d , and a t t h e
end of h e
p r o c e s s ,
wh en
h e r e
a r e no
m o r e promising
l i n e s
of
development,
h i s w i l l
be
h e
answer, h e
b e s t
match.
This
h y b r i d i z a t i o n of
t h e G r a p h
T r a v e r s e r
and
t h e Branch
-and-Bound
a l g o r i t h m
i s complete
e c a u s e
i t
cannot a i l t o f i n d
t h e
b e s t
node n t h e
s e a r c h
s p a c e , but
i s m o r e
e f f i c i e n t than a n
e x h a u s t i v e
s e a r c h
p r o c e d u r e . In t h i s
p a r t i c u l a r
c a s e ,
h e
f i n a l
r e s u l t , t h e
b e s t
match,
may
e
a
a r t i a l or
a
omplete
c o r r e s p o n d e n c e .
In
r a c t i c e ,
we
l s o
r e t a i n
matches
which r e almost s
g o od
as h e l a s t .
TE CHING THE
PROGR M TO
RECOGNIZE
Th e a c i l i t y wa s
r o v i d e d
i n
t h e
p r o g r am o r
e n a b l i n g
i t
t o
l e a r n
i n t h e l i g h t
of x p e r i e n c e and
g u i d a n c e .
I t
wa s
not
r i g i n a l l y i n t e n d e d t o e x i s t , but w h en
t h e
n a t u r e
of e l a t i o n s and p r o p e r t i e s
b ec am e
s t a b l i s h e d , t wa s
e a l i z e d t h a t
such
a f a c i l i t y
could
e a s i l y
be p r o v i d e d and
would
e a s e
c o n s i d e r a b l y
t h e
problems of
o n s t r u c t i n g models.
I t
w i l l
be r e c a l l e d
t h a t
t h e
r e l a t i o n s i n a
model a r e i n f a c t
m e a s u r e s , a nd
t h e
b e s t
w ay
t o
o b t a i n v a l u e s f o r t h e
model s t o m a k e
measurements o n
s e v e r a l p i c t u r e s of h e
o b j e c t and to
c a l c u l a t e
t h e mean. I f
t h e d i f f e r e n c e
between
t h e measure
and
t h e m e a n s
used t o compute
badness of match,
then
t h e i d e n t i f i c a t i o n
m a d e by
h e p r o g r am
w i l l
be unduly
swayed by h o s e
measures
which r e
l e a s t
r e l i a b l e ,
t h a t s
t h o s e which have
h e
most
a r i a t i o n .
As we a r e
c a l c u l a t i n g means,
t
i s
a s i m p l e
m a t t e r t o c a l c u l a t e
s t a n d a r d
d e v i a t i o n s
a s w e l l and
to r e p l a c e
t h e d i s c r e p a n c y
measure
by
d e v i a t i o n i n
u n i t s of
t a n d a r d d e v i a t i o n .
Compensation s
t h u s i n t r o d u c e d
a u t o m a t i c a l l y ,
so
t h a t
a l l
measures c a r r y t h e
s a m e w e i g h t .
Th e
p r o b a b i l i t y of
e x c e e d i n g
3sd
s
roughly
h e
s a m e o r
a l l t h e
m e a s u r e s .
I t
w i l l
be
noted
h a t , i n c e
we
r e
u s i n g
n u m e r i c a l m e a s u r e s ,
h e
a d a p t a t i o n
mechanism
which
i s
a p p r o p r i a t e ,
namely, s i m p l e
s t a t i s t i c a l
c a l c u l a t i o n ,
i s
w e l l
u n d e r s t o o d .
I f
t h e measures
were b i n a r y ,
a
system
of
e i g h t i n g would
probably have
o be
n t r o d u c e d .
The r a i n i n g
p r o c e d u r e
i s a s f o l l o w s .
F i r s t , t h e o b j e c t i s
p l a c e d b e f o r e
t h e
TV
c am e r a and
h e
p i c t u r e
i s
a n a l y z e d
i n t o
r e g i o n s .
Th e
e g i o n s
a r e exhaus-
t i v e l y
d e s c r i b e d
i n
terms of
r o p e r t i e s and
r e l a t i o n s . T h e
matching
phase of
t h e p r o g r am
m a y be e n t e r e d ,
i f
d e s i r e d , t o
s e e
what t h e
p r o g r am
would
g u e s s t h e
o b j e c t t o
b e . )
Th e
c o m m a n d
LEARN s
then g i v e n ,
t o g e t h e r w i t h
390
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B RROW ND
POPPLESTONE
two v i t a l
p i e c e s
of
n f o r m a t i o n . The
i r s t
i s
t h e o b j e c t
or
view
of
an
o b j e c t )
which
i s t h e
c o r r e c t
r e s p o n s e , and t h e
second
a c o r r e s p o n d e n c e ,
which
e x p l a i n s which
r e g i o n s
i n
t h e
p i c t u r e
c o r r e s p o n d
t o
which
i n t h e
v i e w .
Comparisons
between
p i c t u r e
and view
d e s c r i p t i o n s
may
be made b e f o r e and
a f t e r t h e updating
r o c e s s ,
t o
s e e
what
i s c r e p a n c i e s e x i s t e d
and
whether
h e y
remain. U s u a l l y
t h e y
a r e
e l i m i n a t e d
by h e l e a r n i n g
p r o c e s s .
The
p r o v i s i o n of
h e
c o r r e s p o n d e n c e
may
appear
a r t i f i c i a l .
The l e a r n i n g
p r o c e s s was
not
i n t e n d e d
t o
be used
s p o r t i n g l y , but
r a t h e r
t o
s a v e
time
i n
s u p p l y i n g
t h e
model
d a t a .
With a
i t t l e
m o d i f i c a t i o n , however, t c o u l d be
made more
l e x i b l e .
For
example,
n s t e a d
of u p p l y i n g
t h e c o r r e s p o n d e n c e ,
h e
program c o u l d
be
made
o
r e p l a c e
t h e
l i s t of
i e w s
of b j e c t s
a g a i n s t
which t
matches h e
p i c t u r e by a
i s t of only one, h e s p e c i f i e d
o b j e c t
or
perhaps
by
t h e
v i e w s
of
h a t
o b j e c t ) .
The
matching
p r o c e s s c o u l d then
be
e n t e r e d , and
t h e
b e s t
c o r r e s p o n d e n c e
found
and
used
n
t h e
updating
r o c e s s . O c c a s i o n a l l y
t h e
c o r r e c t
c o r r e s p o n d e n c e
might
not be found, but
n
such
c a s e s t h e p i c t u r e
would have
t o
be
ambiguous,
or d e g r a d e d . Perhaps t h e updating p r o c e s s
c o u l d
be
i n h i b i t e d
i f t h e
d i s c r e p a n c y
i s too g r e a t ,
i n d i c a t i n g
p o s s i b l e g r o s s
e r r o r .
DIS USSION
ND
CONCLUSIONS
F i r s t ,
t h e
program
can
r e c o g n i z e
a
v a r i e t y
of o b j e c t s , both r e g u l a r
and i r
r e g u l a r , when
p r e s e n t e d
s i n g l y ,
i n
s t a n d a r d
p o s i t i o n s
and
d i f f u s e
l i g h t i n g .
I t
can
d i s t i n g u i s h
on
t h e b a s i s of shape b a l l v e r s u s
p e n c i l )
a s w e l l
a s
com-
p l e x i t y
tube
v e r s u s
c y l i n d e r )
and r e g i o n
r e l a t i o n s h i p s
cup,
s p e c t a c l e s ) .
I t
has
n i n e
o b j e c t s
i n
i t s c u r r e n t
r e p e r t o i r e , and
t h e r e
i s
no
doubt t h a t
t h i s
c o u l d
be
c o n s i d e r a b l y
e x t e n d e d .
I t
i s
d i f f i c u l t t o
a s s e s s
performance,
b e c a u s e
i t depends
upon t h e t r a i n i n g
g i v e n . I f
a
c u p s
p r e s e n t e d i n n e a r l y
t h e
same p o s i t i o n e v e r y
t i m e ,
t h e r e
w i l l
be
l i t t l e
t o l e r a n c e
i n
t h e
l e a r n e d
d e s c r i p t i o n . S i n c e
i d e n t i f i c a t i o n
p r o c e e d s
on t h e
b a s i s
of
h e
b e s t match, cups
i n
n o n - s t a n d a r d
p o s i t i o n s
may t i l l be
c o r r e c t l y
i d e n t i f i e d , but may a l s o
be
m i s i d e n t i f i e d
i f
o t h e r
o b j e c t s of
t h e
r e p e r t o i r e
e x i s t
w i t h
s u f f i c i e n t
t o l e r a n c e .
I f t h e
c u p
i s
p r e s e n t e d
w i t h
t h e
h a n d l e
hidden
b e h i n d ,
whereas
l l l e a r n i n g
had been
made
w i t h t h e
handle
n i c e l y
out
o
t h e
s i d e , t would
probably
be m i s i d e n t i f i e d .
I f
t h e
program were
f o r c e d
t o l e a r n
t h i s
view
a s s i m p l y
a
form of h e
one
view of
h e
model,
h e
consequence
would undoubtedly
be
bad and
subsequent performance
d e -
g r a d e d . At
r e s e n t
t h e
onus
s u pon
h e
o p e r a t o r t o
d e c i d e
when
a new view
should
be
c r e a t e d ,
though
c o n c e i v a b l y a program could
be
w r i t t e n which
would
do
so
i f t h e match
w i t h
e x i s t i n g v i e w s was
s u f f i c i e n t l y
bad. The
performance
of h e
c u r r e n t
program
depends
upon
h e
t r a i n i n g
p r o c e s s . I f
a
new
p i c t u r e
can
be
d e s c r i b e d
c o r r e c t l y
by
a
model
d e s c r i p t i o n ,
t h a t
model
w i l l i n e v i t a b l y
be
r e t u r n e d
a s
a
p o s s i b l e
i n t e r p r e t a t i o n
of
h e p i c t u r e . I f
n o t ,
then t h e b e s t
f i t t i n g model
w i l l
be c h o s e n .
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PPRO CHES
FOR
PICTURE
N LYSIS
RESULTS
With t h e
above
r e s e r v a t i o n s ,
some
e x p e r i m e n t a l
r e s u l t s a r e
r e c o r d e d
i n t h e
t a b l e .
Ten
t e s t o b j e c t s were
used to t e a c h
t h e
program n i n e c a t e g o r i e s t h e r e
were
t w o
cups of i f f e r e n t s o r t s ) .
Each
o b j e c t
was
p r e s e n t e d
d u r i n g t e a c h i n g
a t
l e a s t
s i x
t i m e s .
Table 1 . Performance of
O b j e c t R e c o g n i t i o n program:
h r e e t r i a l s w i t h
each of e n o b j e c t s i n c l u d i n g two cups).
P e r c e n t a g e
c o r r e c t :
8 5 .
Average time:
5
in 40 e c . ]
OBJECTS
IDENTIFIC TION
~ ~
03
IL
o .
. . . . I
t • I
0 . ,
. . . . . ,
c . .
• . . . . .
.
.
. . . . ‘ . . .
. .
O
• , . . .
O
v u
WO
I Z I , co
O
P e n c i l 3
Ball
3
Hammer
2 . 5
0 . 5
W e d ge
3
C y l i n d e r 3
Doughnut
Tube
1
2
Cup
6
S p e c t a c l e s 1
2
An
s s i s t a n t ,
u n a s s o c i a t e d
w i t h
i t s
t r a i n i n g , p l a c e d
o b j e c t s
i n
t h e f i e l d of
view of h e camera
n
accordance
w i t h
b r i e f w r i t t e n i n s t r u c t i o n s for example,
CUP: o l e i n h a n d l e
must
be v i s i b l e , r i g h t
way
up ). Each b j e c t was
r e s e n t e d
3
i m e s , i n
d i f f e r e n t p o s i t i o n s .
A s
can be
s e e n from
t a b l e
1 ,
o b j e c t s
were
c o r r e c t l y i d e n t i f i e d 2 5 . 5
t i m e s
out
of
0 .
The
. 5
r e s u l t
was
a
dead
h e a t between
h amme r
and
p e n c i l . )
The
r a t e of u c c e s s i s about 85 p e r c e n t .
Limitations
There
a r e
two
obvious
i m i t a t i o n s :
time
and
s p a c e . The program t a k e s
about
5 minutes 40 seconds
o n
a v e r a g e to a n a l y z e a p i c t u r e
though t h e time
ma y
range
from 70
e c s
t o 15
mins).
t must
be
remembered t h a t t i s
w r i t t e n
i n
a
h i g h - l e v e l
language and could
probably
be speeded u p by
a a c t o r
of
10
by
machine
c o d i n g .
Program, t o r e d p i c t u r e , r e g i o n d a t a
s t r u c t u r e s ,
p i c t u r e
and
o b j e c t d e s c r i p -
t i o n s , t o g e t h e r
occupy
about
2 K
of 24 b i t
words.
Some m o n i t o r i n g
and
u t i l i t y f u n c t i o n s not concerned w i t h t h e
mainstream
of h e
a n a l y s i s
c o u l d be
removed,
w h i l e a g a i n
machine
coding
could
probably e f f e c t
improvements.
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B RROW NDPOPPLESTONE
There
a r e
some
l o g i c a l l i m i t a t i o n s . I f
p i c t u r e s or
o b j e c t s w i t h more than
about e g i o n s a r e
