PROGRESS I N EXTENDING THE VIRGIN PROGRAM
VISION FLASH #20
Mark Dowson
Massachusetts I n s t i t u t e o f Techno1ogy
A r t i f i c i a l I n t e l 1igence Laboratory
Vision Group
September 1971
ABSTRACT
The VIRGIN program w i l l i n t e r p r e t pictures o f simple scenes. This paper
describes a program, SINNER, which w i l l deal with pictures which cont a i n cracks and shadows. In addition t o handling pictures o f t h i s
r i c h e r world, SINNER employs heuristics which use know1edge about
the s t r u t t u r e o f the three dimensional world t o reduce the number o f
interpretations o f some pictures and t o augment the e f f i c i e n c y o f the
parsing process.
Work reported herein was conducted a t the A r t i f i c i a l Intelligence
Laboratory, a Massachusetts I n s t i t u t e o f Technology research program
supported i n p a r t by the Advanced Research Projects Agency o f the
Department of Defense and monitored by the Offjce of Naval Research
under Contract Number NO0014-70-A-0362-0002.
introduction
V i s i o n F l a s h #14 (1) discusses extensions o f t h e V I R G I N p i c t u r e
p a r s i n g program ( 2 1 , whlch assigns I n t e r p r e t a t i o n s t o simple
s t r a i g h t l i n e drawings,
and "shadows".
First,
t o handle p i c t u r e s which i n c l u d e "cracks"
T h i s proposed e x t e n s i o n c o n s i s t s of two p a r t s ,
the se.t o f j u n c t i o n theorems i s expanded t;o I n c l u d e
l a b e l l n g s of "crack"
and "shadow'' j u n c t i o n s .
Second,
a number o f
11
h e u r i s t i c s " a r e described which w i 1 1 a c t t o reduce the number o f
p o s s i b l e i n t e r p r e t a t ions
o f each p l c t u r e .
B o t h these types o f exterlsion correspond t o
a d d i t i o n a l knowledge about the v i s u a l w o r l d and i t s
representat ion i n pictures.
The e x t r a j u n c t i o n theorems c a r r y
i n f o r m a t i o n about how the l o c a l f e a t u r e s o f a r i c h e r t h r e e
dlmensional w o r l d a r e represented I n a two dlrnenslonal p i c t u r e ;
the h e u r i s t i c s embody knowledge of a more g l o b a l n a t u r e about t h e
s t r u c t u r e o f t h e t h r e e dimensional w o r l d so represented.
The SINNER Program
A program has been w r i t t e n ,
c a l l e d SINNER,
which incl.udes a
subset o f t h e a d d i t i o n a l j u n c t i o n theorems and soma o f the
h e u r i s t i c s d e s c r i b e d i n F l a s h 114.
Even t h i s p a r t i a l e x t e n s i o n
r a i s e s enough issues t o be w o r t h d i s c u s s i o n a t t h l s stage.
F i g u r e 2 shows the j u n c t i o n l a b e l t n g s which a r e embodied as
j u n c t i o n theorems i n the o r i g i n a l V I R G I N program w h i l e f i g u r e 3
shows the a d d i t i o n a l shadow and crack l a b e l i n g s i n c l u d e d I n
PAGE 2
SINNER,
I n these labelings,
an a r r o w a c r o s s a l i n e i n d i c a t e s
t h a t t h e 1 i n e r e p r e s e n t s a shadow edge w i t h t h e shadow or) t h e
s i d e o f t h e a r r o w head.
Note that,
A 1 i n e marked ' C R '
represents a crack.
u n d e r t h e assumptfons g i v e n I n F l a s h #14,
r e g i o n s on e i t h e r s i d e o f a " c r a c k "
o r "shadow"
t h e two
1 ine represent
coplanar surfaces.
F i g u r e 1 shows a p i c t u r e o f a scene w i t h b o t h
c r a c k s and shadows.
I t i s l a b e l e d w i t h one p o s s i b l e
i r l t e r p r e t a t i o n t o i l l u s t r a t e t h e s e c o n v e n t ions.
FIGURE
1
PAGE 3
FIGURE
2
The V I R G I N J u n c t i o n Label lngs
PAGE 4
FIGURE
3
A d d i t i o n a l J u n c t i o n L a b e l i n g s I n c l u d e d i n SINNER
ELLS
The S I N N E R Heuristics
The t e r m " h e u r i s t i c "
i n t h i s context;
i f i t does.
c a r r i e s a c o n n o t a t i o n which i s u n f o r t u n a t e
a t r i c k which may o r may n o t work b u t 1s u s e f u l
I n general h e u r i s t i c s are,
In a d i s g u i s e d form,
the
progranimer's u r l a r t f c u l a t e d knowledge about the p r o b a b l e s t r u c t u r e
o f t h e w o r l d h i s program l i v e s i n .
below a r e q u i t e d i f f e r e n t .
explicitly,
program.
The h e u r ~ s t i c sd e s c r i b e d
They a r e intended t o a r t l c u l a t e ,
knowledge about t h e s t r u c t u r e of t h e domaln o f t h e
They can be thought o f as the p r o c e d u r a l analogues o f
theorems i n p r o j e c t i v e geometry,
o p t i c s and mechanics.
The 'IShadow Source" H e u r t s t i c
One c o n s t r a i n t on the scenes and v i e w i n g p o s i t i o n s which y i e l d
p i c t u r e s t h a t SINNER w i l l I n t e r p r e t 1s t h a t small changes i n t h e
v i e w i n g p o s i t i o n o r i n t h e p o s i t i o n o f the s i n g l e l i g h t source
i l l u m i n a t i n g t h e scene w i l l n o t a l t e r t h e t o p o l o g y o f t h e
resulting picture.
This,
I n p a r t lcular,
excludes p i c t u r e s 1 i k e
t h a t shown I n f i g u r e 4a where one body i n t h e scene c a s t s a
shadow which f a l l s p r e c i s e l y on a v e r t e x o f a n o t h e r body.
PAGE 6
FIGURE
4
Thus,
no 1 i n e j o i n i n g a p a i r o f j u n c t i o n s which must r e p r e s e n t
real,
physical,
v e r t i c e s may be i n t e r p r e t e d as a shadow edge.
w
When such a j u n c t i o n (Any ARROW,
FORK,
KAY
, PEAK
o r MULTl)
r e c e I v e s an I n t e r p r e t a t i o n which l a b e l s one o f I t s l i n e s as a
shadow
, an
a s s e r t i o n i s made whlch marks the j u n c t l o n a t the f a r
end o f t h e 1 I n e as a "SHADOWEND".
I n addition,
each such
j u n c t f o n theorem t e s t s t h a t t h e jtunctlon I t I s about t o l a b e l I s
n o t so marked.
F i g u r e 4b shows a n o t h e r w i s e a c c e p t a b l e l a b e l i n g
o f a fragment o f a p i c t u r e e x c l u d e d by th1s h e u r i s t i c .
PAGE 7
The S H A D D W ~ ~ E G I U NH e u r i s t i c
Tho a d j acerit r e g i o n s may r e p r e s e n t . t h e shadowed p o r t f ons o f a
p a i r of surfaces.
s u r f a c e s nus;
I f t h e r e I s h u t a s i n g l e 1 I g h t source t h e t w o
--
be p h y s i c a l l y d i s t i n c t
whtch I s t o say t h a t t h e
l i n e separating t h e r e g i o n s cannot be a shadow l'ine.
constraint
This
i s embodied I n S l NNER by marking as a "SHADOWREGION"
t h e reglon on t h e a p p r o p r i a t e s i d e o f each l i n e l a b e l e d as a
shadow edge;
then,
as each j u n c t i o n l a b e l i n g I s completed,
a test
i s made o f any new SHADOWREGION t o make sure t h a t i t does n o t
share a shadow l i n e w i t h any o t h e r SHADOWREGI.ON. F i e u r e 5 shows a
l a b e l trig o f a p i c t u r e fragment excluded b y t h l s t e s t .
The
procedure which marks r e g i o n s as SHADOWREGIONS i s an antecedant
theorem,
one o f a f a m i l y invoked by each l a b e l I n g a s s e r t i o n
~ l t h i neach j u n c t i o n theorem.
Other members o f t h i s f a m i l y o f
antecedant theorems make a s s e r t i o n s which a r e used i n t h e
h e u r i s t i c s n e x t described.
FIGURE
5
PAGE 8
Region P r e d i c a t e H e u r i s t i c s
A s s i g n i n g an I n t e r p r e t a t i o n ,
as an edge,
t o a 1 i n e which
associates a p a i r o f regions a r t i c u l a t e s the r e l a t i v e i n c l i n a t i o n
of t h e two s u r f a c e s t h a t t h e r e g i o n s represent;
t h a t is,
it tells
whether t h e s u r f a c e s a r e c o p l a n a r o r meet a t a r e l a t i v e angle o f
g r e a t e r o r l e s s than 180 degrees.
Whenever a l l n e a s s o c i a t i n g a p a i r o f r e g l o n s (as do a l l l i n e s )
I s labeled,
one o f t h e f a m i l y o f antecedant theorems mentioned
above a s s e r t s a predicate o f the, form:
(PRED J RA < p r e d i c a t e > R B I
Where RA and RB a r e t h e names o f t h e two regions,
J t h e name o f
t h e j u n c t i o n b e i n g l a b e l e d and <pred.tcate> i s COPLANAR, V X o r CV
appropriately.
L i n e s l a b e l e d "crack" o r "shadow"
COPLANAR p r e d i c a t e ,
1 i n e s l a b e l e d "VX"
o r "CV"
give r i s e t o a
t o VX o r C V
p r e d i c a t e s r e s p e c t i v e l y.
NOW s h o u l d a p a l r o f r e g l o n s have more than one l l n e -In common,
t h e i n t e r p r e t a t i o n s t h a t t h e l i n e s may r e c e i v e a r e c o n s t r a i n e d .
No two r e g l o n s may be a s s a c f a t e d by more t h a n one o f t h e
p r e d i c a t e s above a t a time snd,
if two o r more 1 Ines a t 1 g i v e
r l se t o V X p r e d i c a t e s o r a1 1 g i v e r i s e t o CV p r e d i c a t e s ,
the
1 i n e s must be c o l l n e a r . F l g u r e 6 i l l u s t r a t e s these c o n s t r a i n t s .
The l a b e l i n g g i v e n I n f i g ,
6a i s unacceptable as the l i n e s AB and
CD a r e b o t h common t o t h e p a l r o f r e g l o n s RO and R 1 so a t l e a s t
one o f them must t a k e an g c > c c l u d i n gedge'
fig.
i n t e r p r e t a t i o n as i n
6b u n l e s s t h e y a r e c o l i n e a r as I n f i g .
6c.
PAGE 9
FIGURE
6
PAGE 1 0 '
A s i m p l e e x t e n s i o n o f these c o n s t r a i n t s i s t o make t h e
P r e d i c a t e COPLANAR t r a n s 1 t l v e and t r e a t any p a l r o f adjacent,
coplanar,
s u r f a c e s as a s i n g l e s u r f a c e f o r t e s t s based on t h e
above c o n s t r a i n t s .
More complex e x t e n s i o n s a r e p o s s i b l e . For
i n s t a r i c e ( r e p r e s e n t l n g t h e f u l l p r e d i c a t e as ( R A < p r e d i c a t e > R B I
for clarity)
( R A VX RB).(RB
and s o on.
VX R C ) I,
W ( R A COPLANAR R C )
These e x t e n s i o n s have n o t y e t been I n v e s t i g a t e d
systematical ly.
A t e s t t o see whether any r e g i o n p r e d i c a t e c o n s t r a i n t s have
been v i o l a t e d i s made a f t e r each j u n c t i o n has been l a b e l e d .
The
p r e s e n t v e r s i o n o f S I N N E R mere1 y t e s t s t o see t h a t no more than
one o f t h e l t n e s common t o t h e same p a i r o f r e g i o n s has r e c e i v e d
a V X o r CV l a b e l ,
b u t e x t e n d i n g t h i s t o i n c l u d e the whole range
o f r e g i o n p r e d t c a t e c o n s t r a i n t s w i l l be a s i m p l e m a t t e r .
PAGE 11
Rssul t s
A1 thol..~p;fat h e p r i m a r y i n t e n t i o n o f t h e h e u r i s t i c s d e s c r i b e d
above f s t o e x c l u d e some I n t e r p r e t a t i o n s o f p i c t u r e s which would
o t t ~ e r w l : ;he
~ admissable,
.[,rIthm
r)arC,1n7
they augment t h e e f f l c l e n c y o f the
i n a t h e r ways,
Some J u n c t i o n I n t e r p r e t a t i o n s
wf~lr:tl
..
-4
or11 y he d i s c o v e r e d t o he i r ~ c o r r e c tl a t e r I n t h e
parsIr~l
*;
::
r e j e c t e d Imniedlately b y the h e u r l s t i c s .
I n the
c u r r e r r t Ir~!plerbtentatI o n t h i s prov Ides o n l y a mare1n a l s a v i n g I n
corrtputation t i m e s i n c e the r~echanisms f o r making t h e t e s t s a r e
relatfvely "expensive'' and o n l y a sirhset o f the p o s s i b l e
h e u r l s a i c s a r e a c t u a l l y applied;
b u t l t i s expected t h a t , w i t h a
r u l l e r s e t of heuristics, the savtng I n t i m e w i l l be more
s l g n f f lcant,
p a r t i c u l a r l y w i t h more compl i c a t e d p i c t u r e s .
For comparlson,
f I g u r e 7 i l l u s t r a t e s t h e performance of V I R G I N
on a s i m p l e p l c t u r e ,
F i g u r e 7a I s the p i c t u r e p r e s e n t e d as d a t a
t o V I R G I N ( I n t h e form o f a l i s t o f angle and j u n c t i o n t y p e
a s s e r t i o n s ) and f i g u r e s 7 b t o 7e show the r e s u l t i n g p a r s i n g s .
The time g i v e n b e s l d e each i n t e r p r e t a t i o n I s t h e processor t i m e
taken, a f t e r s t a r t i n g t h e program, t o produce t h e I n t e r p r e t a t i o n .
These times a r e g i v e n f o r comparlson o n l y s i n c e t h e a b s o l u t e
t i m e s depend e n t i r e l y on t h e ImplementatIon.
between t h e l a s t o f these and t h e
t ime taken,
'
The discrepancy
t o t a l time'
represents the
a f t e r p r o d u c i n g the l a s t poss I b l e i n t e r p r e t a t i o n ,
to
d i s c o v e r t h a t no o t h e r I n t e r p r e t a t i o n i s possible. Time taken up
i n garbage c o l l e c t i o n has been s u b t r a c t e d throughout,
PAGE 1 2
FIGURE
7
'
The f o u r f n t e r p r e t a t i o n s correspond t o e l t h e r a cube I n v i s i b l v
supported c l e a r o f t h e s u r f a c e r e p r e s e n t e d b y t h e background o f
t h e p i c t u r e o r s t u c k t o i t along some p a l r o f edges o f the cube.
T h e p i c t u r e o f f i g u r e 8 has o n l y a s i n g l e I n t e r p r e t a t i o n w i t h
t h e r e g i o n R 4 r e p r e s e n t i n g a shadow c a s t by the cube on I t s
s l ~ p p a r Irlg
t
surface. S l N N E R takes 1 5 seconds t o produce t h i s
t o t e r p r e t a t i a n and a f u r t h e r 65 seconds t o d i s c o v e r t h a t no
f u r t h e r tnterpretatlons are possible.
FIGURE
8
Note t h a t no e x p l i c i t I n f o r m a t i o n t e l l s SINNER t h a t R4 Is a
shadow;
t h e r e I s no o t h e r p o s s l h l e i n t e r p r e t a t i o n under t h e
constraints we have s e t up.
ambiguous.
The p i c t u r e o f f i g u r e 9 I s more
F i g u r e s 10a through 1 0 f g i v e t h e i n t e r p r e t a t i o n s t h a t
SINNER r e t u r n s .
t h e J u n c t i o n J27,
Here t h e r e a r e f o u r d i f f e r e n t I n t e r p r e t a t ions o f
two o f t h e J u n c t i o n J 2 6 and two o f J25.
a l l o f t h e 16 combinations a r e p o s s i b l e ,
however,
Not
as
Interdependencies amongst t h e I n t e r p r e t a t i o n s o f the j u n c t i o n s
reduce the number o f p o s s i b l e t n t e r p r e t a t l o n s t o s i x .
PAGE 14
PAGE 15
FIGURE
10a
a '~hadocydirection'
hevristie w o u l d
eduk t k ~
i n kerprotat;oh
~
FIGURE
IQe
FIGURE
105
PAGE 1 8 .
f t I s now p o s s i b l e t o see how more knowledge about t h e w o r l d
c a n reduce t h e number o f i n t e r p r e t a t i o n s s t i l l f u r t h e r .
The
i n t e r p r e t a t i o n g i v e n i n 1 0 f would n o t appear i f the r e g i o n
p r e d i c a t e s were made t r a n s f t i v e a s ' dtscussed above I n the s e c t i o n
o n Regiarl P r e d i c a t e heuristics.
with RO
R 7 would be t r e a t e d as coplanar
b o t h o f whlch a r e concavely r e l a t e d by non-col I n e a r
lines to R6.
The two o t h e r i n t e r p r e t a t i o n s which g i v e R 7 as a
shadow region,
l o b and 10d,
c o u l d be e x c l u d e d by an h e u r i s t i c
whlch t o o k i n t o account d i r e c t i o n s o f shadows s i n c e i f R 4 and R 5
a r e shadow r e g i o n s t h e d i r e c t i o n o f t h e 1 i g h t source must be such
t h a t t h e r e i s no o b j e c t I n t h e scene t o c a s t a shadow I n the
p o s i t i o n o f R7.
T h i s leaves t h r e e i n t e r p r e t a t i o n s which
c o r r e s p o n d t o the intuitively acceptable ones o f the bottom b l o c k
b e i n g a t t a c h e d t o a w a l l (lOa),
t n v t s l b l y supported ( 1 0 ~ )o r
a t t a c h e d t o t h e f l o o r (10e).
The p l c t u r e o f f i g u r e 11 has o n l y two I n t e r p r e t a t i o n s shown as
l l a and l a b , and i t I s c l e a r t h a t t h e i n t e r p r e t a t i o n o f Ilb can
be e x c l u d e d by t h e same h e u r i s t i c as \vould exclude 1 0 f above.
However,
t h e v e r y l o n g t i m e t h a t S I N N E R takes ( o f the 'order o f
f o r t y m i n u t e s ) t o produce these i n t e r p r e t a t i o n s exposes a m a j o r
d e f i c i e n c y I n t h e b a s i c s t r u c t u r e o f the SINNER program.
PAGE 19
FIGURE
lla
FIGURE
llb
PAGE 20
What happens I s t h a t ,
I s R12,
as one o f t h e f i r s t regtons t o be t a c k l e d
t h e T - j u n c t i o n J l I s one o f the f i r s t t o be l a b e l e d .
Due
t o t h e o r d e r o f j u n c t i o n theorems i n t h e database t h e s h a f t o f
t h e T g e t s l a b e l e d as an o c c l u d i n g edge.
Now t h l s i s i n c o r r e c t
as t h e o n l y p o s s i b l e l n t e r p r e t a t i o n o f R 1 Is as a shadow region.
However,
s i n c e R1 Is t h e l a s t r e g i o n t o be d e a l t w i t h ,
t h l s error
can o n l y be c o r r e c t e d a f t e r b a c k i n g up through almost t h e whole
i n t e r p r e t a t i o n t r e e t r y i n g d i f f e r e n t s i d e branches,
u n s u c c e s s f u l 1 y,
a t each l e v e l .
What i s worse i s t h a t when backup
f i n a l l y reaches J l , , t h e I n t e r p r e t a t i o n n e x t chosen f o r t h e s h a f t
o f t h e TEE i s n o t t h e r l g h t one,
Interpretatton.
b u t a n o t h e r wrong
I n a l l t h l s process i s repeated f i v e times
b e f o r e the r l g h t i n t e r p r e t a t i o n surfaces.
s t u p i d way t o I n t e r p r e t t h i s p i c t u r e .
Clearly t h i s I s a
For t h i s p a r t i c u l a r p i c t u r e
t h e t r o u b l e c o u l d be c u r e d by r e o r d e r i n g the theorems i n the
data-base,
b u t t h e n t h e same t r o u b l e would be encountered on some
d i f f e r e n t p i c t u r e . There a r e o t h e r p o s s i b i l l t l e s .
One m i g h t be
t o d e f e r t h e I n t e r p r e t a t i o n o f t h e s h a f t s o f TEE'S u n t i l t h e end
o f an i n t e r p r e t a t i o n .
worst trouble,
Although t h l s would e l i m i n a t e some o f t h e
i t would d e s t r o y t h e u n l f o r m l t y wi'th which t h e t o p
l e v e l program handles v a r l o u s types o f p l c t u r e fragment.
A mare g e n e r a l approach would be f o r the program t o t a k e some
ftweral l v i e w a f t h e p i c t u r e i n advance o f t r y i n g t o make a
r r e t a f l e d interpretation so as t o f o r m u l a t e same s t r a t e g i c plam
;3?mut how t o conduct t h e i n t e r p r e t a t Ian
F l r s t , and s o on.
::.srnbit~nfior; o f t h i s
-- whfch
reglon t o t a c k l e
The f i n a l approach 1s l i k e l y t o use some
and o t h e r methods,
i l ! v c > l v ~': a r e rlot even w e l l formulated,
b u t as y e t t h e problenis
much less c l e a r l y
(ir-rd~a
~"s.tr.~~d.
Cnncluslcns
E x t e n d f n g t h e V I R G I N program t o deal w l t h a r i c h e r w o r l d and t o
deal w i t h t h a t w o r l d l e s s n a i v e l y has answered some q u e s t i o n s
about s h i s approach t o p i c t u r e I n t e r p r e t a t i o n and has opened many
We have seen t h a t the approach f i r s t
avenues f o r f u t u r e work.
delfneated by Clowes ( 3 ) and Huffman ( 4 ) i s s t i l l a p p l i c a b l e In a
~ t c h e rv l s u a l world. The e f f o r t r e q u i r e d t o parse a p i c t u r e grows
bv!th t h e tncreased v a r i e t y of p i c t u r e f e a t u r e s and w l t h the
complexity o f the plcture,
approach I m p r a c t l c a b l e ,
b u t n o t a t a r a t e which makes the
Knowledge about t h e w o r l d l e s s l o c a l
than t h a t c a r r i e d by a t a b l e o f permissable j u n c t i o n l a b e l l n g s
w t l l reduce t h e a m b i g u i t y o t h e r w i s e i n h e r e n t I n some p l c t u r e s and
decrease t h e e f f o r t requ l r e d t o I n t e r p r e t o t h e r s ,
Work i n t h e immediate f u t u r e w i l l c o n c e n t r a t e on I n c r e a s i n g t h e
amount o f such knowledge a v a i l a b l e t o the SINNER program. T h i s
vdi
1 1 i n c l u d e some knowledge o f geometry;
here the t h e o r e t f c a l
PAGE 2 2
framework p r o v l d e d by Clowes e t a1 ( 5 ) w i l l be o f use.
long,
however,
Before
t h e more c h a l l e n g i n g and d l f f l c u l t problem w i l l
have t o be f a c e d o f g e t t i n g the program t o f o r m u l a t e some
s t r a t e g i c p l a n i n advance o f a c t u a l l y making an i n t e r p r e t a t t o n o f
t h e p i c t u r e . This,
t o g e t h e r w i t h o t h e r v e r y g l o b a l methods o f
irnpt.ov i n g t h e performance o f the pars l n g a1 g o r 1 thm,
t o a more ' g e n e r a l '
kind o f Intelligence.
corresponds
I t seems l i k e l y t h a t
t h e r e s u l t s o b t a i n e d I n the course o f t h l s e x e r c f s e w i l l be o f
w i d e r a p y l i c a b i l I t y than t o j u s t t h l s s i n g l e v i s i o n program and
w i l l open up many more avenues f o r f u t u r e research.
'
PAGE 2 3
REFERENCES
(1)
Mark
ti Hal tz, Oav f d
Dnwsoti,
' c r a c k s and Shadows,
A.I.
Lab. Vlslon F l a s h 1 4 ,
1971
(2)
[lowson, Hark
' V I R G I N : a program which i n t e r p r e t s 1 ine
drawings. I
A r t l f l c l a l I n t e l l i g e n c e Lab, M.I.T,
Memo Ne.244.
( I n progress)
(3)
Clowes, M.B,
' o n Seeing T h i n g s '
Artificial Intel1 igence Vo1.2,
1
Huffrt~an D.A.
(5)
Clowes M,B,
t!ackwart:h A . K .
Star] t a n R . 6..
1971
' I m p o s s i b l e O b j e c t s as Nonsense sentences'
Machine I n t e l 1 Igence 6. Ed. C a l l I n s b M t c h i e
1970.
' P i c t u r e I n t e r p r e t a t I o n as a problem-:-olving
process'
Lab, o f E x p e r i m e n t a l Psychology
U n i v e r s i t y o f Sussex June 1971.