A Comparative Study of Texture Measures(1996-Cited1797)

7/28/2019 A Comparative Study of Texture Measures(1996-Cited1797)

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Pergamon Pat ternRecoonit ion, Vol . 29, No. l , pp. 51 59, 1996Elsevier Science LtdCop yright 1996 Pat te rn Recogni tion Socie tyPrinted in Great Bri ta in. Al l r ights reserved0031-3203 / 96 $15 .00+ .00

0031-3203(95)00067-4A C O M P A R A T I V E S T U D Y O F T E X T U R E M E A S U R E S

W I T H C L A S S I F IC A T I O N B A S E D O NF E A T U R E D I S T R IB U T I O N S

TIMO OJALA,* MATTI PIE TIK AINE N*t and DAVID HARWOOD:~* Department of Electrical Engineering, University of Oulu, FIN-90570 Oulu, FinlandCenter for Automation Research, University of Maryland, College Park, MD 20742, U.S.A.

(Received 19 Janua ry 1994; n revised orm 11 April 1995;accepted for publication 15 Ma y 1995)Abstract--This paper evaluates the performance both of some texture measures which have been success-fully used in various applications and of some new promising approaches proposed recently. For classifica-tion a method based on Kullback discrimination of sample and prototype distributions is used. Theclassification results for single features with one-dimensional feature value distributions and for pairs ofcomplementary features with two-dimensional distributions are presentedTexture analysis Cl as si fi ca ti on Feature distributionKullback discriminant Performance evaluation Brodatz textures

l . I N T R O D U C T I O NTexture is an impo rtan t characteristic for the analysisof many types of images. A wide variety of measures fordiscrimina ting extures have been proposed, c1'2~ Com-parative studies to evaluate the performance of sometexture measures have been carried out by Weszkaet al., ~3~Du Bufet al . ~4~and Ohani an and Dubes,~s) forexample.

Most of the approaches to texture analysis quantifythe texture measures by single values (means, variancesetc.). These values are used as elements of featurevectors in performing classification. In this way muchimport ant information contained in the distributionsof feature values might be lost. Some earlier studiesalso suggest that distr ibutions of joi nt occurrences ofpairs of features give better results than distr ibutions ofsingle features on their own.

This paper evaluates the performance both of sometexture measures which have been successfully usedin various applications and of some new promisingapproaches proposed recently. For classification amethod based on K ullback discrimination of sampleand prototype dis tribut ions is used. 16) The classifica-tion performances for single features with one-dimen-sional feature value distributions and for pairs ofcompl ementary features with two-dimensional dis-tributions are evaluated. Two different types of datasets are used in experiments : a set of Brodatz 's images,and images used in a recent comparative study byOha nia n and Dubes. S) Our study provides one of thelargest comparison of texture measures presented in

t Author for whom correspondence should be addressed.51

the literature and completes the study carried out byOhan ian and Dubes.

2 . T E X T U R E M E A S U R E S U S E D I N T H I S S T U D Y

2 .1 . Gr ay - l eve l d i f f e r ence me th odA class of local properties based on differences

between pairs of gray levels or of average gray levelshas been sometimes used in texture analysis, 3,7~ Ourfeature set contai ned four measures based on the gray-level difference method: D IF FX and DI FF Y are histo-grams of absolu te gray-level differences betweenneighboring pixels computed in horizontal and verti-cal directions, respectively, while DIF F2 accumulatesabsol ute differences in horizontal and vert ical direc-tions and DI FF 4 in all four principal directions, res-pectively, in a single histogram, providing rotationinva rian t texture measures.2.2. L a w s ' t e x t u r e m e a s u r e s

The "texture energy measures" developed byLaws s) or related measures developed by others havebeen used in various applications. Four Laws' 3 x 3operators were considered in this study. L3E3 andE3L3 perform edge detection in vertical and hor izon-tal directions, respectively, and L3S3 and $3L3 are linedetectors in these two orthogona l directions.

2.3. C e n t e r - s y m m e t r i c c o v a r i a n c e m e a s u re sLaws' and other related studies of texture analysissuggest that many natural and artificial textures aremeasurab ly "loaded" with distri butions of various spe-cific local patterns of texture having these abstract


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52 T. OJA LA et al.

s y m m e t r i c a l f o r m s . M o r e o v e r , t o m e a s u r e t h e l o c a l" l o a d i n g " o f g r a y - l e v e l s y m m e t r i c ( p o s i t i v e ) o r a n t i -s y m m e t r i c ( n e g a ti v e ) te x t u r e , w e h a v e o n l y t o c o m p u t el o c a l a u t o - c o v a r i a n c e s o r a u t o - c o r r e l a t i o n s o f c e n t e r -s y m m e t r i c pi xe l v a l u e s o f s u i ta b l y s i ze d n e i g h b o r -h o o d s . I n a r e c en t s t u d y o f H a r w o o d et al. , t6) a set ofr e l a t e d m e a s u r e s w a s i n t r o d u c e d , i n c l u d i n g t w o l o c a lc e n t e r - s y m m e t r i c a u t o - c o r r e l a t i o n m e a s u r e s , w i t h l in -e a r ( S A C ) a n d r a n k - o r d e r v e r s i o n s ( S R A C ) , t o g e t h e rw i t h a r e l a t e d c o v a r i a n c e m e a s u r e ( S C O V ) . W e a p -p l ie d t h e s e th r e e m e a s u r e s i n t h e p r e s e n t w o r k .2.4. L o c a l b i n a r y p a t t e r n s

R e c e nt ly , W a n g a n d H e 9 ) i n t r o d u c e d a n e w m o d e lo f t e x tu r e a n a l y s i s b a s e d o n t h e s o - c a l l e d t e x tu r e u n i t,w h e r e a t e x t u r e i m a g e c a n b e c h a r a c t e r i z e d b y i tst e x t u r e s p e c t r u m . A t e x t u r e u n i t ( T U ) i s r e p r e se n t e d b ye i g h t e l em e n t s , e a c h o f w h i c h h a s o n e o f t h r e e p o s s i b lev a l u e s ( 0 ,1 , 2 ) o b t a i n e d f r o m a n e i g h b o r h o o d o f 3 x 3pixe ls . In to ta l , t h e re a re 38 - - 6561 poss ib le t ex tureuni t s desc r ib ing spa t i a l th ree - l eve l pa t t e rns in a 3 x 3n e i g h b o r h o o d . T h e o c c u r r e n c e o f d is t ri b u t io n o f t ex -t u r e u n i t s c o m p u t e d o v e r a r e g i o n i s c a l le d t h e t e x t u r es p e c t r u m .

I n t h i s s t u d y w e p r o p o s e t o u s e a t w o - le v e l v e r s io n o ft h e m e t h o d o f W a n g a n d H e . I t p r o v id e s a r o b u s t w a yf o r d e s c r i b i n g p u r e l o c a l b i n a r y p a t t e r n s ( L B P ) ina t ex ture . In the two- leve l ve rs ion , the re a re only2 8 = 2 5 6 p o s s ib l e t e x t u r e u n i t s i n s t e a d o f 6 56 1 . I nt h e b i n a r y c a s e, t h e o r i g i n a l 3 x 3 n e i g h b o r h o o d[ F i g . l ( a )] i s t h r e s h o l d e d b y t h e v a l u e o f t h e c e n t e rp ixe l. Th e va lues of the p ixe ls in the thresh olde dn e i g h b o r h o o d [ F i g . l ( b ) ] a re m u l t ip l i e d b y t h e w e i g h t sg i v e n t o t h e c o r r e s p o n d i n g p i x e l s [ F i g . 1 (c )] . T h e r e s u ltfor th i s exam ple i s show n in F ig . l (d) . F ina l ly , thev a l u e s o f t h e e i g h t p ix e l s a r e s u m m e d t o o b t a i n t h en u m b e r ( 1 69 ) o f t h is t e x t u r e u n i t. T h e L B P m e t h o d i sa g r a y - s c a le i n v a r i a n t a n d c a n b e e a s i ly c o m b i n e d w i t ha s i m p l e c o n t r a s t m e a s u r e b y c o m p u t i n g f o r e a c hn e i g h b o r h o o d t h e d i ff e re n c e o f t h e a v e r a g e g r a y l ev e lo f th o s e p i x e ls w h i c h h a v e t h e v a l u e 1 , a n d t h o s e w h i c hhav e the va lu e 0 , re spec t ive ly [ s ee F ig . l (b) ] .2.5. C o m p l e m e n t a r y f e a t u r e p a ir s

I n m o s t c a s es a si n g le t e x tu r e m e a s u r e c a n n o t p r o -v i d e e n o u g h i n f o r m a t i o n a b o u t t h e a m o u n t a n d s p a -t i a l s t ruc tu re of loca l t ex ture . Be t t e r d i sc r im ina t ion oft e x t u r e s s h o u l d b e o b t a i n e d b y c o n s i d e r i n g j o i n t o c -c u r r e n c e s o f tw o o r m o r e f e a t u re s . A s a n e x a m p l e o ft h is k i n d o f a p p r o a c h , t h e s p a t i a l g r a y - le v e l d e p e n d -

7 6 19 3 7

(a ) (b) (c ) (d)Fig. 1. Two-level version (LBP) of the texture unit.

e n c e m e t h o d ( c o - o c c u r r e n c e m e t h o d ) e s t i m a t e s t h ejo in t gray- l eve l d i s t r ibu t ion for two gra y level s loca teda t a spec i f ied d i s t ance and angle . Shen and B ie " )c o n s i d e r e d t h e u s e o f g r a d i e n t m a g n i t u d e a n d d i r e c-t i o n , g r a y l ev e l a n d g r a d i e n t d i r e c t io n , a n d g r a y l e ve la n d g r a d i e n t m a g n i t u d e , r e sp e c t iv e l y , j o i n t l y i n t h e i rf e a t u r e f r e q u e n c y m a t r i x ( F F M ) s c h e m e .

O u r p r i m a r y g o a l w a s t o f i n d p a ir s o f su c h f e a tu r e sw h i c h p r o v i d e c o m p l e m e n t a r y in f o r m a t i o n a b o u t t e x -tures , us ing a two-dimens iona l Kul lback c las s i f i ca t ions c he m e . C o m p l e m e n t a r y f e a t u re s s h o u l d p r o v i d e m o r eo r l es s u n c o r r e l a t e d t e x t u r e i n f o r m a t i o n .

T h e c e n t e r - s y m m e t r i c c o v a r i a n c e m e a s u r e s a r e a b -s t ra c t , m e a s u r i n g c o v a r i a n c e s o f a n y l o c a l c e n te r -s y m m e t r i c p a tt e rn s . T h e y p r o v i d e r o b u s t i n f o r m a t i o na b o u t t h e a m o u n t o f l o c a l te x t u r e , b u t v e r y li tt le a b o u te x a c t l o c a l s p a ti a l p a t t e r n s . T h i s i m m e d i a t e l y s u g g e s tst h a t w e s h o u l d c o n s i d e r t e x t u r e a n a l y s is o f p u r e s p a t i alp a t t e r n s , w h i c h w o u l d c o m p l e m e n t t h e a n a l y s i s . T h el o c a l b i n a r y p a t t e r n s ( L B P ) w e r e c h o s e n f o r t h is p u r -p o s e . T w o d i f fe r e n t f e a tu r e s w e r e c o m b i n e d w i t h L B P .L B P / C i s b a s e d o n t h e c o n t r a s t m e a s u r e i n t r o d u c e de a rl ie r a n d t h e o t h e r p a i r is L B P / S C O V . T h e c o n t r a s ta n d S C O V m e a s u r es w e r e q u a n t iz e d t o h a v e o n l y e ig h tv a l u e s t o m a k e s u r e t h a t t h e t w o - d i m e n s i o n a l f e a tu r eh i s to g r a m s w o u l d n o t b e c o m e t o o s p a r se .

L a w s ' m a s k s c h o s e n f o r t h is s t u d y p e r f o r m e d g e o rl ine de tec t ions in hor i zonta l or ve r t i ca l d i rec t ions .T h e s e k i n d s o f p a t t e r n s c a n o c c u r , h o w e v e r , i n a r b i t-r a r y d i r e c t i o n s , w h i c h s u g g e s t s t h a t a j o i n t u s e o f e d g eo r l i n e d e t e c t o r s i n th e o r t h o g o n a l d i r e c t io n s s h o u l d b ec o n s i d e r e d . I n a s i m i l a r w a y , d i ff e r en c e h i s t o g r a m s a r eu s u a l l y c o m p u t e d f o r d i s p l a c e m e n t s i n h o r i z o n t a l o rv e r t ic a l d i r e c ti o n s , a n d a jo i n t u s e o f t h e se o r t h o g o n a ld i r e c t io n s s h o u l d p r o v i d e u se fu l i n f o r m a t i o n f o r t e x -t u r e d i s c r i m i n a t i o n .

T h e p a i r L 3 E 3 / E 3 L 3 c o r r e s p o n d s e d g e d e t e c t i o n ,L 3 S 3 /S 3 L 3 li ne d e te c ti o n a n d D I F F X / D I F F Y a b s o -l u t e g r a y - s c a l e d if f er e n c es i n t h e t w o o r t h o g o n a l d i r e c -t io n s , r e sp e c ti ve ly . D I F F Y / S C O V c o m b i n e s a b s o l u t egray-sc a le d if fe rences in the ve r t i ca l d i rec t ion wi th thec e n te r -s y m m e t r ic c o v a r ia n c e m e a s u re S C O V . G M A G /G D I R i s u s i n g g r a d i e n t m a g n i t u d e s a n d d i r e c t i o n sobta in ed by a 3 x 3 Sobe l edge opera tor . A l l o f thesefea ture com bina t io ns were quant i zed in to 32 x 32 b ins .

3. NEAREST-NEIGHBOR LASSIFICATIONUSINGK U L LB A CK D I S C R I M I N A T I O N

I n e x p e r i m e n t s w i t h I m a g e S e t I , t h e c l a ss i fi c a ti o n o fa s a m p l e w a s b a s e d o n c o m p a r i n g t h e s a m p l e d is t r ib u -t o n o f fe a t u r e v a l u e s t o s e v e r a l p r e - d e f in e d m o d e ld i s t r ib u t i o n s o f f e a t u r e v a l u es w i t h k n o w n t r u e c l as sl ab e ls . T h e s a m p l e w a s a s s ig n e d t h e l a b e l o f t h e m o d e lt h a t o p t i m i z e d K u l l b a c k ' s m i n i m u m c r o s s - e n t r o p ypr inc ip le [eq ua t i on (1)l . 11) He re s a nd m a re thes a m p l e a n d m o d e l d i s t r i b u t i o n s , n i s t h e n u m b e r o fb ins an d s , m~ a re the respec t ive s ample and mo de lprobabi l i t i e s a t b in i . Thi s (pseudo- ) me t r i c measuresl i k e l i h o o d s t h a t s a m p l e s a r e f r o m a l t e r n a t i v e t e x t u r e


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Co mp arative study of texture measures 53

c l a ss e s , b a s e d o n e x a c t p r o b a b i l i t i e s o f f e a t u r e v a l u e s o fp r e - c l a s s i fi e d t e x t u r e p r o t o t y p e s .

D ( s : m ) = ~ s i l o g s i . ( 1 )i = 1 m i

T h e m o d e l d i s t r i b u t i o n f or e a c h c l as s w a s o b t a i n e db y s c a n n i n g t h e g r a y - s c a l e c o r r e c t e d 2 5 6 x 2 5 6 t e x t u r ei m a g e w i t h t h e l o c a l t e x t u r e o p e r a t o r . T h e d i s t r i b u -t i o n s o f l o c a l s t a t i s t i c s w e r e d i v i d e d i n t o h i s t o g r a m sh a v i n g a f i x e d n u m b e r o f b i n s ; h e n c e , t h e K u l l b a c k ' sc r o s s - e n t r o p y m e a s u r e h a d t h e s a m e n u m b e r o f d e-g r e e s - o f - f r e e d o m f o r e v e r y p a i r i n g o f a s a m p l e a n da m o d e l . T h e n u m b e r o f b in s u s e d i n q u a n t i z a t io n o ft h e f e a t u r e s p a c e p l a y s a c r u c i a l r o l e . H i s t o g r a m s w i t ht o o m o d e s t a n u m b e r o f b i n s fa il t o p r o v i d e e n o u g hd i s c r i m i n a t iv e i n f o r m a t i o n a b o u t t h e d i s t r i b u ti o n s .H o w e v e r , s i n c e t h e d i s t r i b u t i o n s h a v e a f i n i te a m o u n to f e n t r i es , it d o e s n o t m a k e s e n s e to g o t o t h e o t h e re x t re m e . I f h i s t o g r a m s h a v e t o o m a n y b i n s, a n d t h ea v e r a g e n u m b e r o f e n t r i e s p e r b i n i s v e r y s m a l l , h i s t o -g r a m s b e c o m e s p a r s e a n d u n s t a b l e . I n m o s t o f o u re x p e r i m e n t s , h i s t o g r a m s w i t h 3 2 b i n s w e r e u s ed . T h i sc o r r e s p o n d s t o a n a v e r a g e n u m b e r o f 3 2 e n tr i es p e r b i nf o r s a m p l e s 3 2 x 3 2 i n s i z e a n d e i g h t e n t r i e s p e r b i n f o rsam ple 16 16 i n s iz e , r e spec t i ve ly .

T h e f e a t u r e sp a c e w a s q u a n t i z e d b y a d d i n g t o g e t h e rf e a t u r e d i s t r i b u t i o n s f o r e v e r y s i n g l e m o d e l i m a g e i na t o t a l d i s t r i b u t i o n , w h i c h w a s d i v i d e d i n t o 3 2 b i n sh a v i n g a n e q u a l n u m b e r o f e n t r ie s . H e n c e , t h e c u tv a l u e s o f t h e b i n s o f t h e h i s t o g r a m s c o r r e s p o n d e d t o3 .1 25 ( 1 0 0/ 3 2) p e r c e n t i l e o f th e c o m b i n e d d a t a . D e r i v -i n g t h e c u t v a l u e s f r o m t h e t o t a l d i s t r i b u t i o n a n da l l o c a t in g e v e r y b in t h e s a m e a m o u n t o f c o m b i n e dd a t a g u a r a n t e e s t h a t t h e h i g h e s t r e s o l u t i o n o f t h eq u a n t i z a t i o n i s u s e d w h e r e t h e n u m b e r o f e n t r ie s i sl a r g e s t a n d v ice versa . I t s h o u l d b e n o t e d t h a t t h eq u a n t i z a t i o n o f f e a t u r e s p a c e i s o n l y r e q u i r e d f o r t e x -t u r e o p e r a t o r s w i t h a c o n t in u o u s - v a l u e d o u t p u t . O u t -p u t o f s o m e d i s c r e te o p e r a t o r s l i k e L B P , w h e r e t w os u c c e s s iv e v a l u e s c a n h a v e t o t a l l y d i f fe r e n t m e a n i n g ,d o e s n o t r e q u i re a n y f u r th e r p r o c e s s in g ; o p e r a t o r o u t -p u t s a r e j u s t a c c u m u l a t e d i n t o a h i s t o g r a m . T h e e m p t yb i n s w e r e s e t t o o n e .I n e x p e r i m e n t s w i t h I m a g e S e t I I , a s i n g le m o d e ld i s t r i b u t i o n f o r e v e r y c l a s s w a s n o t u s e d a s w i t h t h eB r o d a t z ' s i m a g e s . E v e r y s a m p l e w a s i n i t s t u r n c l a s s i -f i e d u s i n g t h e o t h e r s a m p l e s a s m o d e l s , h e n c e t h el e a v e - o n e - o u t a p p r o a c h w a s a p p l i e d . T h e s a m p l e w a sa s s i g n ed t h e l a b e l o f t h e m o d e l t h a t m i n i m i z e d t w o -w a y t e s t - o f - i n d e p e n d e n c e [ - eq u a t io n (2 )] t h a t i sa m o d i f i c a t i o n fr o m K u l l b a c k ' s c r i t e r i o n : ~2~G = 2 o - - o

i = 1 - I I s , m X i = l / \ i = 1

[ ( . ) ) ] )E ~ , f , l o g f i , (2 )s , m i = 1 \ s , m i =

w h e r e s , m a r e t h e t w o t e x t u r e s a m p l e s ( te s t s a m p l e a n dm o d e l ) , n is th e n u m b e r o f b i n s a n d f l i s t h e f r e q u e n c ya t b in i .

T o c o m p a r e d i s t r i b u t i o n s o f c o m p l e m e n t a r y f e a t u rep a i r s , m e t r i c s D a n d G w e r e e x t e n d e d i n a s tr a i g h t f o r -w a r d m a n n e r t o s c a n t h r o u g h t h e t w o - d i m e n s i o n a lh i s t o g r a m s . I f q u a n t i z a t i o n o f t h e f e a t u r e s p a c e w a sr e q u i r e d , it w a s d o n e s e p a r a t e l y f o r b o t h f e a t u r e s u s i n gt h e s a m e a p p r o a c h a s w i t h s i n g l e f e a tu r e s . T h e r e f o r e ,t h e t w o - d i m e n s i o n a l d i s t r i b u t i o n w a s l ik e l y t o h a v eb i n s w i t h z e r o e n t r ie s . R e g a r d i n g t h e s t a b i l i t y o f th ec l a s s i f ic a t i o n p r o c e s s i t w a s i m p o r t a n t t o h a n d l e t h e s ee m p t y b i n s c o r r e c t l y . S e t t i n g e v e r y e m p t y b i n t o o n et u r n e d o u t t o b e a g o o d s o l u t i o n .

4 . E X P E R I M E N T S W I T H I M A G E S E T I

I n t h e s e e x p e r i m e n t s , n i n e c l a s s e s o f t e x t u r e s - -g r a s s , p a p e r , w a v e s , r a f fi a , s a n d , w o o d , c a lf , h e r r i n g -b o n e a n d w o o l - - t a k e n f r om B r o d a t z' s a l b u m " s~ w e reu s e d ( F i g . 2 ). T h e t e x t u r e i m a g e s w e r e c o r r e c t e d b ym e a n a n d s t a n d a r d d e v i a t i o n in o r d e r t o m i n i m i z ed i s c r i m i n a t i o n b y o v e r a l l g r a y - l e v e l v a r i a t i o n , w h i c h i su n r e l a t e d t o l o c a l i m a g e t e x t u r e . T h e c o r r e c t i o n w a sa p p l i e d t o t h e w h o l e 2 5 6 x 2 5 6 i m a g e s i n s t e a d o fc o r r e c t in g e v er y s a m p l e w i n d o w s e p a r a te l y . T h e m e a ng r a y v a l u e o f e a c h c o r r e c t e d i m a g e w a s s e t to 2 5 6 a n dt h e s t a n d a r d d e v i a t i o n t o 4 0.

T h e t e s t s a m p l e s w e r e o b t a i n e d b y r a n d o m l y s u b -s a m p l i n g t h e o r i g i n a l t e x t u r e i m a g e s . 1 0 00 s u b s a m p l e so f 32 x 32 o r 16 x 16 p ixe l s i n s i z e we re ex t r ac t e df r o m e v e r y t e x t u r e c l a s s, r e s u l t in g i n a c l a s s i f ic a t i o n o f9 0 0 0 r a n d o m s a m p l e s i n t o t a l . W h e n c l a s s i fy i n g a p a r -t i c u l a r s a m p l e , th e s a m p l e d i s t r i b u t i o n w a s s u b t r a c t e df r o m t h e m o d e l d i s t r i b u t i o n o f t h e t r u e c l a s s o f t h i ss a m p l e s o t h a t a n u n b i a s e d e r r o r e s t i m a t e w a s o b -t a i n e d .

T a b l e 1 s h o w s t h e c l a s s i f i c a ti o n e r r o r r a t e s f o r32 x 32 and 16 x 16 sam ple s f rom n ine 256 256 im -a g e s r e p r e s e n t i n g n i n e t e x t u r e c l as s e s .

T h e b e s t p e r f o r m a n c e i s o b t a i n e d f o r t h e l o c a l b i n a r yp a t t e r n ( L B P ) f e a t u r e . T h e d i f f e r e n c e h i s t o g r a m f e a -t u r e s a l s o p e r f o r m e d v e r y w e l l . T h e c o v a r i a n c em e a s u r e s p e r f o r m b e t t e r t h a n L a w s ' m e a s u r e s , b u t t h ee r r o r r a t e s f o r t h e 1 6 x 1 6 s a m p l e s a r e q u i t e p o o r f o rt h e s e t w o r e l a t e d a p p r o a c h e s . T h i s i n d i c a t e s t h a t f o rg o o d r e s u l t s t h e c o v a r i a n c e a n d L a w s ' m e a s u r e s r e -q u i r e l a r g e r s a m p l e s i z e s t h a n t h e o t h e r a p p r o a c h e sc o n s i d e r e d h e r e .

T a b l e 2 p r e s e n t s t h e r e s u l t s f o r p a i r s o f c o m p l e -m e n t a r y m e a s u r e s . L B P / C a c h i e v e s v e r y l o w e r r o rr a te s . T h e r e s u l ts fo r L B P / S C O V a r e a l m o s t a s g o o da n d v e r y g o o d r e s u l t s a r e a l s o o b t a i n e d w i t hD I F F X / D I F F Y a n d L 3 S 3 / S 3L 3 f ea tu re s . T h e p o o r e s tp e r fo r m a n c e w a s o b ta i n e d fo r G M A G / G D I R . A f t e rc o m p a r i n g T a b l e 1 a n d 2 w e c a n c o n c l u d e t h a t p a i r s o fc o m p l e m e n t a r y f e a t u r e s g i v e s i g n i f i c a n t l y b e t t e r r e -s u l t s t h a n s i n g l e f e a t u r e s . T h e s m a l l e r r o r r a t e s o b -t a i n e d f o r s m a l l 1 6 x 1 6 s a m p l e s d e m o n s t r a t e t h ep o w e r o f o u r c l a s s i f ic a t i o n s c h e m e .


4/9

54 T. OJA LA e t a l .

g r a s s ( D 9 ) p a p e r ( D 5 7 ) w a v e s ( D 3 8 )

r a f fi a ( D 8 4 ) s a n d ( D 2 9 ) w o o d ( D 6 8 )

calf (D24) herringbone (D17) wool ( D 1 9 )Fig. 2. Broda tz textures. The white rectangle s in grass demo nstr ate the size of the test samples, 32 32 and16 x 16 pixels, respectively.

Table 1. Erro r rates for single features with ImageSet IFeature 32 32 16 16LBPD1FFXDIFFYDIFF2DIFF4L3E3E3L3L3S3$3L3SCOVSACSRAC

2.30 12.523.04 14.31 Table 2. Err or rates for pairs of feature s with Ima ge Set I3.30 12.848.43 13.50 Fea tur es No. of bin s 32 x 32 16 168.73 14.3219.82 42.46 LBP/ C 256 8 0.19 1.9017.62 39.58 LBP/ SC OV 256 x 8 0.23 2.60

14.28 33.78 L3E 3/E 3L3 32 32 0.89 12.187.58 23.68 L3S3/S3L3 32 x 32 0.22 4.008.07 29.62 DI FF X/ DI FF Y 32 x 32 1.51 3.8911.83 36.92 DI FF Y/ SCO V 32 x 32 0.86 6.578.46 32.77 G MAG /GD I R 32 x 32 1.81 16.13


5/9

Com parative study of texture measures 55

5. E X P E R I M E N T S W I T H I M A G E S E T I I

R e c e n t l y , O h a n i a n a n d D u b e s tSJ s t u d i e d t h e p e r -f o r m a n c e o f f o u r t y p es o f fe a tu r e s: M a r k o v R a n d o mF i e ld p a r a m e t e r s , G a b o r m u l t i - c h a n n e l f e a tu r e s , f r a c -t a l -b a s e d f e a tu r e s a n d c o - o c c u r r e n c e f ea t u re s . T h e yused fo ur c l as ses of imag es in exper imen t s : f rac ta li m a g e s , G a u s s i a n M a r k o v R a n d o m F i e l d ( G M R F )i m a g e s , le a t h e r i m a g e s a n d p a i n t e d i m a g e s ( F i g . 3 ).E a c h i m a g e c l a s s c o n t a i n e d f o u r t y p e s o f i m a g e s : t h es y n th e t ic f ra c ta l a n d G R M F i m a g e s w e re g e n e r at e d b yu s i n g d i f f e r e n t p a r a m e t e r v a l u e s a n d t h e n a t u r a l i m -a g e s r e p r e s e n t e d d i f f e re n t t y p e s o f l e a t h e r o r p a i n t e dsur face , re spec t ive ly . Wi th these images four 4-c las sprob lem s and a 16-c las s pro blem were es t ab l i shed .W h i t n e y ' s f o r w a r d s e l e c ti o n m e t h o d w a s u s e d f o r f e a-t u r e s e l e c t io n a n d a k N N ( k = 9 ) d e c i s io n r u l e f o rc las s i f i ca t ion . The co-occur rence fea tures genera l lyo u t p e r f o r m e d o t h e r f e a t u r e s f o l l o w e d b y f r a c t a l f e a -tures .I n o u r s t u d y , t h e s a m e s e t o f i m a g e s w a s u s e d . T h ei m a g e s w e re a g a i n c o r r e c te d b y m e a n a n d s t a n d a r dd e v i a t io n , a s d e s c r i b e d i n S e c ti o n 4 . L i k e O h a n i a n a n dD u b e s , w e t r e a t e d e a c h o f th e f o u r c l a s se s o f i m a g e sa s a s e p a r a t e 4 - c l a s s p r o b l e m . 2 0 0 n o n o v e r l a p p i n gs a m p l e s o f si z e 3 2 x 3 2 w e r e e x t r a c te d f r o m e a c h i m a g e( tex ture type) , re su l t ing in a c l as s i f i ca t ion problem of800 samples . Every sample was in i t s tu rn c l as s i f i edu s i n g t h e o t h e r 7 9 9 s a m p l e s a s m o d e l s ( 3 19 9 m o d e l s i nt h e 1 6 - cl as s p r o b l e m ) b y a p p l y i n g a t w o - w a y - o f - i n d e -p e n d e n c e G t e s t w i t h t h e l e a v e - o n e - o u t a p p r o a c h .A 9 - N N c l a ss i fi c a ti o n r e s e m b l i n g t h e p r i n c i p l e o fO h a n i a n a n d D u b e s w a s u s e d . A d d i t i o n a l l y , t h e 1 6 -c l a s s p r o b l e m , i n c l u d i n g a l l 3 2 0 0 n o n o v e r l a p p i n gs a m p l e s e x t r a c t e d f r o m a l l 1 6 i m a g e s w a s c o n s i d e r e d .

T h e e r r o r r a t e s f o r t h e f o u r 4 -c l a ss p r o b l e m s a n d t h el 6 - c la s s p r o b l e m u s i n g d i s t r ib u t i o n s o f s in g l e f e at u r e sa r e s u m m a r i z e d i n T a b l e 3 .

I t c a n b e s e e n t h a t f r a c ta l i m a g e s w e r e q u i t e e a s y t od i s c r i m i n a t e w i t h m o s t o f t h e f e a tu r e s. H o w e v e r , g r a y -s c a l e i n v a r i a n t f e a t u r e s L B P , S A C a n d S R A C d i d n o tp e r f o r m w e ll . T h i s i n d i c a te s t h a t g r a y - s c a l e c o n t r a s t i si m p o r t a n t f o r d i s c r im i n a t i n g t h e s e i m a g e s .

L B P , S R A C a n d S C O V p e r f o r m e d b es t f o r G M R Fimages . The wors t re su l t s for the d i f fe rence h i s togramfea tures were ob ta ine d wi th these images . Th e c las si fi -c a t i o n o f l e a th e r i m a g e s i s s o m e w h a t m o r e d if fi cu lt .T h e e x c e l l e n t r e s u l t s o b t a i n e d w i t h D I F F Y , D I F F 4a n d D I F F 2 a r e s u r p ri s in g l y g o o d . T h e r e s u lt s w i th t h eo t h e r f e a t u r e s a r e m u c h p o o r e r . T h e p a i n t e d s u r f a c e swere a l so d i f f i cu l t for some fea tures to d i sc r imina te .D I F F 4 , D I F F 2 a n d D I F F Y , a g a in , ac h ie v e d ve r y l owe r r o r ra te s. D I F F X , L B P a n d S R A C a l so p e rf o r m e dqui t e we l l , bu t the resu l t s for the o the r fea tures a rem u c h p o o r e r.

T h e d i f f e re n c e h i s t o g r a m f e a t u re s p e r f o r m e d b e s t i nt h e 1 6 -c la ss p r o b l e m a l s o . S C O V , L B P a n d S R A C a l s op e r f o r m e d q u i t e w e ll. T h e p o o r p e r f o r m a n c e o f L a w s 'fea tures i s ma in ly c aused by the d i f f i cu lty of d i sc r imi -n a t i n g l e a t h e r a n d p a i n t i m a g e s w i t h t h e s e m e a s u r e s .

S C O V a n d S R A C p e r f o rm e d b e t t er t h a n L a w s 'm e a s u r e s , b u t , a s e x p e c te d t h e y a l s o h a d p r o b l e m s w i t hl e a t h e r a n d p a i n t e d i m a g e s .

Th e c las s if i ca t ion resu l t s for pa i r s of fea tures a rep r e s e n t e d i n T a b l e 4 . T h e b e s t o v e r a l l p e r f o r m a n c e isf o r D I F F Y / S C O V , a n d a l m o s t a s g o o d r e s u l t s w e r eo b t a i n e d b y D I F F X / D I F F Y . T h e p e r f o r m a n c e o fG M A G / G D I R w a s p o o re s t. I n g e n er al , th e i m p r o v e-m e n t a c h i e v e d w i t h p a i rs o f f e a tu r e s c o m p a r e d w i t hthe bes t re su l ts for s ingle fea tures i s no t a s s igni f i cantfor th i s image se t a s for B ro da tz ' s t ex tures.

6. D I S C U S S I O N A N D C O N C L U S I O N S

M o s t o f t h e e a rl i er a p p r o a c h e s t o t e x t u r e c l a s si fi c a-t i o n q u a n t i f y t h e t e x t u r e m e a s u r e s b y s i n g l e v a l u e s .T h e v e r y g o o d r e s u lt s t h a t w e o b t a i n e d b y u s i n gd i s t r ib u t i o n s o f si m p l e t e x t u r e m e a s u r e s s u g g e s t t h a tt h e d i s t r ib u t i o n s o f fe a t u r e v a l u e s s h o u l d b e u s e dins tead of s ingle va lues .T h e g r a y - l ev e l d if f e re n c e m e t h o d a c h i e v e d t h e b e s to v e r a l l p e r f o r m a n c e d i s c r im i n a t i n g m o s t o f t h e te x -tures ve ry we l l . I t i s ve ry easy to compute , and i tpe r fo rm ed well even wi th smal l 16 x 16 samples , whichm a k e t h is a p p r o a c h v e r y a tt r ac t iv e f o r m a n y a p p l i c a -t ions , inc luding t ex ture c l as s i f i ca t ion and segmenta -t ion .

T h e t e x t u r e m e a s u r e s b a s e d o n l o c a l b i n a r y p a t t e r n sa r e a l s o c o m p u t a t i o n a l l y e x t r e m e l y s i m p l e . T h e s emeasures pe r formed very we l l , e spec ia l ly wi th theB r o d a t z t e x t u r es . L B P i s g r a y - s c a l e i n v a r i a n t a n d c a nb e c o m b i n e d w i t h a si m p l e c o n t r a s t m e a s u r e t o m a k e i te v e n m o r e p o w e r fu l . T h e m e t h o d is r o t a t io n v a r i a n twhich i s undes i rab le in ce r t a in appl i ca t ions , bu t i ts h o u l d b e p o s s i b l e t o d e r i v e r o t a t i o n i n v a r i a n t v e r -s io n s o f L B P .

C e n t e r - s y m m e t r i c c o v a r i a n c e f e a t u r e s p e r f o r m e dv e r y w e ll f o r s o m e o f t h e t e x t u r e s b e i n g m o r e p o w e r f u lt h a n L a w s ' m e a s u r e s . B o t h o f t h e s e a p p r o a c h e s r e q u i r el a rge r s ample s i zes than the gray- l eve l d i f fe rence andL B P m e t h o d s . A r e a s o n f o r th i s is t h a t m o s t o f t h ed i s c r im i n a t i v e i n f o r m a t i o n f o r th e s e k i n d s o f m e a s u r e si s c o n t a i n e d i n t h e m a t c h m a x i m a , a s s h o w n b yPietik~iinen eta l. ~4~ To obta in s t a t i s t i ca l ly re l i ab lei n f o r m a t i o n o n t h e d i s tr i b u t i o n s o f l o c a l e x t r e m a ,q u i t e la r g e i m a g e w i n d o w s m a y b e n e e d e d . C o v a r i a n c em e a s u r e s a r e c o m p u t a t i o n a l l y m o r e c o m p l e x t h a nL a w s ' m e a s u r e s , b u t t h e y a r e a l l r o t a t i o n i n v a r i a n tw h i le L a w s ' m e a s u r e s a r e n o t . I n a d d i t i o n , t h e S R A Cm e a s u r e , w h i c h p e r f o r m e d q u i t e w e ll , is i n v a r i a n t u n -d e r a n y m o n o t o n i c t r a n s f o r m a t i o n i n c l u d i n g c o r r e c -t i o n b y m e a n a n d s t a n d a r d d e v i a ti o n a n d h i s t o g r a me q u a l i z a t i o n .

T h e r e a r e m a n y a p p l i c a t io n s , f o r e x a m p l e in i n d u s -t r ia l i n s p e c t io n a n d r e m o t e s e n s in g , i n w h i c h t h e g r a y -s c a le i n v a r i a n c e o f a t e x t u r e m e a s u r e i s o f g r e a t i m p o r t -a n c e d u e t o u n e v e n i l l u m i n a t i o n o r g r e a t w i t h i n -c l a ssv a r i a b i l i t y . R e c e n t r e s u l t s w h i c h w e h a v e o b t a i n e dwi th ap ply in g t ex ture c l as s i f i ca t ion to a d if fi cu l t m e ta ls h e e t i n s p e c t i o n p r o b l e m h a v e d e m o n s t r a t e d t h a t t h e


6/9

5 6

D = 2 . 1 D = 2 . 4

. . . . . . ,

D = 2 . 7 D = 2 . 9 9 9

. . . . i . . . . . . : . . . . . . .

(a ~

0 = (0 . 4 , 0 . 4 , - 0 . 2 , - 0 . 2 ) 0 = ( - 0 . 3 , 0 . 0 , 0 . 5 , 0 . 5 )

0 = ( - 0 . 3 , - 0 . 3 , 0 . 5 , 0 . 5 )( b )

0 = ( - o . 3 , - 0 . 1 , o . 5 , 0 . 5 )

F i g . 3 . ( a ) F r a c t a l i m a g e s w i t h f r a ct a l d i m e n s i o n D ; ( b ) G a u s s i a n M a r k o v R a n d o m F i e l d I m a g e s ; ( c ) l e a t h e ri m a g e s ; ( d ) p a i n t e d s u r f a c e i m a g e s .


7/9

0

i

~D

0 c~

I:=

c~


8/9

58 T . O JA L A et al.

Table 3 . Erro r ra tes for single features w i th Imag e Set I IFea t u r e Fr ac t a l G M R F L ea t he r Pa i n t ed 16-c la ssLB P 37.75 0.00 24.12 10.75 18.16D IF F X 0.00 10.62 2.25 6.25 5.75D IF F Y 0.00 10.50 0.00 2.88 3.72D IF F 2 0.00 7.88 0.12 1.75 2.81D IF F 4 0.00 14.50 0.00 0.88 3.69L3 E3 1.00 6.88 23.12 40.62 33.06E3L 3 2.00 26.50 27.25 49.25 36.09L3S3 0.00 7 .38 39.25 50.12 31.53$3L 3 0.00 13.25 36.38 22.00 27.22SC O V 0.130 3 .38 28.38 31.37 16.56SA C 43.25 10.88 46.12 34.00 46.28SR A C 12.75 2.12 34.75 12.00 18.25

Table 4 . Erro r ra tes for pai rs of fea tures wi th Im age Set I IFea t u r e s N o . o f b i ns Fr ac t a l G M R F L ea t he r Pa i n t 16 -c la ssLB P/ C 256 x 8 0.00 1.75 29.62 23.12 12.38LB P/ SC O V 256 x 8 0.00 1.25 30.38 32.62 14.97L3E 3/E3 L3 32 x 32 0.88 7.00 16.38 43.62 29.66L3S3/S3 L3 32 x 32 0.00 0.75 11.50 15.00 11.81D IF FX /D IF FY 32 x 32 0.12 5.12 0.25 1.12 3.44DI FF Y/ SC O V 32 x 32 0.12 4.75 1.75 1.62 2.88G M A G /G D IR 32 x 32 1.88 9.38 35.25 44.12 35.79

g r a y -s c a le i n v a r ia n t L B P a n d S R A C m e a s u r e s c a n b em o r e p o w e r f u l i n su c h a p p l i ca t i o n s t h a n t h e ' o t h e ra p p r o a c h e s c o n s i d e r e d i n t h i s p a p e r , i ts )

T h e q u i t e p o o r p e r f o r m a n c e o f L a w s ' a p p r o a c hi n d i c a t e s t h a t t h e d i s c r i m i n a t i v e p o w e r o f th e s em e a s u r e s i s m o s t l y c o n t a i n e d i n t h e v a r i a n c e s o f t h ef e a t u r e d i s t r i b u t i o n s w h i c h h a v e b e e n u s e d i n m o s t o ft h e e a r l i e r s t u d i e s . T h e w h o l e d i s t r i b u t i o n d o e s n o ts e e m to p r o v i d e m u c h a d d i t i o n i n f o r m a t io n .

T h e u s e o f p a i rs o f c o m p l e m e n t a r y m e a s u r e s g e n -e r a l l y i m p r o v e s t h e c l a s s i f i c a t i o n a c c u r a c y . T h i s w a sp a r t i c u l a r l y e v i d e n t i n t h e c a s e o f B r o d a t z ' s t e x t u r e s .T h e c o m p u t a t i o n a ll y si m p le D I F F X / D I F F Y a n dL B P / C p a i r s w e r e a m o n g t h e b e s t fe a t u r e p a ir s . T h ep e r f o r m a n c e o f L a w s ' a p p r o a c h c a n a l s o b e si g n if i-c a n t ly i m p r o v e d b y u s i n g p a ir s o f o r t h o g o n a l m a s k si n s t e a d o f s in g l e fe a t u re s . T h e g r a d i e n t m a g n i -t u d e / d i r e c t i o n p a i r d i d n o t p e r f o r m a s w e l l a s t h e o t h e rp a i r s i n o u r e x p e r i m e n t s .

Ac k now l e dge m e n t s - - The f i nanc i a l suppor t p r ov i ded byt he T echno l ogy D eve l opment C en t e r o f F i n l and and t heA cademy o f F i n l and i s g r a t e f u l l y acknow l edged . We a l sow i sh t o t hank Pr o f e s so r R i cha r d C . D ubes and John L eesf r om t he Mi ch i gan S t a t e U ni ve r s i t y fo r p r ov i d i ng a s e t o f t es timages used in this study.

RE FERENCE S1. L . Van Gool , P. Dewaele and A. Ooster l inck, Textureanalysis anno 1983, Comput. Vis. Graphics Image Process.29(3), 336-35 7 (1985).2 . R .M. H ar a l i ck and L . Shap i r o , Computer and RobotVision. Vol. 1. Addison-Wesley, Ne w Yo rk (1992).

3 . J . Weszka, C. Dyer and A. Rosenfeld, A comparat ivestudy of textu re mea sures for terrain classification, I E E ETrans. Syst . Ma n. C ybernet . SMC-6, 269-285'(1976).4 . J. M. H. D u Buf , M. K arda n and M. S pann, Textu refeature per formance for image segmentat ion, Pat ternRecognition 23(3/4), 291-30 9 (1990).5 . P. P. Oh ania n and R. C. Dubes , Per form ance evaluat ionfor four classes o f textural features, Pattern Recognit ion2 5 , 819-833 (1992).6 . D. Harwood, T . Ojala , M. Pie t ikt i inen, S. Kelman andL. S. Dav is, Te xtu re classification by cen ter-sym me tricauto-corre la t ion, us ing Kul lback di scr iminat ion ofdis t r ibut ions , Pattern Recognit ion Lett . 16(1) , 1-10(1995).7 . M. Unser , Sum and di f ference hi s tograms for t extureclassification, IE EE Trans. Pat tern Anal . M ac k ln te l l.8 ( 1 ) , 118-125 (1986).8 . K.I . Laws, Textured imag e segmen tat ion, Repor t 940,Imag e Process ing Ins t i tute , Univ. of Southern C al i fornia(1980).9 . L . W ang and D. C. He, Texture c lassi fica t ion us ing tex-ture spect rum, Pattern Recognition 23, 905-910 (1990).10. H. C. Shen an d C . Y. C. Bie , Fea ture f requency m at r icesas texture image representa t ion, Pattern RecoonitionLett . 13(3), 195-205 (1992).11. S. Kullback, Information Theory and Statistics, D o v e rPubl icat ions , New York (1968).12. R.R . S okal and F. J . Rohlf , Biometry. W. H . Fr eemanand Co (1969).13. P. Brodatz, Textures: A Photographic Alb um for A rt istsand Designers. Dover Publ icat ions , New York (1966) .14. M. Piet ik/ i inen, A. Rosenfeld and L.S. Davis, Experi-ments wi th texture c lass if ica tion us ing averages o f localpat tern matches , IEEE Trans . Sys t . Man Cybern.SMC-13(3), 421-426 (1983).15. M. Piet ik/i inen, T. Ojala, J. Nisu la and J. Heik kinen ,Exper iments wi th two indust r ia l problems us ing textureclassificat ion based on feature distr ibution, SPI E Vo l .2354 Intel l igent Robots and Computer Vision XIII: 3DVision, Product Inspection and Active Vision. 197-204.Boston, Massach usset t s (1994).


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C o m p a r a t i v e s t u d y o f t e x t u r e m e a s u r e s 5 9

A b o u t t h e A u t b o r - - T I M O O J A L A r e c ei v e d t h e D i p l o m a E n g i n e e r d e g r e e i n e l e c tr i ca l e n g i n e e r in g f ro m t h eU n i v e r s i t y o f O u l u , F i n l a n d , i n 1 99 2. C u r r e n t l y h e is a d o c t o r a l s t u d e n t a n d m e m b e r o f t h e M a c h i n e V i s i o nG r o u p a t t h e s a m e d e p a r t m e n t . H i s r e s e a r c h i n te r e s ts i n c lu d e p a t t e r n r e c o g n i ti o n , te x t u r e a n a l y si s a n dn e u r a l n e t w o r k s .

A b o u t t h e A u t b o r - - M A T T I P I E T I K . ~ I N E N r e c ei v e d h i s D o c t o r o f T e c h n o l o g y d e g r e e i n e l e ct ri c a le n g i n e e r i n g f r o m t h e U n i v e r s it y o f O u l u , F i n l a n d , i n 1 9 8 2 . C u r r e n t l y h e i s P r o f e s s o r o f I n f o r m a t i o nT e c h n o l o g y a n d H e a d o f M a c h i n e V i s i o n G r o u p i n t h e D e p a r t m e n t o f E l e c t r i c a l E n g i n e e r i n g o f t h eUn i ve r s i t y o f Ou l u . F r o m 1980 t o 1981 a nd f r om 1984 t o 1985 he wa s v i s i t ing t he Com pu t e r V i s i onL a b o r a t o r y a t t h e U n i v e r s i ty o f M a r y l a n d , U . S .A . H i s r e s e a r c h i n te r e s t s i n c l u d e m a c h i n e v i s i o n a l g o ri t h m s ,s y s t e ms a nd t he i r a pp l i c a t i ons i n i ndus t r y . He h a s s upe r v i s e d s e ve r a l Dr . Te c h . the s e s a nd r e s e a r c h p r o j e c t s ,a n d p u b l i s h e d a b o u t 8 0 s c ie n ti fi c p a p e r s i n j o u r n a l s , b o o k s o r i n t e r n a t i o n a l co n f e re n c e s, a n d a b o u t 6 0 o t h e rpa pe r s o r r e s e a r c h r e po r t s . P r o f e s s o r P i e ti k~ i ine n i s one o f t he f ound i ng F e l l ows o f I n t e r n a t i on a l As s oc i a t i onf o r P a t t e r n R e c o g n i t i o n ( I A P R ) , s e rv e s a s M e m b e r o f t h e G o v e r n i n g B o a r d o f IA P R , B o a r d o f t h e P a t t e r nR e c o g n i t i o n S o c ie t y o f F in l a n d , a n d C o o r d i n a t i n g C o m m i t t e e o f t h e F i n n i s h M a c h i n e V i s i o n t e c h n o l o g yp r o g r a m m e . H e i s e d i t i n g ( a n d L . F . P a u ) a s p e c i a l i s su e o n M a c h i n e V i s i o n fo r A d v a n c e d P r o d u c t i o n t o b ep u b l i s h e d b y I n t e r n a t i o n a l J o u r n a l o f P a t t e r n R e c o g n i t i o n a n d A r t if i ci a l I n te l li g e nc e .

A b o u t t he A u t h o r - - D A V I D H A R W O O D i s a r e s e a r c h a s s o c i a te o f t h e U n i v e r s i t y o f M a r y l a n d I n s t i t u te fo rA d v a n c e d C o m p u t e r S t u di e s, w o r k i n g o n c o m p u t e r v i s io n a n d s u p e r c o m p u t i n g . I n 1 99 2 h e s t a y e d 7 m o n t h sa t t h e U n i v e r s i t y o f O u l u a n d t h e T e c h n i c a l R e s e a rc h C e n t r e , O u l u , F i n l a n d .

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