Analytical Cellular Pathology 8 (1995) I 17-133

ANALYTICAL CELLULAR

PATHOLOGY

' '

Invariance of textural features in image cy-tometry under variation of size and pixel magnitude

Karsten Rodenacker GSF Forschungszentrum fur Umwelt und Gesuntlhel' mbll, /n.YiiluP for HU!hologie, Postfach I 1 29.

D-85758 Oberschleijlheim,. Gomtmy'

Received 20 December 1993; revision received 12 July n~ acaqped 9 September 1994

Abstract

Textural features oft he granufa."l.~ofstaimrdc::dlntJ!llri,and nuclear sections derived from eo-occurrence and runJlen-gtl\'l~areoft.m ns.111!1 fO'.I"nn•iclation with external (clini-cal) parameters. The representlition1 C!l'tf d 'dlllldQ and mudlear~~·ary oonsiderabJy under changes of preparation andl1l5mHO.lll~imr~ .. MosLobvious mJ!(~;:mges; iq'size e.g. by fixa· tion as well as changes in tl:te!alllUllntttt€~ stain. Computer-simulated variations in size and pixeJ magnitude of a settoffim~cJtf <mtll m~ stained with FenJGCD ~'ere featured and compared. Resulting featureedd~~ <fte L\bW for the settin~ ~r parameters of feature extraction procedures as weUihssf~rttiles~•ll .. ~1~P d iiifi1l'ariant feat1ill1ll!:ti.foll' texture quantifica-tion of material with variatitin~oe~~~·~·

K~ywords: Cytometry; Texture anlily$~;>~r~~;1RJ.nr::llmgth features; Feature - . rnvanance

1. Introduction

In image cyto- and histometry, quantitative features ofgmmular structures or tex-tures of cell nuclei are measured for correlation with cellll amxdY0r tissue properties. An often used set of methods is derived by consideriiJll~ tJeX:tures in images as generated by a stochastical process. The estimated pai1Jllillt1te11& of the probability density function of such a (2nd order) process are qU3lliit!ilt1avive textural features.

• Corruponding author, Tel.: "t49 89 31 873401; Fax: +49 89 3D &~i e-mail: rodena@gsf.de

0921 -8912195/$09..50 © 1995 Elsevier Science Ireland lld. All rilgflm;mserved SSDJ 0921 -89 12(94)00251-U

1 18 K . Rodennckf!r l .!full!. Ci!ll. Pa1hof. 8 ( J995) 117- 111

Most well-known are the eo-occurrence and the run length matrix as estimates of the probability density function, introduced by Haralick et al. (4)_ and Galloway (3). A recent review with an abundant reference list concerning these features can be found in [6].

Invariance of quantitative features from different influenet..'S and disttort.ions in digital image analysis is one of the most important property of any analysis and forthcoming interpretation. Well-known influences in cyto· and histometry from specimen pr,eparation and staining, as well as from the material itself and from the wrro<ee€1'1!lrnes, appl»ed, result in geometric and densitomet~ric variations. Often, such '~:-lllfi13l~im'III& amc or diagnostic value and reflect speciJi<e p1i0perties oJ the material under <P.~rvn1iilifafilon. However, feature extraction methods rmj;ght not react properly to such '(;;ni:a~rm.~ or distortions.

F«atur~ c~lraction methods in digital image analysis have. reached such a degree of" complexity [7), that the analysis of the algorithms. alc)llle is not sufticieut to detcr-m~rnc rdiable answer:; to th.e question of feacure mllliW~IriJa!lil<te [!2). In this paper. tbre methods of feature ex traction for eo--occurrence oodluundength features are succinct-ly stated, analyzed and app1ied to a set of digitized i.nmges of stained cell nuc1ei. Each original digital image from a 'Slttined cell nucleus is a'Lntrediin terms of size and grey value and analyzed with t'he whole feature set. All~dlllions-.are performed by calcula-tion in the digi tized image. Fc;ature values an p~iarunnst the varied parameters. Classifications as in 15) weFe not performed. Tllm:~lwaNo find out how far experi-mental influences in a limited range on cell inu2,!t$aantJlrelend differences in textural features . The algorithms .applied are •ascd rm mmtiilt\! ceU image analysis at our laboratory (7].

2. Material and methods

From a larger project, JO~~Uioun:ltrii(~Hcr:TI=A-J) were arbitrarily chosen. The alcohol-filod ~~~~ '~~ s:laliiamdl ammnilnggt0"0Ur standard Feulgen prttcedurc (hydrolysis: 5 N HO, ~C~ ~ miin;; $dtifmsreagc,nt I h). Feulgen stain is deposited only at the Ol A lnsidrc t!M:: ~HIJDlWdlnl.a), tHe:roffuetthe cytoplasm is trans-parent and mostly invisible. The~ 0Afi!G!milsta:iil1irnone..nucleus is directly re-lated to the amount of DNA.

2_ 1/. lmage sampling The nuclei were digitized with an Alti:0llmaltt ~1lEI!(0Wss, Oberkochen, Ger-

many) and a high resolution TV meas:l!l!f1t1JlWDtl <tall'llfml ((l}hsdl, Stuttgart, Germany, Plumbicon, TIVK9Bl ). Pixel size was;0..2S ,rm,,w;iiih.l.m:sizct ll2.'8 x 128 pixel and the nominal resolution of grey values was 25~ Tfut smlm!ndi W'lig!nal nucki are shown in Fig. I. The value of transmilted Ji'glhtl W'<ll$ tiiWtB:llllld!, digitized and stored in an ima;ge file.

2.2. Image variation IE~til(i)Ol is. de6i:ne4 as.~h~ furgamit!lbmHofftftrenanroooit!Retransmitted outgoing light

1f ad* i:m®'ming; Ji'gllln 'WlWI <t~~ lf?,y msro-eallbdll:tia(!)kk.sh'oulder SW, which

•

•

K. 'Rro/ienada!r ! A.ttal. Cell. Patho/. 8 (1995) J/7-133 119

• -..c !:1) ---"t:l <I) ... ... ·e "' c: 01 .. -a ·-·-.!! g = ~ -a .... 0

t ·-I ~-

~

1 l

' -t

120 K. Rodem~cker ! t1nal. C~J/. Puthol. R ( 1995) 117- 133

is related to digitizcr effects and/or the amount of stray light (Fig. 2) (formula 1).

T-SW E:::: - I 50 log to --- - -

\VW- SW (1)

Extinction E retlccls the amount and dte distribution of DNA and js of greatest in-terest in cyto- and bistometry, Acoording1ly11 .alte.r.alions 10f grey values were perform-ed in extinction . PixeJwbc, each calculated e'ltia'tioo value of each digitjzed image P,. i:::: A, ... tJ (OBJECf)A was mwliplied by lite factors~= (0.5, 0.6, 0.7, 0.8, 1.2~ I. 4. 1.6, l .8, 2.0) (FACTOR), recalcubred jnto tramJmnssion valllles and then stored in an image file. The calculation wa.~ pelformed a~ a ~ble caJc-tdation of exponential law according tl1e fom1ula without taking into acaJunt the black shoulder SW (for-mula (2)).

T ' T E' :::: - log = - fl Jog = IJE ~ T 1 = WJV'' - 111 7'11

w~v JVW (2)

Subsequently, this set of JO x 10 images P,JJ were a ltered by size using an affine transformation \vith lioe3r irtterpolation (procedure AFINl t SPIDER software package [9]) rc.~ulting il1l I Ox lOx .S images 1'1J1.a· The x and y scaling factors were ~ :::: ( 0.5, 0.7, 1.0,. L4, 20) (SlZE). Fig. 3 hows one cell varied by $0me grey and size seal~. Some cftilac:cd rtur\:ki did not fit in1o 128 x 128 pixeJ image size and were truncated .

2.3. Ft:ature extra~t/(11) Each of the cell pictu:.l~ '~~~:()( wa. evaluated using ahe following described feature

oxtraction procedure. (i) ~tM-tutiion or the object m ask M by an automaticaJly es timated threshold. (riij T~..amf~ttrma1i0cn of transmis ion pixeJs to extinction by for-mula (I) with WW = 2~.md SW= 6. (iii)Calcufation of the mean extinction of the background region DG'UD~ This value is subtracted from each pixel. This is equiva-lent to the estimation @fttiae mean trnnsm1ssion value of the background region and usiog this value as Mfl iim founula ( I )~ The reiulting image is caUed the extinction fimagc E and js used im .aJJB further feature extractions (Fig. 4a). (i\') Estimation of the fllat texture image F as tllte ~ifTerence of extinction image E and the median smoothed

T outgoing Hght

--~~ ;::;~-..__-:;;:'~~~--- cover glass stained nucleus

:=:=::::::=:::=:::~~======~~~== glass slide

WW incoming light

fij. 2. Scheme of transmission through u specimen.

K. Rodenacker l A11a/. Cell. Patllo/. 8 (1995) 117-133 121

4 Scale variation ~ (SIZE) 0.5

0.5 0.7 20

'

2.0

Fig. 3. Variation of one cell in grey magnitude and size.

extinction image (Fig. 4b). Window size of the median transformation was 7 x 7 pixel. This setting ensures that all contrasted areas with pixel numbers less than (7 x 7)/2 (= 25 =median) are smoothed away by the median operation and hence will re-appear in the so-called flat texture image F (Fig. 4b). The eo-occurrence and run length features are calculated from both images E and F. (v) Normalization of im-ages to a given number of grey values Ng: This parameter NOGV = Ng estimates the sizes of eo-occurrence and run length matrix. Two different methods are im-plemented: first, histogram equalization is made on the histognam of the pixels of the region of interest without subdivision of classes (Fig. 5ru) and second, a linear histogram transformation is applied (Fig. 5b). The ooatm-gnam• equalization is per-formed on the frequency distribution of the pixels i~ ct\a:ol:>jeot mask M (proce-

122 K. Rodenackcr / ArUIL ull. Pat/to/. 8 ( 1995) 117-133

Fig. 4. (a) Original extinction image E and (b) flat tex~ure Image F.

dure HTBLI , SPIDER software package (9]). The normalization with linear transformation is done according the fonnulu

, _ x - (m - 3o) N. X - ___ ..:....__ _ ___:: __

(m + 3o) - (m - 3a) 8 (3)

where m is the mean and a the standard deviation of the plxel values in the object mask M. {vi) Calculation of eo-occurrence features: Wirh a given displacement vec-tor d (DISP) (Fig. 5d), the 2-dimensional frequency malm of pixel pair value eo-occurrences {P,. Pi) is calculated, with both pixels located in the object mask M . Assuming isotropy of the structures in the cell nuclei, a second eo-occurrence fre-quency matrix is calculated with the given displacement vector rotated by 90° d .L

for (PI> P2) and added to the first one. This procedure wiJI smooth out random artefacts. Upon division by the number of eo-occurrences, the frequency matrix is transformed to a probability matrix.. A calculated 16 x 16 probability matrix is

d displacement vectors

Fig. S. (a) Normalized extinction image E with histogram equalization, (b) normalized flat texture image F with linear transformation (NOGV = 16), (c) eo-occurrence matrix of (a) and (d) illustration of dis-placement vectors d used.

K. Rodenacker l Anal. Cell. Parlro/. 8 (1995) 117-133 123

shown in Fig. Se. Bright areas reflect high probabilities. In this representation the

normalized pixel values run from left to right and from top to bottom. The major

diagonal drawn in white shows the symmetry of the matrix. This follows from the

counting of occurrences (P1, P2) and (P2, P1). The list of features calculated follows

Haralick [4] and is essentially a set of directional 1-dimensional Oth, l st and 2nd

moments from a 2-dimensionaJ probability distribution. The direction of integration

is described by constancy of the index sum (x + y), difference (x - y) and the vertical

(x) and horizontal (y) coordina tes. Vertical (4), horizontal (5), major diagonal (6)

and minor diagonal sums (7) form the basis for most of the feature algorithms pro-

posed (formulae 14-27).

Ng - I

Pii) = E p(i,j),

Ng- I

Py(i ) = E p{i,j) (4,5)

J =O i= 0

Ng - I Ng - I

E E p(i,j), P:c - y(k ) = (6,7)

i=:O j = 0 i + j = k

From these directional probability distributions, some moments, the average (8), the

2nd moment (9), and the variance as centred 2nd moment (l(i)) are defined as

JJ.(.) = E ip oeo. I

Eo = Ei2p c.,U)~ j

and some entropies

H0 = - I> 0 (j ) log (pc.)V )) j

Ng- I E p(i,J) log (p (i,j)) i=O i= O

H xyl = -Ng- I

r; Ng- I

r; p(i,j) log (px (i)py(J))

j = 0 }=0

Ng - I N - l g

i

Directional entropy

Entropy

Hxy2 =- r; r; px(l)py(j) log (px (i)py(J)) i= 0 j=O

(8,9,10)

( 11)

(12)

(13)

(14)

With these preliminaries, the eo-occurrence features are calculated as follows:

COl NCI ~

i=O j = O

Angular 2nd moment, energy ( IS)

124 If(. IRol.leftsuke~lAtml, C~/1. Pruhol. 8 ( 1995) 117-111

C0 2 NC2=Ex-J"

A'g-1 .Vg-1

Contrast, inertia

E E ,. j P u.n - P.xP.,· C03 •= 0 j =O NC3- ----~----------- Correlation

C04 NC4 =a~

cos N11 - I N11 - I

- E E NC5-; = 0 i= 0

C0 6 NC6 = P.u + ·'"'

C08 NC8 = Hx+ ,.,

COIO NCIO = ax-J•

COI2 -NCI2 -Hxy- 11,_.,

mnx(H ~.H.,)

CO l4 NCl4 = 1-Lx + P.y

Sum of squares: variance

I p(i,j) Inverse 2nd dillerem:e moment I + (i -.i)2

CO? Sum average, varia.,ce NC7 = U:x +y

C09 NC9 = H~ Sum entiopy, entropy

cou NCH = H.'t=Y Oiff. variance, entropy

COl3 _ .fl- e-2aT.n2 - H~)l NCil = •

Measure of corr. I, 2

Local mean

(([J(&)

(17)

(l9»

(20,21)

(22,23)

(24,25)

(26,27)

(28)

Parameters controlling the feature extraction from the eo-occurrence matrix are the displacement vector d (DJSP), changed according to the size factor {3 (SIZE), the type of normalization (NORM) of the grey values and the matrix size (NOGV). Hence, from each image P;,a.a the eo-occurrence features CO 1-CO 14 and NCl-NCI4 were calculated for DISP = I , 3, 6, 10, 15; NORM= 1 (linear), 2 (h istogram equalization); NOGV = 8, 16, 32, 64. (vii) Calculation of run length fea-tures: The number of runs, consecutive pixels of identical value, for each pixel value, are counted into the frequency distribution P(i,J) with SPIDER routine RUNL [9]. This is performed in horizontal and vertical directions to smooth out possible artefacts. The formulae used foJJow GaJJoway [3]:

•

K. Rodenacker I A11al. Cell. PathoL 8 (1995) J/7-133

RLO NRO-

p(i,j) =

RLI -NRl-

RL2 -NR2-

RL3 -NR3-

RL4 -NR4-

.V -1 g E p(i.j) i= O J= l

p (i,j) RLO NRO

Ng - I N p(i,j) r

E E . 2 ; = 0 j = l J

Ng - I N r

E E j 2p(i,j) i = 0 i= l

Ng - I ( .V, ) 2

~~ j~ p(i,j)

N,

c~· pU.J)r E j = I

RLS _ RLO NRS- NRO

number of sections

probability matrix

short runs emphasis

long runs emphasis

grey level non-uniformity

run length non-uniformity

run length percentage

125

(29)

(30)

(31)

(32)

(33)

(34)

(35)

For run length features RLl-RLS and NRI -NR5, only the normalization NORM and matrix size NOGV were varied. The maximum run length N, was set to 128.

AU 20 000 sets of C01-COJ4. NC1-NCI4 feat.ures and 4000 sets of RLI -RL5, NRl-NRS features from the cell images were plotted above the varied parameters w~tn the statistical analysis system SAS [8).

2.4. Analysis of algorithms Using HaraJick's [4] formulation, a histogram equalization is proposed. In exten-

sio, the frequency distribution is constant after such a normalization, hence vertical and horizontal sums of the eo-occurrence matrix are column- or row-wise constant Q.P xU = const., Py(i = const.). However, an equalization without subdivision of the same grey values rarely results in a completely equalized distribution (see Fig. Sa). Ccmplete eq ualization (with subdivision of pixels) will, in general, reduce the capa-city of features based on directional sums like Px(i).

11 follows from symmetry of the eo-occurrence probability matrix that the hori-~ and vertical sum probabilities are identical (P.r(i = Py(i), i = O, ... ,Ng - 1) am:illletm~t,. !h.+!= llx + l'y (C06 = C014).

'

,., ..... -

-

126 IK. fRoill!fll•dl.<er i .AML Cell. Pa1hol. 8 (1995) 117-133

3. Results

3.1. Variation of pixe1 magnitude (FACTOR) For a typical parameter constellations (SIZE = l.O, NORM = 2, NOGV = 16,

DISP = 6) features CO I-COI4 and features RLI - RL5 for SIZE = 1.0, NORM = 2 and NOGV = 16 are plotted against the magnitude varying parameter FACTOR (Fig. 6). In spite of the rigid normalization, several features show some dependency on pixel magnitude (FACTOR), see COl , C04, C09 and RL2-RL5. Other ap-parently dependent features have very small ranges. These dependencies can be dif-ferentiated further on for groups of bright images (OBJECT = A, E, F, H), medium images (D, D, J) and dark images (C, G, 1) (sec Fig. 1). This is especially valid for COl , C08- C09 where features from bright images decrease or increase more for fACTOR < 1.0.

To illustrate the variation of features under changes of magnitude each feature was normalized by division by the corresponding feature calculated from the original • Image (FACTOR = 1.0). In Fig. 7 the dotted lines show the mean with ± 2 S. E. M. bars of the I 0 objects for NORM = 2. Reference lines for value 'I ' , independence

•

00180 •u OOOIG 4400

00\St ... 0- cG80 C04 Uttt C01 J:lt OOQI<I a >tO

OIJOM ,.,. o.cao 344~ 0- ~,. ·- 31>0

000<0 24.0 10000 -oe·~

,.., 3.~0

02~· 18~ :).>00

0~ 1U ~210

01 .. 171 , '"' COB Oil$ • - ,.,. )IJ2

" ,, n ,,., 30110

I ' "'" ••c ........ ••• ~-.; u• ~~ ...OG't-s

<98 ll G ,,.,. .... _ '" •c• 7 <64

........ 4.45 9.t 2<22

......... ..O~t.O

• 20 0 .. t.aeo I . .. f ' 2)

0440 ~~ .... a .. o 0.39> ... o ate Ol« >U OlW

0.298 "" IPM

o.2AII ~ .... 0.744

0<00 "" ono 0. ' I

,. u 2-0 3 60 RL2

0,131) RL3 01560 o.no

3 .32 D 1t8 0 .,.. 0.142

3 .04 0,102 0.592 0 , , ..

2.70 oose o.sSI O.ea&

~ ... Q.(l,. O.U< O.G!ie

2.20 ...... 0410 0.8)0

Fig. 6. All CO-features for SIZE"' 1.0, NOGV "' 16, DISP = 6, NORM"' 2 and all RL-features for ~~V= 16, DISP = 6, NORM = 2 above FACTOR.

•

i(. !Rolienlldo::!Cf"l AMI. Cell. Patlwl. 8 (1995) /17-133 127

or invariance from FACTOR, are added. SmaJl variations ( < ± 100/o) are recognizable for C02, COS-COil, C014, RLI, R1A-RL5 (vertical axis range 0. 86- 1.11 ). Medium variations ( < ±50%) appear for C03-C04, CO 12, RL2 -RL3 and large variations (about ± 1000/o) only for COl.

Finally, each feature should define an order relation above the set of images. The invariance of the latter holds for C02-C03, COS, C07-C08, C010-COl3 with some individual exceptions.

This can easily be recognized by the small number of crossing lines in the cor-responding plots (Fig. 6). The features of different parameters of SIZE, DISP, NORM and NOGV show similar behaviour.

3.2. Variation of pixel size (SIZE) The same procedure in the previous paragraph was applied to show the influence

of scale changes. For FACTOR = 1.0, NORM = 2, NOGV = 16 and DISP = 6 fea-tures C01-C014 and for FACTOR= 1.0, NORM= 2 and NOGV = 16 features RLl - RL5 are plotted against the size varying parameter SIZE (Fig. 8). The dependencies in this case are much larger compared to the previous ones. Largest

C01

0.92

1 11

I 06

I 01

0.;6

0.9!

C02 •

CIO

o.so 0

_......__,....--....,..._,... ..,.,---n o.et> 0 u t1 i'l:i -o• ~~m..---n;~.--;,.-'.111 1 11 •. n I '" 007 1.()8 ~ cos I 01 - f ..._ 1.:01 ~~~-- ,.,

~M t . 4 I· f I I 0 96 r -- ·• ' E ' t ~-

1.1!6

0.91 0$1 01 ..

1 .:Y.l

1 1& C04

I .OZ jj4::f+ . ""'P+=<P¥"1 0 !Ill •

0 74

000 o. e 1 1 ··• , 1 a.c

111

UJ6 COB 101 n,...,.... _ _ __.. __ 0 96 0.91

o.eo 0ho1r0. =:=~n---.-, ...... , ""'•'"".t-,..2.0 oet o·hnril-;r"IJ u ii1l •• ohs n t u • r 0.86 ,\---><r--.-2:0 0. o. 1 I 1.i 11 2-6

C09 1.11 I QP C010

' I

'" lOG I 01

OM Ofl

con

o.e_e 0 8Q h...-.....--."'r-.,.r=;;- Q N .~-.n-""TT---;cr-....--,. ~ o:a 1. 1 ,. 1'7'2:0 · o~- lll li n n o ::o o. - 1

11:)()

1 16 C013

I.C2 h.~-~~~ ... .. .. 088

0.7.C

oro -~~ .. -n~~rn 0:,~~ o. 1. 1. nso RL2 , . 38!

1122

,_ L~~~ ~"'9"=F'F'Fi c.go li"

o:so lll~;nr-n;--n..-r,.--;rn

1.11

1.06

I Ot

0.3 1

C014 ..•

- ~ . ,

0 86 .---,,........,..... ;-.=-c:n; o.s o.e 1-l •t n 1-8 1so fibs l-pto 1.38 1 0?#

1.22 'J, LOB 1". 0.9-4

0.80 0. o.

oa10 0.824

• ····•·-· ··- ····I 0.112

·~ ] C012 , 16

1o:1 L 0.88

0.1<

C.60 fiS 0 8 1 I 1.4 1.7 2.0

o.an 0.820 o.!) a

RL1 ' -· .. . . . . .. . ...

1.4. 1 2.

fis. 71. Mean and ±2 S.E.M. bars from all objects for NORM::: I (solid), 2 (dotted) for all CO-features If" SIZE= 1.0. NOGV = 16, DISP = 6 and all RL-features for SIZE:::; 1.0, NOGV = 16 normalized by 1tlfe ~~~ fe3ture from FACTOR = 1.0 plotted above FACTOR..

128 K. Rqd<'tlad<« I Anal. Cell. Pat/IQI. 8 ( 1995) 117-1 JJ

000940

eo~ 00 000170 COj..-c C02 OOOS<2 so O.GCJI2:'

...:.---~--.?~ 000144 «> 0.00014 3~20 . 000646 0.00!12<> 3180 30 000!548 ~.00022 26<10 20 ~0007() 0004!>0

~ I I I > ?fJ(}() 10 ""21> 5 8 , • 7 0 g e-.,- ," I 1 211 5 8 0 1 ... 1 n:ISO 190 C06 330 C07 ~370 ' cos 023-0 IS• 2<0 3316 - ~ 02()5 ' 70 I ell 3262 -1': 0 1!\2 ,, .2 120 3208

:11 S6 166 6D 3 IS-1 . 0130 16.0 I 0o'r 'o.A 3 100 0 ~ 1 7 2b I l -. ' a I 7 20 0.& I 1 I 4 o] OB I l ... I 7 ~0

60 2.660 0000 C01 0 ~ 016 <8 258<

:l6 2.504 -<) 036

24 2~26 0 054

12 2 3-ta -11.072 C0 12 ...._ 2270 ---~ -<) 090 0 l !t 1} -:, I ) 20 0. 1J 1 • 1.1 ~ () M " 0 .• fl ,.

0600 190 0 900 AL1

CO~ 0 64& o ~· a 16-C 0 4;)0 n.e 0 .796

0 3S• 17.2 0 744

1Gfl 05:12

ISO 0 6<0 \l

O.ciS 0 770 ~850

~· . AL2 I).De9 ()692 AL4 0.7M

<6 00!!3 06H 07!6

H l>Dn 0!& ow 22 01111 0.458 0,72

l(l QjlflS 0 .. 1 )

0 :1110 0!>00 g I • I 2

Fig. 8. All CO-featurcs for FACTOR = l.Q NOGV = 16. OISP = 6. ORM = Z and all RL-features for FACTOR = 1.0, NOGV ... 16. NOR.\.f = 2 plotted above SIZE.

influences exist fo r RLl-Rl2. RL4-RL5 and C0 2-C03. Th~ c:Jependency of RL-features is expected since run length is directly related to size. Tk strange behaviour of C07 and COlO seems to be a result of the image inteFJl0l'ation during scale changes interfering with the integer adjustment of displacement veeter size (DISP x SIZE).

To a lso illustrate the variation of features under changes ofsize, each feature was d ivided by the corresponding feature calculated from the original image (SIZE = 1.0) again. In Fig. 9 mean and ± 2 S.E.M. bars of the 10 objects are shown, Large variations( ± 100%) appear for C03, C07, COIO, C012. Medium variatit'O§ ( < ±50%) exist in CO I-C02, C04-C05, CO 13 and small variations appear in C0 6, C0 8- C0 9, COl i , COI4.

No order relationship could be discerned in the set of images in Fig. 8.

3.3. Variation of grey value normalization (NORM) In Figs. 7 and 9, aJl normalized features are plotted above FACTOR and SIZE

for NORM = 1 (solid) and NORM = 2 (dotted). For orientaiiom, reference bars for normal (= 1.0) are added. The variation of the features for the ttw;CD methods of grey

130 K. Rodetwcker I A rut/. Cell, Patho/, 8 ( 199J) 117- 1 JJ

0.0220 0.0176

00132 0 0088 00044

0 0000

0.39

O.J:>

0.25

019

0.11

C01

cos

C09

700

S60 420

3 ~llr"!OT""l>r-.,.-;r.---u 0.00 0 €8

OS2 0 31!

024

CO 1.,3~;:::::::::::0 60

:::; G 60 <8

32 E

1 0 0 150

58 0.124 •.a RL2 o.o9& 34 0 .072

C02

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Fig. 10. All CC-features for FACTOR = 1.0, SIZE = l.O. DISP =6. NORM = 2 and all RlAeatures for FACTOR = 1.0, SIZE= 1.0, NORM= 2 plotted abo,,.e NOOV.

3.5. Variation of displacement vector size ( DTSP) The variation of the size (and/or of the direction for ~..61D.tlropic textures) of the

displacement vector is usually described as resulting m a 'Williatrion of sensitivity of eo-features for certain textures. ln our experiment, then~ ov different textures is quite limited and by no means distinct as used by OlnamiWll et al. [5] or in the l!!lftem.tsed set of example images by Brodatz ( 1). Howe¥er, ~gnaqphic representation f!.l,f the features as a function of DISP (Fig. 11) show that at l'eastl CO 1 and C09 do Irot: reflect any different sensitivity (similar behaviour for eae:b 0bj,ect, order relation-mi.IJ> quite stable, nearly no line crossings). All other features sh0w: only minor differ-€llf&es for DISPs 6 and DISP:::: 10. This is even less prOiil<l>unced for features €ai\t:unllated with NORM = 1. Small deviations appear in nearly all CO-features for OBUJJE'CT = C, F, G, I. These are just the smallest objects.

1.&. Features derived f rom flat texture image ( NC- and NR-jeatures.) ~)t!ign.res are displayed for features derived from flat textme:image F. They show

dl§m~ll: khaviour, except for the two diffen:nt utdhciYds. ofi grey value nor-lt1lftlWcilWml ttNORM). For the NC-features 1he linear 1llrllniHfmmlation (NORM = I) ib<imUllre~tl.. Thiis 6 vaDid in ta:'Jm of &pmd!crlkt:J ffinlmn lf~'fi<i)R and in preser-

X. i?.~nacker l Arral. Cell. Pathol. 8 (1995) 117-133 131

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vation of o rder rela tionships (NC3, NC7, NC9, Cll).. 'Tfut<iUidlurreJationships dif-fer from those defined by CO-features. In tenns of~ off the displacement vecto r (DISP) only, sizes less o r equal than the window sii& offllltc..median transfor-mation are adequate. The median window size was not altma::ti fun different SIZE parameters in this experiment.

4. Discussion and summary

Only some results have been given out of all varied parameters.. The most surpris-ing properties are the frequently existing dependencies of fea tures. from grey value variat ions for images with low grey values (FACTOR < 1.0). We suppose that the process of normalization by equa lization is not efficient enough for sma ll ranges of grey values. In other words, if there is only a small number of different grey values, the equal ization will and cannot perform properly. This would explain the better performance of linearly-normalized NC-features. The difference of the original ex-tinction image and the median smoothed one, that is the range of grey values in the flat texture image F , is naturally small.

F or size a ltera tions the resulting features are influenced by three additional effects: first, the interpolation during the scale cha nging algorithm, second (more severely) the cutoff for images not fitting into the frame of 128 x 128 pixels for SIZE > 1.0 and third, the calcula tion of the displacement vector.

Applying scale changes using minimum or maximum ope~alerrs instead of any in-

132 K.IRv/JanDdlceri AYJd.. 0!11 Parbnl. 8 (1995J 117-IJJ

terpolation would :resuillt m unwished strong edge effects. This influence may have been reduced by usi111g optical means for size changes. However, the use of different optics, zooms, light settings, etc. would considerably reduce the interpretability of the textural features. Single cell images were anatyzed and connpared in th~ study. Hence, statistics cannot be used to smooth out those effects. Furtbermor.e, with pixel sizes of 0.25 llffi we are at the border of optical resolution. The main goal of :sire changes in this study was also to estimate shrinking artefacts resulting from prepara-tion parameters like time of air-drying or concentration of fixative.

Concerning the second influence only OBJECT = C, G, I fit into the given frame under SIZE = 2.0. For the third, the displacement vector was calculated as a round-ed integer from DISP x SIZE resulting in e.g. DISP = 6 in 3, 4, 6, 8, 12 pixds for SIZE = 0.5, 0. 7, 1.0, 1.4, 2.0, respectively, instead of 3, 4.2, 6, 8.4, 12. Non-integer displacements are either not possible or would necessitate another interpolation with unpredictable results.

The number of pixels in the nuclei for original size (SIZE = LO) range between 1700 and 4200. This means that numbers of grey vaJues €NOGV) greater or equal than 32 result in sparsely occupied eo-occurrence and nm Length matrices. However, the results do not prohibit large matrix sizes.

U nder the assumption of isotropic objects, the fW~at!Wm o~ the direction of the dis-placement vector and alteration of its magnitude is jmttilre.d The small changes of features under varied displacement vec;tor sizes lea. muufP:J10"Se. that the textures in our example images (and usually in cell nuclei) are noJit 81$different as macroscopic tex-tures e.g. used by Obanian et al. (5] or derived fmm Brodhtv[l].

Variations of the -size of the region of inten:s.t ·~ outttaken into account. We suppose that the number of pixels and beDa: tk muud&mrof•occurrences affects the features . This will be examined in a later ~tt.

At least for larger grey values., most of tk ~WNlffiined show satisfying in-variance from changes in grey value.. Also the cammr mlllrianship is relatively stable for the chosen texture examples as far as theyQJlllhJ:f~ive. For size changes the features are much more scattered. 0()-w~~t~r,. td~~a.sufficient continuity in the range of size changes.

Derived from the results presented here. «mmr I!W.Utimnwgerffumed cytometry fea-ture calculations will be performed with tk ~lmwh& narameters: DISP = 6, NOGV = 16 and NORM = 2 (histogram. cquadiirMJriiln1) for CO-features and NORM = 1 (linear normalization) for NC-featuns>.

The actual set of 500 images is available for fWlld•m ~venments.

References

El] B'rodatz P. Textures. New York: Dover. 1966, (21 Caliter P. Some comments on texture analysis and tho lli!lt llblf~OOllR'ence matrices. Oxfocdshire:

UK At0mic Energy Authority Harwell. AERE M-~ U~IJl PD Ga1Jil'0'\1!3¥' MM. Texture analysis using gray level run~. CCQ!nn.uterrGnphics and Image Pro· ~ U~JN5i;:4: n1'2-n79.

~ Jlftmdlidk 2,. Sl'mlnmlag~~ 'm K. Dinstein I. Textural lfrt:alrmf!S linrima~classifieation. IEEE Trans Syst /Mml «:'~tmm llmtSM<C-3'~ 611>'-611.

•

t

K. Rodenacker I Anal. Cell. Patltol. 8 (1995) 1/7-133 133

[5] Ohanian PP, Dubcs RC. Performance evaluation for four classes of tex.tural features. Pattern Re-cognition 1992;25:8 19- 833.

[6) Reed TR, Hans du Buf JM. A review of recent texture segmentation and feature extraction techni-ques. CVGIP: Image Understanding 1993;57:359-372.

[7] Rodenacker K, A\abele M, Burger G , Gais P, Jutting U, Oossner W, Oberholzer ¥· Image cyto-metry in histological sections of colon carcinoma. Acta Stereologica 1992;11/Suppl I :249- 254.

[8] SAS-Manu.als SAS/STAT. SAS/GRAPH. Cary, NC, USA: SAS Institute Inc., 1990. [9] SPIDER User's Manual. Tokyo: JSD, 1983 .