Shape texture analysis ofliver cell nuclei in hepatomas by

J Clin Pathol 1984;37:755-762

Shape and texture analysis of liver cell nuclei inhepatomas by computer aided microscopyROGER JAGOE, CHRISTOPHER SOWTER,* GERARD SLAVIN*

From the Clinical Research Centre and Northwick Park Hospital, Harrow, Middlesex, HA 1 3UJ

SUMMARY Nuclei from non-neoplastic hepatocytes and from hepatoma cells have been examinedby image analysis techniques which measure size, shape, and texture. There are significant differ-ences in these parameters between malignant and non-neoplastic cells. When values are obtainedfrom multiple cells in a single biopsy, discriminant programs satisfactorily separate benign andmalignant tissues. Techniques of image analysis offer an opportunity to quantify the nuclearchanges associated with malignancy and may provide an objective basis for tumour gradingsystems.

Changes in cell nuclei are important in the assess-ment of neoplasia by pathologists. In routine prac-tice they are assessed subjectively and are used notonly in diagnosis but also as the basis of gradingsystems which may be extrapolated as a guide totherapy or prognosis. There is a need to quantifysuch changes and to verify their importance. Meas-urements of nuclear features have been made inuterine carcinoma,' malignant lymphoma,2 normallymphoid tissue,3 gastric carcinoma,4 and urothelialtumours.56 Most of these measurements have beenrelated to nuclear size and shape, though textureanalysis has been applied in carcinoma of thebreast.7We have previously distinguished between liver

cell nuclei from normal hepatocytes and those fromhepatoma cells by means of nuclear size and shape.'In this report we have extended our observations,considering further measurements of shape and alsoof texture in the assessment of nuclear changes inneoplasia. Moreover, in this study definition of thenuclear boundary has been made semiautomaticallyby edge tracing routines rather than by a simpledrawing technique.

Material and methods

Liver biopsy material was obtained from the diag-nostic files of Northwick Park Hospital and the Clin-ical Research Centre. Ten livers coded as "normal"

Accepted for publication 12 March 1984

*Present address: Department of Histopathology, St Bar-tholomewis Hospital Medical College, West Smithfield, London

and 10 livers coded as "hepatoma" were examined.All the material had been fixed in formol saline andprocessed by standard procedures to produce 4 ,umparaffin sections stained by haematoxylin and eosin.The sections were then examined using a

Magiscan (Joyce-Loebl) Image Analysis System, inwhich a standard 625 line TV camera is used to scanthe microscope image. This signal is then digitised toa 512 x 512 square matrix of grey values or pixels.Each pixel has a discrete value between 0 and 63which represents the minimum and maximum lightintensities. Each section was examined using a x 100oil immersion objective, giving a resolution of 0-2,Lm/pixel. Maximum nuclear contrast was obtainedusing a Kodak green filter. The grey level images ofthe liver cell nuclei were then analysed.One section was examined from each liver, and

liver parenchymal cell nuclei were chosen at randomin each section. A computer program selected ran-domly any one of 81 possible fields. The boundariesof up to five hepatocyte nuclei nearest to the centreof the field were selected until a total of 30 nucleihad been counted. The nuclei were detected by asemiautomatic edge tracking program in about 85%of non-neoplastic cells and in about 60% of hepato-cytes from neoplastic biopsies. Those nuclear boun-daries not detected by the edge tracking routinewere partially or entirely drawn by the operatorusing a light pen. The nuclear tracking routine willbe reported separately.The magnification gave a monitor image of about

1000 square pixels for the smallest nucleusexamined. This was large enough to reduce the errorof area measurement in repeated manual tracing ofa nuclear boundary to less than 5%.

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The delineated boundary of each nucleus wasenlarged automatically so that a small amount ofcytoplasm was included as background to thenucleus. This was done by expanding the distance ofeach boundary point from the centre of gravity by afactor of 1-2. The grey level values of each pixelpoint in this enlarged area were recorded on diskfiles.

MEASUREMENTSThirty measurements or derived values of nuclearsize, shape, and texture were made.

Size measurement(1) SIZE. The area within each nuclear boundarywas used as a measurement of size.

Shape measurementsEleven shape measurements were made on thenuclear boundary data.(2) P2A. The simplest and best known shape meas-urement P2A (perimeter squared divided by 4 x PIx AREA) has been used by many workers and is acomponent of commercial packages. Deviations ofthe value from unity reflect deviations from circular-ity.

While P2A was computed from the original traceof the nuclear boundary other shape measurementsare size dependent. To compensate for this theboundary of each nucleus was expanded about itscentre of gravity to enclose an almost constant area.A smoothing procedure was applied to even outsmall irregularities generated by the normalisation.Ninety three percent of the resulting boundaries hadareas within 0-5% of 10 000 square pixels and theremainder were within 1% of this value. Ten meas-urements were derived from the normalised bound-ary.(3) PERIM. The length of the normalised bound-ary.Shape measurements were made based on

alteration of a discrete boundary curvature functionf(C). This is derived by applying a filtering techniqueto a direction coded boundary list. This consists of asequence of integer values which represent changesin direction from point to point along the boundary.Left turn is coded as -1, straight ahead as 0, rightturn as + 1. The filter acts by replacing each value inthis list by the average of itself and its eight neigh-bours. This is repeated four times.'0 A plot of theresulting function shows peaks and troughs corres-ponding to convexities and concavities along theboundary.(4) AVCURV. Mean value of f(C).(5) STDCURV. Standard deviation of f(C).(6) MINCURV. Minimum value of f(C).

Jagoe, Sowter, Slavin

(7) MAXCURV. Maximum value of f(C) .(8) SSQCURV. Sum of squared values of f(C).

Changes in the shape of the nuclear boundarywere also measured by alterations in the distancebetween the boundary and the centre of gravity ofthe nucleus. Four values were obtained:(9) AVDIS. The average distance of the nuclearboundary from the centre of gravity of the nucleus.(10) STDIS. The standard deviation of the distanceof the nuclear boundary from the centre of gravity.(11) MINDIS. The minimum distance of thenuclear boundary from the centre of gravity.(12) MAXDIS. The maximum distance of thenuclear boundary from the centre of gravity.

Texture and densitometric measurementsFour categories of nuclear texture measurementwere used.(a) Simple grey level values and gradient statistics.These are derived from the grey level value of eachpixel point in the nuclear image. The gradientstrength, which measures the local rate of change ingrey levels, was computed from the 3 x 3 Sobeloperator (Fig. 1) for those operators where all thenine points were contained within the nuclear boun-dary. Six values were derived from these measure-ments:(13) MGREY. Mean nuclear grey level over thewhole nucleus.(14) STDGREY. Standard deviation of the nuclear

Fig. 1 Gradient values calculated from a 3 x 3 operator. IfGi is the grey value ofeach point (I S i S 9) in the 3 x 3area then the gradient strength at the central point (5) ofthearea is computed as: GRAD = SQRT((G, +2 xG2 +G 3-G7 -2xG8 -G9)2 + (G3 +2XG, +G, -G, -2xG4-~G7J2),



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Shape and texture analysis of liver cell nuclei in hepatomas

grey levels.(15) STDGREY/MGREY. Coefficient of variationof nuclear grey levels.(16) MGRAD. Mean gradient of nuclear greylevel.(17) STDGRAD. Standard deviation of the gra-dient of nuclear grey levels.(18) STDGRAD/MGRAD. Coefficient of varia-tion of the gradient of nuclear grey levels.(19) IOD. The integrated nuclear optical densitywas estimated by computing

IOD = - Y (Log(Gij/MGC))where Gij is the grey level of a nuclear pixel at point(i, j) and MGC is the mean grey level of the back-ground cytoplasm.(b) Measurements designed to reflect the distribu-tions of grey levels relative to their distances fromthe nuclear boundary or relative to their angulardistributions within the nucleus. These were under-taken because visual assessment suggested that neo-plastic nuclei have a relatively higher concentrationof densely stained material closer to the nuclearboundary than non-neoplastic nuclei.(20) ARANGE. The annular range of grey levelswas computed for each nucleus by calculating therange between the mean grey levels of eight bands ata relative distance Dr (0 - Dr - 7) from thenuclear boundary. The relative distance Dr isrelated to the actual distance Da by the relation

Dr = integral part ((8 x Da)/Dmax)where Dmax is the maximum internal distance fromthe boundary (Fig. 2).(21) SRANGE. The sector range of grey levels isthe range between the mean grey levels of eightequiangular sectors with the origin at the centre ofgravity.(22) MGREYO/MGREY. The ratio of the meangrey level of pixels in the outer most band to themean grey level of the total nucleus.(23) BMOM. A grey level moment about the origi-nal boundary was computed for all eight relativedistances (d = Dr)

7 Nd

L (d + 1) ZGidBMOM 7

MGREY x E (d +l)Ndd=O

where Gid is the grey level of a point i in band d, Ndis the number of pixels in band d, and MGREY isthe mean nuclear grey level over the whole nucleus.

In nuclei with evenly spread grey level valuesBMOM is close to unity. If hyperchromatic regionsof the nucleus are represented by relatively lower

Fig. 2 Division ofnuclear area into eight bands and eightsectors to assess the distribution ofdensely stained materialin relation to the nuclear boundary.

grey values a nucleus with a darkly stained rimregion will give a value greater than unity.(c) Measurements extracted from co-occurrence orgrey level spatial dependency matrices. These havebeen extensively reviewed in the published work"and used as discriminators of terrain types in Land-sat images.'2 13 Only an outline of them is given here.A nuclear image point has eight nearest neigh-

bours in the directions 0, 45, 90,. .. 360 degrees. Ineach of these directions eight grey level densityprobability functions can be estimated for any dis-tance d between image points. Each grey leveldensity function can be written in the form:

p(O,oId.O) p(O. Id.) .P(O..O,No d,@)p(I.OId.6) p(l. Id, ) ..P(l.p I,N-I Id.G)

f(d.) =

p(Ng-I.OId.0) p(Ng 1.IId.@) .. p(Ng I N I IId.6)

where Ng = the number of grey levels in the image(0 to Ng-1) and p(i,j Id,6) is the estimated probabil-ity of a transition from grey level i to grey level j at asampling interval d in the direction 6. The densityfunctions for opposite directions are summed to givefour symmetric matrices.A digitised image may have 64 grey levels, but

typically a nuclear region exhibits a range of only 15to 30 grey levels. This range may then be dividedinto N intervals each of equal probability of occur-rence. A transformed digital image is derived fromthe original by assigning to each pixel a value of 1 toN, corresponding to the interval in which it lay in theoriginal image. Thus the transformed image willhave N possible grey levels and the probability mat-

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rices will be of size N x N. This process is invariantwith respect to monotonic grey level transforma-tions such as alterations in light levels.9

In preliminary trials it was found that the power ofthe features derived from such matrices to discrimi-nate normal from neoplastic nuclei did not varysignificantly for different values of N above thevalue of N = 8. In this study a value of N = 8 waschosen. The raw digital data were preprocessed bythe above method before the computation of theco-occurrence matrices. Since directional textureinformation cannot be relevant to randomlyoriented cell nuclei, the four directional symmetricmatrices were averaged to a single matrix. As unitsample interval between pixels was used (d = 1), theaveraging is equivalent to tabulating the transitionsof transformed grey levels between a central pixeland its eight surrounding neighbours. An example ofmatrices derived from Fig. 3 where the image hasthree grey levels (0-2) is given in Table 1.

Five commonly used texture features" were com-puted from the co-occurrence matrices for eachnucleus.(24) ENTROPY. This is calculated as:

Ng-I Ng- 1

ENT = - E E p(i, j) ln (p(i, j))i=0 j=0

where Ng is the number of equiprobable grey levelintervals.

Entropy is minimal when the image consists of asingle grey level and maximum when all grey levels

1 2 2 2 1

0 1 0 2 2

0 0 1 2 0

2 1 0 1 1

1 2 2 0 0

Fig. 3 Three recurring grey level values 0, 1, and 2 areused in an arbitrary S x S pixel array to produce a simulatedimage.


are equally likely to occur at adjacent pixel points.(25) ASM. The angular second moment is calcu-lated as:

Ng-1 Ng- 1

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

The angular second moment measures the degree ofgrey level homogeneity in the image and is closelybut inversely related to entropy.(26) LHOM. The local homogeneity is calculatedas:

Ng-I Ng- 1

LHOM= E Ez _ j2P0,i)i=0 j=0 1 + (i

It measures the similarity between neighbouringimage points due to a weighting factor which givesmore weight to neighbouring points with similargrey levels.(27) INERT. The moment of inertia about the mat-rix diagonal is calculated as:

Ng-I Ng- 1

INERT= E E (i-j)2p(i,j)i=0 j=0

This measures the, dissimilarity of grey levelsbetween adjacent points.(28) CORREL. The correlation is calculated as:

N9- 1IN9-I

i=O j=OCORREL= where

ax Sy

N9 I N9- 1

AlX= Z i E p(i,j)i=0 j=0N9 I N9- I

Iy j E p(ioj)N9- 1 N9- 1

= Z (i -)2 Z p(ij)i=O j=O

N9 1 N- 1

ay E ty)2 E p( ji)j=O i=0

CORREL measures the degree to which the ele-ments of the matrices are concentrated along thediagonal.(d) Other texture measurements. Two additionaltexture features which have been found useful incomputer analysis of chest radiographs were alsocalculated.'4 These are:(29) MDIVERS. This measurement is based on the



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Shape and texture analysis of liver cell nuclei in hepatomas

Table 1 Four symmetric grey level co-occurrence matricesderived from the image represented by Fig. 3. The numbersin the matrices indicate the estimated probability ofchangesin grey level values between adjacent pixels for horizontal,vertical, and the two diagonal directions. The matrix valuesare derived from the observed frequency ofdifferencesbetween neighbouring pixels

4 53 23 5SI= 40 5 2 5 S45= -2 3 4 4

3 5 8 5 4 2

2 8 4 6 2 340 8 0 5 S3 2- 2 6 2

4 54 32 6

diversity of the quantitised directions of the gradientvector within a local 3 x 3 window as it scans thenuclear area. The direction of the gradient vector iscomputed at each image element, which is labelledwith an integer value from 1 to 8 according to whichof the eight compass points it is most closely alignedto. In the nine elements of any 3 x 3 window theremay be from one to eight differently labelled ele-ments. The mean value of the number of differentlylabelled elements for all the 3 x 3 windows of thenuclear region is used as the texture measurement.This value will increase as adjacent gradient direc-tions become more scattered.(30) STDLAP. A measure of spottiness" of thenucleus was made based on grey levels in a 4 x 4local operator. If C is the average grey value of thefour central pixels and S is the average value of theeight axially adjacent cells, then the value C-S iscomputed for each 4 x 4 window. The ''spottiness"of a region can be estimated from the standarddeviation of this value over the region, provided thatthe spots" are of the same order of magnitude asthe size of the operator.

Results

The data file consisting of 30 variables for each

nucleus was transferred to a DEC-20 computer andanalysed using the BMDP statistical package.The distributions of many of the measured vari-

ables are very asymmetric. Rather than attempt toapply normalising transformations, we chose tosummarise the distribution of each by its medianvalue and its range as defined by the differencebetween the 5th and 95th percentile values. Eachbiopsy was thus characterised by 30 median and 30range variables.

In order to identify those variables which in isola-tion gave the best discrimination between nucleifrom neoplastic and non-neoplastic biopsies, anested random factors analysis of variance was com-

puted for each of the 60 variables. There were 21variables for which the estimated component ofvariance between the groups (normal v neoplastic)was greater than the variance within the groups(Table 2). Expressing the variance ratio for 1 and 18degrees of freedom in the usual way by a significancelevel is not meaningful because the variances of thevariables in the neoplastic group were greater thanthose from the non-neoplastic group. An indicationof the group differences is given by the differencebetween group means divided by the pooled stan-dard deviation (d). The non-parametric Kruskal-Wallis test'7 was used to compute a significance levelfor each of these variables.The features which most effectively distinguished

between the two groups were shape measurements.It is seen from Table 2 that the range of a shapemeasurement within biopsy samples is a better dis-criminant than the corresponding median value.

Five of the 21 variables were derived from thenuclear texture. The most effective of these are themedian values of three measurements derived fromthe co-occurrence matrices. Surprisingly, the size ofthe nuclei played a less important role, but the rangeof nuclear sizes within a biopsy did show a minordiscriminatory effect.Many of the variables measure similar characteris-

Table 2 Eleven median and 10 range features for which the estimated component of variance between the normal andneoplastic biopsies was greater than the variance between biopsy samples. The distance between means divided by the pooledstandard deviation (d) is an indication ofthe feature discriminatory power. The significance level p is derived from thenon-paranetric Kru skal-Wallis test statistic

Median feature d p Range feature d p

PERIM 1-78 0-0005 SIZE 1-66 0-002P2A 1-78 0-0008 PERIM 3-20 0-0002AVCURV 1-72 0-001 P2A 2-96 0-0002AVDIS 2-42 0-0008 AVCURV 1-99 0-0002STDIS 2-35 0-001 SSQCURV 1-61 0-0007MINDIS 2 04 0 001 AVDIS 2-60 0-0002MAXDIS 1-81 0-002 STDIS 3-60 0-0002ARANGE 1-50 0-005 MINDIS 2-99 0-0002CORREL 2-15 0-0007 MAXDIS 2-81 0-0002LHOM 1-98 0-001 MGRAD 1-71 0-008INERT 2-23 0-0007

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Table 3 Correlations between five features derived fromthe co-occurrence matrices. There,are strong correlationsbetween ENTand ASM and between LHOM, INERT, andCORREL

ASM LHOM INERT CORREL

ENT 0-92 0-65 -0-55 056ASM 0-64 -0-48 0-50LHOM -0-97 0-94INERT -0-93

tics and are therefore correlated. For example, themean of the ranked correlation coefficients for thefive textural measurements derived from the co-occurrence matrices are shown in Table 3, fromwhich it is apparent that they fall into two groups. Itis possible that ASM and ENTROPY are measuringa different nuclear characteristic from LHOM,INERT, and CORREL.A stepwise linear discriminant program was used

to select a combination of variables which best sepa-rated the two groups of biopsies. Because of thesmall number of specimens (20 biopsies), the pro-gram was allowed to select only the two most impor-tant variables.The best discriminating variable is the one with

the largest d value (Table 2). This is a shapecharacteristic-the range of STDIS-which meas-ures the range over 30 cells of the standard devia-tion of the distance of the nuclear boundary from itscentre of gravity. This shape feature completelyseparates the two groups of biopsies (Fig. 4).The second most important variable which was

selected by the program after allowing for thebetween variable correlations was the median valueof the texture measurement INERT. On its own thisdid not completely separate the two groups of biop-sies (Fig. 5). The between group separation using acombination of these two variables is shown inFig. 6.

Shape . Neoplastic biopsyNon-neoplastic biopsy

* m_ 0* -Xc §WOG

l - I-4.8 -40 -32 -24 -1 6 -0.8 0 0 8 1 6 24 32 4 0

Discriminant function

Fig. 4 Separation of non-neoplastic and neoplastic liverbiopsies based on the distance ofthe nuclear boundary to itscentre ofgravity in groups of30 cells.


* Neoplastic biopsyo Non-neoplastic biopsy

Texture

* 0000 0* o*o-o 0 00o00 0

I I

-3-0 -24 -1.8 -1 2 -0.6 0 06 1.2 1 8 2.4 3 0Discriminant function

Fig. 5 Separation ofnon-neoplastic and neoplastic liverbiopsies on the texture measurement INERT in groups of30cells.

Texture

* Neoplastic biopsyo Non-neoplastic biopsy

.

0 0

O Shape

Fig. 6 Separation ofthe two groups ofbiopsies using alinear discriminant based on nuclear shape and texture.

Discussion

Histopathologists base their diagnosis and gradingof malignancies on many features: tissue architec-ture, cytoplasmic appearances, and changes in thenuclei. Their diagnoses are based on a consideredsummation of many factors and not on any singleone. Nevertheless, it is important to try to separatethe features and to verify their importance by objec-tive measurement.

Nuclear features such as size and changes in shapeare important. They may be assessed by simplemeasurements and by shape factors such as devia-tions from circularity and changes in curvature func-tions of the nuclear boundary.8

It is more difficult to measure the state of thenucleus described subjectively as "coarse,""spotty," "dispersed," or "clumped." Changesunderlying such nuclear appearances may reflectquantitative alterations in the nuclear content ofDNA, but they also represent functional states ofthe nucleus with dispersion or aggregation of thenuclear material. Nicolini et al15 have reported thatthe texture of W1-38 fibroblast nuclei show differ-ent textures related to stages in the cell cycle, thoughthe DNA content remains constant.Changes in the appearance of the nucleus are

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Shape and texture analysis of liver cell nuclei in hepatomasmeasured by texture analysis. The texture of animage may be defined as regional patterns of greylevel density distributions in an image which areusually locally recurrent.'6 Such techniques havebeen widely used in meteorology and in Landsatdescriptions of terrain,'2 13 but their use in biologyhas been less common, partly because of the com-plexity of the equipment to make such measure-ments. Lipkin and Lipkin,'6 however, have used tex-ture to assess nuclear maturation in granulocytes,and Stenkvist et al7 have characterised breast cancercell populations, partly on the basis of texture.Computer assisted microscopy is now relativelyinexpensive and textural analysis is a potential toolfor pathologists.

In this report we have expanded our previousstudy on nuclear size and shape as discriminants ofhepatoma cells by measurement of additional shapefactors and measurement of the nuclear texture. Thegrouped values of nuclear features obtained fromthe measurements on 30 cells in each biopsy showthat when malignant samples are compared withnon-neoplastic samples there are many differencesbetween the two groups in size, shape, and texturemeasurements. The best separation is given by a fea-ture which is a measurement of the range of valueswithin a biopsy of a function derived from the dis-tance of the nuclear boundary from its centre ofgravity. This feature is closely related to one derivedfrom the curvature function which was previouslyidentified as a good discriminator of neoplasticcells.8 A random selection of cells from neoplasticbiopsies is likely to include a proportion of non-neoplastic cells in the sample. This dilution of theneoplastic cells is the most obvious reason for therange- of shape variables to play a greater dis-criminatory role than the median values.The median value of the measurement INERT

was the second best discriminant but this did notcompletely separate the two groups of biopsiesThe range of nuclear sizes within a biopsy did, in

isolation, show some group separating effect. Whenthe two factors of shape and texture were analysedby the linear discriminant -techniques, however, thesize effect disappeared.

It is of interest, but disappointing, that thosemeasurements of texture which reflect aggregationof stained nuclear material near to the nuclearmembrane did not appear to be of value in dis-criminating either individual cells or biopsies. Thesample size in this analysis was small (20 biopsies)and it is likely that with larger samples other fea-tures may have a discriminant role.

This study has shown that objective measure-ments may be made by computer assisted micros-copy on liver cell nuclei in histological sections pre-

pared by standard techniques. Measurements ofsize, shape, and texture show significant differencesbetween neoplastic and non-neoplastic biopsies.The liver was chosen for this study as an ideal sub-ject for computer analysis with widely separatednuclei which facilitated the development of automa-tic nuclear detection. The sections examined werestained by haematoxylin and eosin in order to assessthe images normally seen by pathologists. Automa-tic nuclear detection depends on sophisticated pro-grams, but nuclear definition may be enhanced byalternative embedding and staining techniques. Butthese alternatives may alter the informationobtained. These aspects are under study.

It is important to emphasise that objective meas-urements of nuclei by computer assisted microscopycannot replace the diagnostic process used by thehistopathologist. This is a subtle process of assessingtissue architecture and cellular context as well as thestructure of nuclei and cytoplasm and is underpin-ned by the experience of the pathologist. Moreover,the criteria used may not be the same in differenttissues. Nevertheless, such cellular measurements asdescribed are valuable in that they lead to a morecritical appraisal of what the pathologist actuallysees. Moreover, they may be of importance as anadjunct to diagnosis in providing some objectivedata for tumour grading where human assessment isnotoriously inconsistent and variable.

We thank Mrs Sheila Dandy for her help in thiswork and Mr CE Rossiter and Dr ID Hill for statis-tical help and advice.

References

Baak JPA, Diegenbach PP. Quantitative nuclear image analysis:differentiation between normal, hyperplastic and malignantappearing uterine glands in a paraffin section 1. Elementaryfeatures for differentiation. European Journal of Obstetrics,Gynaecology and Reproductive Biology 1977; 5:33-42.

2 Abbot CR, Blewitt RW, Bird CC. Quantitative analysis of non-Hodgkin's lymphoma. J Clin Pathol 1982;35: 135-8.

3Crocker J, Curran RC. A study of nuclear diameters in lymphnode imprints using the Zeiss Videomat. J Clin Pathol1979;32:670-4.

4 Boon ME, Kurver PJH, Baak JPA, Thompson HT. The applica-tion of morphology in gastric cytological diagnosis. VirchowsArch A (PatholAnat) 1981;393:159-64.

5Stinson SF, Lilga JC, Reese DH, Friedman RD, Spom MB.Quantification with an automated'image analyser of nuclearcytoplasmic changes induced by hydrocortisone in bladderepithelium. Cancer Res 1977;37: 1428-31.

6Ooms ECM, Essed E, Veldhvizen RW, Kurver PJH, Boon ME.The prognostic significance of morphology in TI bladdertumors. Histopathology 1981; 5:311-8.

7Stenkvist B, Westman-Naer S, Holmquist J, et al. Computerisednuclear morphometry as an objective method for characteris-ing human cancer cell populations. Cancer Res 1978;38:4688-97.

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liver cell nuclei in hepatomas using an interactive computertechnique: 1) Nuclear size and shape. J Clin Pathol1982;35:1057-62.

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10 Eccles MJ, McQueen PC, Rosen D. Analysis of the boundariesof planar objects. Pattem Recognition 1977;9:31-41.

"Thomas JO. Texture analysis in image processing. In: ThomasJO, Davey PG, eds. Texture analysis. Proceedings of BritishPattern Recognition Association and Remote Sensing Society.Oxford: Physics Photographic Unit, Oxford University,1977.

12 Harris R. Automatic analysis of meteorological satellite imagery.In: Thomas JO, Davey PG, eds. Texture analysis. Proceed-ings of British Pattern Recognition Association and RemoteSensing Society. Oxford: Physics Photographic Unit, OxfordUniversity, 1977.

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Jagoe, Sowter, Slavinture measures for terrain classification. IEEE Transactionson Systems, Man and Cybernetics 1976;4:269-85.

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5 Nicolini C, Kendall F, Basergen R, Dessaive C, Clarkson B,Fried J. The GO-Gl transition of W138 cells. II. Geometricand densitometric txture analysis. Experimental CellResearck 1977;106: 1 f9-25.

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Requests for reprints to: Mr R Jagoe, Department ofComputing, Northwich Park Hospital, Harrow, MiddlesexHAl 3UJ, England.



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