textural features for image classification...tone spatial-dependence probability-distribution...

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, \O SMc(-3, NO. 6, NOVEMBER 1973

ACKNOWLEDGMENT

The authors wish to acknowledge the invaluable help andadvice of Dr. E. S. Savas, First Deputy City Administratorof New York City, the cooperation of the Department ofSanitation and of the staff of the Neighborhood ActionProgram, and the help of the residents of the WashingtonHeights-Inwood-Marble Hill district.

REFERENCES

[1] L. T. DeStefano and A. H. Levis, "A model for the effect of illegallyparked cars on street cleaning," J. Environ. Syst., vol. 2, pp. 109-130, June 1972,

[2] H. Noel and J. Kaiser, "A citizen's analysis of illegal parking,enforcement and clean streets in a neighborhood," Office ofAdministration, Office of the Mayor, City of New York, May 1971l

[3] R. Bellman, Introduiction to Matrix Algebra. New York: McGra\-Hill, 1960.

[4] S. Tartarone, "On the enforcement of parking regulations fbrstreet cleaning," M.S. thesis, Dep. Elec. Eng., Polytechnic Inst.Brooklyn, Brooklyn, N.Y., June 1972.

[5] A. H. Levis, Ed., "Urban street cleaning-interim report no. 1,'"Dep. Elec. Eng., Polytechnic Inst. Brooklyn, Brooklyn, N.Y.,Rep. PIBEE 71-010, June 1, 1971.

[6] S. Tartarone, P. Bloom, L. T. DeStefano, and A. H. Levis, "Urbanstreet cleaning-interim report no. 2," Dep. Elec. Eng., PolytechnicInst. Brooklyn, Brooklyn, N.Y., Rep. PIBEE 71-014, Oct. 1, 1971.

[7] J. Berenyi, "System analysis of parking regulations, violations, andenforcement activities," Office of Administration, Office of theMayor, City of New York, Jan. 1971.

Textural Features for Image ClassificationROBERT M. HARALICK, K. SHANMUGAM, AND ITS'HAK DINSTEIN

Abstract-Texture is one of the important characteristics used inidentifying objects or regions of interest in an image, whether the imagebe a photomicrograph, an aerial photograph, or a satellite image. Thispaper describes some easily computable textural features based on gray-tone spatial dependancies, and illustrates their application in category-identification tasks of three different kinds of image data: photo-micrographs of five kinds of sandstones, 1:20 000 panchromatic aerialphotographs of eight land-use categories, and Earth Resources Tech-nology Satellite (ERTS) multispecial imagery containing seven land-usecategories. We use two kinds of decision rules: one for which the decisionregions are convex polyhedra (a piecewise linear decision rule), and onefor which the decision regions are rectangular parallelpipeds (a min-maxdecision rule). In each experiment the data set was divided into twoparts, a training set and a test set. Test set identification accuracy is89 percent for the photomicrographs, 82 percent for the aerial photo-graphic imagery, and 83 percent for the satellite imagery. These resultsindicate that the easily computable textural features probably have ageneral applicability for a wide variety of image-classification applica-tions.

I. INTRODUCTION

W .[ITH THE ADVENT of high-speed general-purposedigital computers it is becoming possible to perform

mathematical or algorithmic processes on pictorial datafrom images of photographic quality. In most of theseprocesses, the pictorial information is represented as afunction of two variables (x,y). The image in its digitalform is usually stored in the computer as a two-dimensional

Manuscript received April 25, 1973; revised June 12, 1973. Thiswork was supported by the NASA Goddard Space Flight Center underContract NAS5-21822, and the Geographic Sciences ILaboratory ofthe U.S. Army Engineer Topographic Laboratories under ContractDAAK02-70-C-0388.

R. M. Haralick and 1. Dinstein are with the School of ElectricalEngineering and the Center for Research, Inc., University of Kansas,Lawrence, Kans. 66044.K. Shanmugam was with the Center for Research, Inc., University of

Kansas, Lawrence, Kans. He is now with the Department of ElectricalEngineering, Wichita State University, Wichita, Kans. 67218.

array. If Lx = {1,2, ,N,} and Ly = {1,2, * ,NY} are theX and Y spatial domains, then LX x Ly is the set of resolu-tion cells and the digital image I is a function which assignssome gray-tone value G E { 1,2, ,NJ to each and everyresolution cell; I: Lx x Ly- G. Various two-dimensionalanalyses are performed on I to achieve specific image-processing tasks such as coding, restoration, enhancement,and classification. In recent years a tremendous amount ofcomputer processing of photographs has occurred, withfacilities having been developed to process anything fromaerial photographs to photomicrographs [1], [2].

In this paper we are concerned with the task of developinga set of features for classifying or categorizing pictorialdata. The classification of pictorial data can be done on aresolution cell basis (such as in identifying the crop categoryof a resolution cell on satellite imagery) or on a block ofcontiguous resolution cells (such as in identifying the cropcategory of an entire agricultural field extending over alarge number of resolution cells). The most difficult step incategorizing pictorial information from a large block ofresolution cells is that of defining a set of meaningfulfeatures to describe the pictorial information from the blockof resolution cells. Once these features are defined, imageblocks can be categorized using any one of a multitude ofpattern-recognition techniques.

In a search for meaningful features for describing pic-torial information, it is only natural to look toward thetypes of features which human beings use in interpretingpictorial information. Spectral, textural, and contextualfeatures are three fundamental pattern elements used inhuman interpretation of color photographs. Spectral fea-tures describe the average tonal variations in various bandsof the visible and/or infrared portion of an electromagneticspectrum, whereas textural features contain information

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HARALICK et al.: TEXTURAL FEATURES FOR IMAGE CLASSIFICATION

about the spatial distribution of tonal variations within a

band. Contextual features contain information derived fromblocks of pictorial data surrounding the area being analyzed.When small image areas from black and white photographsare independently processed by a machine, then texture andtone are most important.The concept of tone is based on the varying shades of

gray of resolution cells in a photographic image, whiletexture is concerned with the spatial (statistical) distributionof gray tones. Texture and tone are not independent con-

cepts; rather, they bear an inextricable relationship to one

another very much like the relationship between a particleand a wave. Context, texture, and tone are always present inthe image, although at times one property can dominate theother.

Texture can be evaluated as being fine, coarse, or smooth;rippled, molled, irregular, or lineated. For example, in thehumid tropics, fine texture on radar imagery can be in-dicative of nonresistant fine-grain sedimentary rocks andunconsolidated sediments, while a coarse texture can beindicative of coarser grained sedimentary rocks. A massivetexture with high-contrast components may be indicative ofigneous rocks. A hummocky texture can be indicative oferoded igneous rocks.

Texture is an innate property of virtually all surfaces-the grain of wood, the weave of a fabric, the pattern ofcrops in a field, etc. It contains important informationabout the structural arrangement of surfaces and theirrelationship to the surrounding environment. Although itis quite easy for human observers to recognize and describein empirical terms, texture has been extremely refractory toprecise definition and to analysis by digital computers.Since the textural properties of images appear to carryuseful information for discrimination purposes, it is im-portant to develop features for texture. We present in thispaper a computationally quick procedure for extractingtextural features of images and discuss the usefulness ofthese features for discriminating between different kinds ofimage data.

Early image texture studies have employed autocorrela-tion functions [3], power spectra [4], restricted first- andsecond-order Markov meshes [5], and relative frequenciesof various gray levels on the unnormalized image [6].These had some degree of success, but we know little moreabout texture after finding the results of these experimentsthan before because they did not try to specifically define,characterize, or model texture. They only used some generalmathematical transformation which assigns numbers to thetransformed image in a nonspecific way.

Recent attempts to extract textural features have beenlimited to developing algorithms for extracting specificimage properties such as coarseness and presence of edges.Many such algorithms have been developed and tried on

special imagery. The subjective parameters (such as theselection of thresholds) associated with the techniques donot enable them to be generalized to imagery other thanthat processed by the authors. Recently, Rosenfeld and hiscoinvestigators presented a set of procedures for extractingsome textural properties of pictorial data [7]-[9]. In [7]

Rosenfeld and Troy described a procedure for obtaining ameasure of the texture "coarseness" of images. Their pro-cedures were based on the differences between the gray-tonevalues of adjacent image elements and on the autocorrela-tion of the image gray-tone values. In [8] Rosenfeld andThurston gave a procedure for detecting boundaries separat-ing regions which differ in texture coarseness. In [9] Troyet al. described gray-level manipulation procedures whichcan be used for preprocessing of pictures before applyingthe algorithms given in [7] and [8]. Procedures for detectingtextural properties such as lines and dots have also beensuggested by other investigators (see, for example, [10]-[12]). Before applying these procedures to pictures otherthan the ones processed by the authors of the respectivepapers, the investigator has to make a choice as to themethod appropriate to the picture in question as well as theselection of parameters for the particular method.We are presenting in this paper a general procedure for

extracting textural properties of blocks of image data. Thesefeatures are calculated in the spatial domain, and thestatistical nature of texture is taken into account in ourprocedure, which is based on the assumption that the tex-ture information in an image I is contained in the overallor "average" spatial relationship which the gray tones inthe image have to one another. We compute a set of gray-tone spatial-dependence probability-distribution matricesfor a given image block and suggest a set of 14 texturalfeatures which can be extracted from each of these matrices.These features contain information about such image tex-tural characteristics as homogeneity, gray-tone linear de-pendencies (linear structure), contrast, number and natureof boundaries present, and the complexity of the image. Itis important to note that the number of operations requiredto compute any one of these features is proportional to thenumber of resolution cells in the image block. It is for thisreason that we call these features quickly computable.We also investigate the usefulness of textural features for

categorizing or classifying image blocks from three differentdata sets ranging from high-resolution photomicrographsto low-resolution satellite imagery. The accuracy of clas-sification on multiclass categorization using textural featuresof these data sets was in the range of 80-90 percent.

II. TEXTURAL FEATURES

Our initial perspective of texture and tone is based onthe concept that texture and tone bear an inextricablerelationship to one another. Tone and texture are alwayspresent in an image, although one property can dominatethe other at times. The basic intuitively perceived relation-ships between tone and texture are the following. When asmall-area patch of an image has little variation-i.e., littlevariation of features of discrete gray tone-the dominantproperty of that area is tone. When a small-area patch hasa wide variation of features of discrete gray tone, thedominant property of that area is texture. Crucial to thisdistinction are the size of the small-area patch, the relativesizes of the discrete features, and the number of distin-guishable discrete features. As the number of distinguishabletonal discrete features decreases, the tonal properties will

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IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, NOVEMBER 1973

predominate. In fact, when the small-area patch is only thesize of one resolution cell, so that there is only one discretefeature, the only property present is tone. As the number ofdistinguishable features of discrete gray tone increaseswithin the small-area patch, the texture property willdominate.One important property of tone-texture is the spatial

pattern of the resolution cells composing each discretetonal feature. When there is no spatial pattern and thegray-tone variation between features is wide, a fine textureresults. As the spatial pattern becomes more definite andinvolves more and more resolution cells, a coarser textureresults. An excellent set of photographs of different typesof texture may be found in [13].The preceding description of texture is, of course, a gross

simplification and idealization of what actually occurs.Discrete tonal features are really quite fuzzy in that they donot necessarily stand out as entities by themselves. There-fore the texture analysis we suggest is concerned with moregeneral or macroscopic concepts than discrete tonal features.The procedure we suggest for obtaining the textural

features of an image is based on the assumption that thetexture information on an image I is contained in the overallor "average" spatial relationship which the gray tones inthe image I have to one another. More specifically, we shallassume that this texture information is adequately specifiedby a set of gray-tone spatial-dependence matrices which arecomputed for various angular relationships and distancesbetween neighboring resolution cell pairs on the image. Allof our textural features are derived from these angularnearest-neighbor gray-tone spatial-dependence matrices.

Gray-Tone Spatial-Dependence Matrices

Suppose an image to be analyzed is rectangular and hasN. resolution cells in the horizontal direction and N,resolution cells in the vertical direction. Suppose that thegray tone appearing in each resolution cell is quantized' toNg levels. Let Lx = {1,2, ,Nx} be the horizontal spatialdomain, Ly = {1,2,. ,NY} be the vertical spatial domain,and G = {1,2, .*,NgJ be the set of Ng quantized graytones. The set Ly x Lx is the set of resolution cells of theimage ordered by their row-column designations. The imageI can be represented as a function which assigns some graytone in G to each resolution cell or pair of coordinates inLy x Lx; I: Ly x Lx -+G.An essential component of our conceptual framework of

texture is a measure, or more precisely, four closely relatedmeasures from which all of our texture features are derived.These measures are arrays termed angular nearest-neighborgray-tone spatial-dependence matrices, and to describethese arrays we must emphasize our notion of adjacent or

1 Variations in lighting, lens, film, developer, and digitizer usuallyintroduce monotonic transformations of the "true" image gray-tonevalues. Under these conditions, we would want two images of the samescene, one being a gray-tone monotonic transformation of the otherto produce the same features. Image normalization by equal-prob-ability quantizing guarantees that images which are monotonic trans-formations of one another produce the same results [14], [15]. Anequal-probability quantizing algorithm is given in Appendix III.

90 degrees

135 degrees 45 degrees

6 7 8

5 Odegrees

4 31 2

Fig. 1. Resolution cells 1 and 5 are O (horizontal) nearest neighborsto resolution cell *; resolution cells 2 and 6 are 1350 nearest neigh-bors; resolution cells 3 and 7 are 90° nearest neighbors; and resolu-tion cells 4 and 8 are 450 nearest neighbors to *. (Note this informa-tion is purely spatial, and has nothing to do with gray-tone values.)

nearest-neighbor resolution cells themselves. We consider a

resolution cell-excluding those on the periphery of an

image, etc.-to have eight nearest-neighbor resolution cellsas in Fig. 1.We assume that the texture-context information in an

image I is contained in the overall or "average" spatialrelationship which the gray tones in image I have to one

another. More specifically, we shall assume that this tex-ture-context information is adequately specified by thematrix of relative frequencies Pij with which two neighbor-ing resolution cells separated by distance d occur on theimage, one with gray tone i and the other with gray tone j.Such matrices of gray-tone spatial-dependence frequenciesare a function of the angular relationship between theneighboring resolution cells as well as a function of thedistance between them. Fig. 2 illustrates the set of allhorizontal neighboring resolution cells separated by distance1. This set, along with the image gray tones, would be usedto calculate a distance 1 horizontal gray-tone spatial-de-pendence matrix. Formally, for angles quantized to 450intervals the unnormalized frequencies are defined by

P(i,j,d,00) = #{((k,l),(m,n)) e (Ly x Lx)

x (Ly x Lx) k-m = 0,11 -n =d,

I(k,l) = i, I(m,n) = il

P(i,j,d,450) = #{((k,l),(m,n)) e (Ly x Lx)

x (Lyx Lx)I(k-m = d,l - n =-d)

or (k - m = -d,l - n =d),

I(k,l) = i, I(m,n) = j}

P(i,j,d,900)= #{((k,l),(m,n)) e (Ly x Lx)

x (Ly xLx) I k- mI = d,I - n = 0,I(k,l)=i,I(m,n)=j}

P(i,j,d,1350)= #{((k,l),(m,n)) e (Ly x Lx)x (Ly x Lx) (k - m = d, l- n = d)

or (k-m = -d, l-n= -d),

I(k,l) = i, I(m,n) = j} (1)

where # denotes the number of elements in the set.

Note that these matrices are symmetric; P(i,j; d, a) =P(j, i; d, a). The distance metric p implicit in the preceding

6t2


(1, 1) (1,2) (1,3) (1,4)

(2,1) (2,2) (2,3) (2,4)

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3) (4,4

L = 1,2,3,46

Lx = 11,2,3,4)

RH = {k,l),(m,n)) E (L xLx x (L xL) k-mr 0, j1-nl = 1)~~{l(1,1),(1,2 ((I,(12), (I,I , ((I ,2), (1,3)), ((I,3), (1,2)),((1,3),(1,4)), 1 t4),(1,3)), ((2,1),(2,2)), ((2,2),(2,1)},((2,2),(2,3() , ((2,3),(2,2)) ((2,3),(2,4)), ((2,4), (2,3))

[(3,1), (3,2)) , ((3,2),'(3, 1) ((3,2)' (3,3)), ((3,3), (3,2)) ,

((3,3),(3,41 , f(3,4),(3,3J , ((4,1),(4,21 , ((4,2),(4,1)| r1(4,2),(4,3)1, t4,3), (4,2 1, ((4,3), (4,4)) , ((4,4), (4,3)))

Fig. 2. Set of all distance 1 horizontal neighboring resolution cellson 4 x 4 image.

equations can be explicitly defined by

p((k,l),(m,n)) = max {lk - ml, 11- nl}.

Consider Fig. 3(a), which represents a 4 x 4 image withfour gray tones, ranging from 0 to 3. Fig. 3(b) shows thegeneral form of any gray-tone spatial-dependence matrix.For example, the element in the (2,1) position of thedistance 1 horizontal PH matrix is the total number of timestwo gray tones of value 2 and 1 occurred horizontallyadjacent to each other. To determine this number, we countthe number of pairs of resolution cells in RH such that thefirst resolution cell of the pair has gray tone 2 and thesecond resolution cell of the pair has gray tone 1. In Fig.3(c)-3(f) we calculate all four distance 1 gray-tone spatial-dependence matrices.

If needed, the appropriate frequency normalizations forthe matrices are easily computed. When the relationship isnearest horizontal neighbor (d = 1, a = 0°), there will be2(N - 1) neighboring resolution cell pairs on each rowand there are N, rows, providing a total of 2NY(N - 1)nearest horizontal neighbor pairs (see Fig. 3). When therelationship is nearest right-diagonal neighbor (d = 1,a = 450) there will be 2(NX - 1) 450 neighboring resolutioncell pairs for each row except the first, for which there arenone, and there are Ny rows. This provides a total of2(NY - l)(NX - 1) nearest right-diagonal neighbor pairs.By symmetry there will be 2N -(N-1) nearest verticalneighbor pairs and 2(NX- I)(Ny-1) nearest left-diagonalneighbor pairs. After the number of neighboring resolutioncell pairs R used in computing a particular gray-tonespatial-dependence matrix is obtained, the matrix isnormalized by dividing each entry in the matrix by R.

It is appropriate at this point to comment on the com-putational aspects of obtaining the gray-tone spatial-de-pendence matrices. The number of operations required toprocess an image using our procedure is directly propor-tional to the number of resolution cells n present in theimage. In comparison, the number of operations are of theorder of n log n if one wishes to use Fourier or Hadamardtransform to extract texture information. Also, to computethe entries in the gray-tone spatial-dependence matrices,one needs to keep only two lines of image data in core at atime. Thus no severe storage constraints are imposed. For

IoI I fI

(a)

Oo0 22 4

pH=I 0O O

1

061

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0121

(c)

1 3 013° 1 2 1 0

PLD 3 l 0 200 2 0

Grey Tone

O 1 2 30 #(0,0) #(0,l) #(0,2) #(0,3)

Grey 2 #(2,0) #(2,1) #(2,2) #(2,3)Tone 3 #(3,0) #(3,l) (3,2) #(3,3)

(b)

90° 6 0 2 00 4 2 0

IV 2 2 2 20 2 0/

(d)

° 4 1 o o045 1 2 2 01

RD 0 2 4 1

O 0 1 0

(e) (f)Fig. 3. (a) 4 x 4 image with four gray-tone values 0-3. (b) Generalform of any gray-tone spatial-dependence matrix for image withgray-tone values 0-3. # (i,j,) stands for number of times gray tonesi and j have been neighbors. (c)-(f) Calculation of all four distance1 gray-tone spatial-dependence matrices.

most of the images we have processed, the computationshave been carried out on a small digital computer (PDP15/20 with 12 kwords of core and two DEC tape drives).

Textural Features Extractedfrom Gray-Tone Spatial-Dependence Matrices

Our initial assumption in characterizing image texture isthat all the texture information is contained in the gray-tonespatial-dependence matrices. Hence all the textural featureswe suggest are extracted from these gray-tone spatial-de-pendence matrices. The equations which define a set of 14measures of textural features are given in Appendix I.Some of these measures relate to specific textural charac-teristics of the image such as homogeneity, contrast, andthe presence of organized structure within the image. Othermeasures characterize the complexity and nature of gray-tone transitions which occur in the image. Even thoughthese features contain information about the texturalcharacteristics of the image, it is hard to identify whichspecific textural characteristic is represented by each ofthese features.For illustrative purposes, we will define 3 of the 14

textural features in this section and explain the significanceof these features in terms of the kind of values they take onfor two images of distinctly different textural characteristicsThe features we consider are

Ng Ng /p(ijfl\2

i=1 j=1 \R

f2 = E n2 yEn=O ii-jl=n R

Ng Ng

a , [ijP(i,j)IR] -uxliyf i=1 j=l

ax3y

(2)

(3)

(4)

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* - :, '*:'*~~~~~~. . .. -,, ... 'i.. +i.to$a5**.... .......................... ....

. .

. * ,, , , , -t-t-' 'S-S....... ...,552. ; i, :. .. ........... ..

,., . ..: .0l . ,l. ...

1 ; +S .. P*?tr *!toS *) s........................ .l

r, , ,., ,q, ,., ; . Z *s..........

,:i:S5..:. .. ...... ......_ . . ... .t

J.5-.: . ,* :, :: : i. . ...... ...I

....5 : 1

- ... ....,...

4. _

I_,Ifltl I m.............,_

Corre lation.8075.6366.5987.4610.6259

ASM

.1016

.0771

.0762

.0741

.0822

Water BodyContrast2.1533.0573.1133.1292.863

(b)

Corre lat ion

.7254

.4768

.4646

.4650

.5327

Fig. 4. Textural features for two different land-use category images.

where p., p, a., and a, are the means and standard devi-ations of the marginal distributions associated with P(i,j)/R,and R is a normalizing constant.

Fig. 4 shows the digital printout of two 64 x 64 imageblocks taken from a satellite picture over the Californiacoastline (NASA ERTS Image no. 1002-18134). The imageshown in Fig. 4(a) is a representative sample of grasslandsand Fig. 4(b) is a representative sample of water bodies inthe area. The values of the features fl, f2, and f3 obtainedfrom gray-tone spatial-dependence matrices for distanced = 1, are shown below the images in Fig. 4.The angular second-moment feature (ASM) f, is a

measure of homogeneity of the image. In a homogeneousimage, such as shown in Fig. 4(b), there are very few dom-inant gray-tone transitions. Hence the P matrix for thisimage will have fewer entries of large magnitude. For an

image like the one shown in Fig. 2(a), the P matrix will havea large number of small entries, and hence the ASM feature(which is the sum of squares of the entries) in the P matrixwill be smaller. A comparison of the ASM values given

below the images in Fig. 4 shows the usefulness of the ASMfeature as a measure of the homogeneity of the image.The contrast feature f2 is a difference moment of the P

matrix and is a measure of the contrast or the amount oflocal variations present in an image. Since there is a largeamount of local variation present in the image of Fig. 4(a)compared to the image shown in Fig. 4(b), the contrastfeature for the grassland image has consistently highervalues compared to the water-body image.The correlation feature f3 is a measure of gray-tone

linear-dependencies in the image. For both the imagesshown in Fig. 4, the correlation feature is somewhat higherin the horizontal (00) direction, along the line of scan. Thewater-body image consists mostly of a constant gray-tonevalue for the water plus some additive noise. Since the noisesamples are mostly uncorrelated, the correlation featuresfor the water-body image have lower values compared tothe grassland image. Also, the grassland image has a con-

siderable amount of linear structure along 450 lines across

the image, and hence the value of the correlation feature is

GrasslandAngle

0

45o90o1350Avg.

ASM.0128.0080.0077.0064.0087

Contrast3.0484.0114.0144.7093.945

(a)

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HARAUCK et al.: TEXTURAL FEATUPRS FOR IMAGE CLASSFICATION

higher along this direction compared to the values for 900and 1350 directions. More examples of the significance ofsome of the textural features are presented in Appendix II.The various features which we suggest are all functions

of distance and angle. The angular dependencies present aspecial problem. Suppose image A has features a, b, c, andd for angles 0°, 450, 900, and 1350, respectively, and imageB is identical to A except that B is rotated 90° with respectto A. Then B will have features c, d, a, and b for angles 00,450, 900, and 1350, respectively. Since the texture context ofA is the same as the texture context of B, any decision ruleusing the angular features a,b,c,d must produce the sameresults for c,d,a,b. To guarantee this, we suggest that theangularly dependent features not be used directly. Insteadwe suggest that two functions of a, b, c, and d, their averageand range (which are invariant under rotation), be used asinputs to the classifier.

III. APPLICATIONS OF TEXTURAL FEATURES FOR IMAGECLASSIFICATION

In this section we present the results of our studies onthe usefulness of the textural features for categorizingimages. Three data sets were used in our study. These datasets were extracted from photomicrographs of differentrocks, from aerial photographs of man-made and naturalscenes, and from high-altitude satellite pictures of the earth.A brief description of the data sets and classification al-gorithms used and the results of classification experimentswill be presented. For further details the interested readeris referred to [16]-[18].

Data Set Description1) Photomicrographs of Sandstones: Identification of the

types of rocks (sandstones) present in an undergroundreservoir of crude oil is important in petroleum productionstudies; hence we undertook a study to identify differenttypes of rocks from the textural characteristics of theirphotomicrographs. The data set consisted of 243 imageblocks of size 64 x 64 and the gray tones of the images wereequal-probability quantized into 16 levels. Details of thealgorithm used to perform this quantization are given inAppendix III. There were five sandstone categories in thedata set, and sampies of the photomicrographs are shown inFig. 5. The textural features for the 243 samples werecalculated from distance 1 gray-tone spatial-dependencematrices.

2) Aerial Photographic Data Set: This data set consistedof 170 images belonging to eight categories. These 170images were manually sampled from 9 x 9-in 1:20 000aerial photography negatives provided by the Army En-vironmental Topographic Laboratories, Fort Belvoir, Va.[17]. The digitization of the sampled images was done onthe Image Discrimination, Enhancement, and CombinationSystem (IDECS)/PDP. The IDECS is an analog-digital nearreal-time processing system that has been developed at theUniversity of Kansas Center for Research, Inc. A PDP

(a) (b)

(c)

(d) (e)Fig. 5. Samples of photomicrographs of sandstones. (a) Dexter-L.

(b) Dexter-H. (c) St. Peter. (d) Upper Muddy. (e) Gaskel.

15/20 computer is interfaced to the IDECS and the systemis capable of performing various functions of image pro-cessing [25]. The IDECS is capable of processing up tofour image inputs. Three flying spot scanners can inputtransparencies up to a maximum size of 4 x 5 in. A vidiconscanner accepts larger transparencies as well as printedimages. Multi-image inputs are electronically registered andcombined into a format more suitable for interpretation.Processed images are displayed on a color display unitand/or a black and white monitor. A 24-channel disk issynchronized with the system and used for storage ofprocessed digital images. Either manually or under com-puter control, the IDECS/PDP is able to perform imageenhancement, video level slicing, area integration, categorydiscrimination, display of histograms and scatograms,quantizing, and similar image-processing operations. Thealgorithm used for quantizing the aerial photographic dataset digitized the images into eight levels in such a way thatthe areas of the different levels (in each image) were equal.Each image was digitized into a 20 x 50 array. The eightcategories were residential old (RSOLD), residential new(RESNU), LAKE, SWAMP, MARSH, URBAN, RAIL,and SCRUB or WOOD (SCROD). The first six categoriescontained 20 samples each, the RAIL and SCROD cate-gories contained 10 and 40 samples, respectively. Samplesof the images are shown in Fig. 6.

3) Data Set Derived from Satellite Imagery: A varietyof satellite imagery is currently used for the remote sensingof Earth resources. The most commonly used satellite

615


(a) (b)

I(d) (e)

(c)

(f)

(g) (h) (i)Fig. 6. Samples of aerial photographic data set. (a) RSOLD. (b)RESNU. (c) LAKE. (d) SWAMP. (e) MARSH. (f) URBAN.(g) RAIL. (h) SCRUB. (i) WOOD. (SCRUB and WOOD areclassified together as SCROD.)

imagery is the multispectral scanner (MSS) imagery, whichconsists of a set of images of a scene, where each image inthe set is created by scanning the radiance of the scenefrom the satellite in a narrow band of wavelengths. TheMSS operates in wavelengths ranging from 0.3 to 16 ,um,and up to 24 scanners have been used in the past.The data set used in our study was derived from a high-

altitude four-channel multispectral satellite image takenover the California coastline. The image in one of the fourMSS bands is shown in Fig. 7. The ground area covered bythe image is about 14 400 mi2 and the size of the digitalimage is 2340 x 3200. Out of this large image, a subset of624 contiguous image blocks of size 64 x 64 was takenand used in our study. There were seven land-use categoriesin the image; these are coastal forest, woodlands, annualgrasslands, urban areas, small and large irrigated fields, andwater bodies. The land-use category for each 64 x 64image block was obtained by interpreting the color com-posite of the multispectral image set. The textural featureswere computed from the distance 1 gray-tone spatial-dependence matrix of the second MSS band image in themultispectral image set.

Since the ground truth category information was derivedfrom the color composite image, we used a set of spectral(color) features in addition to the textural features forcategorizing these images. The spectral features consistedof the mean and standard deviation of the gray-tone valuesof the 64 x 64 image blocks in each of the four spectralbands.

Classification Algorithms1) Piecewise Linear Discriminant Function Method: For

categorizing image blocks in data sets 1 and 3, which have

Fig. 7. Satellite picture of Monterey Bay, Calif.

a reasonably large number of samples, we used a piecewiselinear-discriminant function method. The data sets werepartitioned arbitrarily into training and test sets. Theclassification algorithm was developed using the samples inthe training set and it was tested on the samples in the testset.A variety of algorithms have been discussed in the pattern-

recognition literature for obtaining piecewise linear-dis-criminant functions for pattern classification [19]-[22]. Ina widely used algorithm, the pattern space is partitionedinto a number of regions using a set of hyperplanes (decisionboundaries) whose locations are determined by the samplepatterns. Each region is dominated by sample patterns of aparticular category. When a new pattern is presented foridentification, it is assigned a category depending on theregion to which it belongs. If the new pattern X is located ina region dominated by sample patterns of category cj, thenX is classified as coming from category cj.For the multicategory problem involving NR categories,

a total of NR(NR - 1)/2 hyperplanes are used to partitionthe pattern space. These hyperplanes are defined by a setof weight vectors Wj, i = 1,2, - * ,NR, j = 1,2, * * *,NR,j > i, which separates the sample patterns belonging to theith and jth categories. A regression type algorithm given in[19, ch. 4] was used to obtain the weight vectors. After thelocation of the hyperplanes are determined, the classifica-tion of new patterns is done as follows. For each categoryci, the number of hyperplanes Vi which give a positiveresponse when the new pattern X is presented are deter-mined using

NRvi = E

j-lj*i

IWijZ Z+ ijTZ i = 1,2, .-,N. (5)

616


where Z is the augmented pattern vector obtained by addinga component of value 1 to X, i.e.,

[X](6)

X is assigned to category cj if Vj = max {VJi. If there is atie between categories cm and ca, then X is assigned to cm ifW_nTZ > 0, or to cn if WmnTZ < 0. Several modificationsof the linear-discriminant function method and a multitudeof other classification procedures may be found in thereferences cited.

2) Min-Max Decision Rule: For the aerial photographdata set which had a small number of samples per categorywe used a min-max decision rule for categorizing the imagesbased on their textural features. The decision boundarieswere obtained by using all but one of the samples in thedata set, and the sample which was left out was then clas-sified. The procedure was repeated for all the samples inthe data set to obtain the overall accuracy of the classifica-tion scheme. This method of "leaving one sample out" iswidely used by investigators in the pattern-recognition fieldwhen the data set has a small number of samples. Thedecision rule is described as follows.

Decision rule: If bnk and ank define the minimum andmaximum values of the uniform distribution, (X1x2, *,XN)is assigned to category k if and only if

bnk < xn < ank' n = 1,2, ,NN I N 1

n- (ank - bnk) n I(anj bnj)for all j such that b.j < xn < anj, n = 1,2, *,N. If thereexists no k such that bnk < xn < ank, n = 1,2,-^,N, then(x1,x2, ,xJ) is assigned to category k if and only if

N~1m - aflIIxl- bnIE minIn nkllXn- bnkl

n = I (a, - bnkN -nxn aanji,xn - bnjl}

n= I (anj - bnj)j= 1,2, ---,K (8)

where K is the number of categories.

Results of Image Classification Studies

1) Photomicrograph Data Set: A set of 8 variables, com-

prising the mean and variance of the textural features]f1,2,f3, andfg (for definitions of these features, see Appendix I),computed from distance I gray-tone spatial-dependencematrices, was used as an input to the classifier. The dataset was arbitrarily divided into a training set of 143 samplesand a test set of 100 samples. Piecewise linear-discriminantfunctions for separating the patterns belonging to the fivesandstone categories were derived using the samples in thetraining set. The contingency table for classifying thesamples in the test set is shown in Table I. The overallaccuracy of the classification scheme on the test set (ob-tained by summing the diagonal elements in the con-

tingency table and dividing by the total number of samplesin the test set) was 89 percent.

TABLE ICONTINGENCY TABLE FOR THE CLASSIFICATION OF PHOTOMICROCGRAPHS

OF SANDSTONES

ASSIGNED CATEGORY TotalDexter- L Dexter-H St. Peter Upper Gaske

Muddy

>. Dexter- L 29 0 1 0 0 30O Dexter-H 0 15 0 0 0 150W St. Peter 2 0 22 4 0 28

uUpperMuddy 0 0 4 11 0 1 5

c Gaske 0 0 0 0 12 12

TOTAL 31 15 27 15 12 100

Number of samples in test set 100; number of samples in trainingset = 143; overall accuracy of classification of test set = 89 percent.

TABLE IICONTINGENCY TABLE FOR THE CLASSIFICATION OF THE AERIAL

PHOTOGRAPHIC DATA SET

ASSIGNED CATEGORY

RSOLD RESNU LAKE SWAMP MARSH URBAN RAIL SCRODTOTAL

RSOLD 17 0 0 0 1 1 0 1 20>- RESNU 1 15 0 0 1 2 1 0 200 LAKE 0 0 19 0 0 0 0 1 20

SWAMP 0 0 0 19 1 0 0 0 20

u: MARSH 0 0 0 0 12 0 0 8 20v URBAN 2 3 0 0 0 15 0 0 20

RAIL 0 1 0 0 0 1 5 3 10SCROD 0 0 0 0 2 0 0 I8 40

_TOTAL 20 19 19 19 17 19 6 51 170

140 out of 170 images or 82.3 percent of the images were correctlyclassified.

2) Aerial Photographic Data Set: A min-max decisionrule was used for the classification of 170 images into eightcategories. The processing was done as follows. Four gray-tone spatial-dependencies (for four directions) were com-puted for each image. Eleven textural features (f1-flI asdefined in Appendix I) were computed, yielding a measure-ment vector of 4 x 11 = 44 components for each image.Computation of the mean, range, and deviation of eachfeature over the four directions reduced the dimensionalityto 33. The minimum and maximum statistics were computedfor 169 images and the min-max decision rule was used toclassify the image which was left out. This procedure wasrepeated 170 times to classify all the images. Out of these170 images, 140, or 82.3 percent of the images, were correctlyclassified. The contingency table is given in Table 1I.

3) Satellite Imagery Data Set: The piecewise linear-discriminant function method was used for identifying theland-use category of each image block in this data set. Theinput variables to the classifier consisted of the mean vari-ance of the four textural features (f1,f2,f3, andfg obtainedfrom the distance 1 gray-tone spatial-dependence matrices)and eight spectral features (comprised of the mean varianceof the image gray-tone values) in each of the four spectralbands.-The 624 samples in the data set were divided arbi-trarily into a training set of 314 samples and a test set of310 samples. The classifier was trained on the 314 samplesin the training set, and each sample in the test set wasassigned to one of seven possible land-use categories. The

617


TABLE IIICONTINGENCY TABLE FOR LAND-USE CLASSIFICATION OF SATELLITE

IMAGERY

ASSIGNED CATEGORY

CoastalForest

j_

0O

DI

Woodlands Annuol Urban Large SmalGrass- Area Irrigated IrrigatedLands Fields Fields

-I ---4 + I

CoostclForestWoodlandsAnnualGrasslandsUJrban Area

LargeIrrigated Fields

SmallIrrigated Fields

Water

Total

23

0

I

00

25

17

3

3

2

0

0

26

2

10

109

10

6

40

141

0

0

13

0

0

0

0

0

37

3

0

0

0

0

24

24

0

0

0

0

351

14 42 26 136

27

28115

2648

3135310

Number of training samples = 314; number of test samples = 310;accuracy of classification on training set = 84.0 percent; accuracy ofclassification on test set = 83.5 percent.

contingency table for the classification of the test samples isgiven in Table III. The overall accuracy of the classifieron the test samples was found to be 83.5 percent.

Classification of multispectral data such as the satelliteimagery we have processed is usually carried out using onlythe spectral features. We attempted a spectral classificationon the satellite imagery data and achieved a classificationaccuracy of 74-77 percent on the test set. This result, com-pared with the 83.5-percent classification accuracy achievedusing a combination of spectral and textural features, showsthat a significant improvement in the classification accuracymight result if the textural features are used as additionalinputs to the classifier.

IV. CONCLUDING REMARKS

We have described a class of quickly computable texturalfeatures which seem to have general applicability to manykinds of image data. The textural features are based onstatistics which summarize the relative frequency distribu-tion (which describes how often one gray tone will appearin a specified spatial relationship to another gray tone on theimage). We have used these features in category-identifica-tion tasks of three different kinds of image data. Identifica-tion accuracy on independent test sets are 89 percent forthe photomicrograph image set (five categories of sand-stones), 82 percent for the aerial photographs (eight land-use categories), and 83 percent for the satellite imagery(seven land-use categories).

These initial experimental results are promising. Muchwork needs to be done, however, on gray-tone normaliza-tion on the imagery and the use of features which are

invariant under monotonic gray-tone transformations. Thereason is that in one important sense, texture is independentof tone. Two people examining photographs of the sametexture may actually be seeing two different, though related,kinds of tones in the texture. One photograph may havebeen developed such that its tones are light and thin, andthe other photograph may have been developed such that

its tones are dark and heavy. Most people could easilymake the observation that the texture on the two images isthe same. For a machine to find that the textures are thesame, either the images must be probability quantized andthe features computed from the probability quantizedimages (which are invariant under monotonic gray-tonetransformations), or the features themselves must be in-variant under monotonic gray-tone transformations. Of thetextural features described in Appendix I, the angularsecond-moment, the entropy, the sum entropy, the differenceentropy, the information measure of correlation, and themaximal-correlation features have the invariance property.We intend to repeat the experiments reported here usingthese kinds of features. We expect that these features willprovide more generalized results.

Additional investigations are necessary to determine thesize of the subimage region and the distances which shouldbe used in computing the gray-tone dependence matrices.Too small a subimage region will not have enough texturalinformation to separate image categories of interest, whilea large subimage region may have objects belonging toseveral different categories. Also, a large subimage regionwill increase the storage requirements. The distance whichmust be used in computing the gray-tone spatial-de-pendencies may be obtained from the autocorrelation func-tion of the image. The distance at which the normalizedautocorrelation function of the image becomes too smallcan serve as an upper bound on the distance which may beused for computing the gray-tone spatial-dependencematrices.

APPENDIX ITEXTURAL FEATURES

We suggest a set of 28 textural features which can beextracted from each of the gray-tone spatial-dependencematrices. The following equations define these features.

Notation

p(i,j) (i,j)th entry in a normalized gray-tone spatial-dependence matrix, = P(i,j)/R.

p#(i) ith entry in the marginal-probability matrixobtained by summing the rows of p(i,j),= 1 P(i,j).

N, Number of distinct gray levels in the quantizedimage.Ng Nq

E and E E and , respectively.j il j=

Ng

P/i)= E p(i,j).

Ng Ng

px+y(k) = E E p(i,j),i=l i=ti +Ij=0Ng Ng

Px-y(k) = E, E1 p(i,j),i=l j=l

i-jI =k

k = 2,3, ,2Ng.

=0,1, 7Ng-I

i ~~~~~~~~~~~~~~~~~~~~~~~~~i1-

618


Textural Features

1) Angular Second Moment.

f= E {p(i,j)}2.ij

2) Contrast:

f2 n2 [ E PUiJ)|n=O i=j1 j=1

li-jl=nJ

3) Correlation:

f3 j

uxfywhere p,u, py, c., and ay are the means and standard devi-ations ofpx and py.

4) Sum of Squares: Variance

f4 a (i P)2p(i,j).i

5) Inverse Diference Moment

A = E 1+ i_j2 p(i,j).

i + (i j)2

6) Sum Average:2Ng

= E ipx+Y(i).i-2

7) Sum Variance:2Ng

= E (i - f8)2px+y(i).i=2

8) Sum Entropy:22Ng

A= -£ Px+y(i) log {pX+Y(i)}.i=2

9) Entropy:

= -E E p(i,j) log (p(i,j)).i J

10) Diference Variance:

f10 = variance of px-y.

11) Difference Entropy:Ng 1

fIl = - E Px-y(i) log {Px-Y(i)}i=o

12), 13) Information Measures of Correlation:

HXY - HXYImax {HX,HY}

f13 = (1 -exp [-2.0(HXY2 -HXy)])12HXY = -E i p(i,j) log (p(i,j))

iJ

2 Since some of the probabilities may be zero, and log (0) is notdefined, it is recommended that the term log (p + e) (e an arbitrarilysmall positive constant) be used in place of log (p) in entropy com-putations.

where HX and HY are entropies of p, and py, and

HXY1 = - i p(i,Uj) log {pX(i)pY(i)}

HXY2 = - P, p,(i)p/J) log {pX(i)pY()}.

14) Maximal Correlation Coefficient:

f 4= (Second largest eigenvalue of Q)112where

Q( i,j) = E p(i, k)p(j,k)kpf(i)py(k)

These measures of correlation have some desirable proper-ties which are not brought out in the rectangular correlationmeasuref3. For details, see [23], [24].

Referring to (1) in the text, for a chosen distance d wehave four angular gray-tone spatial-dependency matrices.Hence we obtain a set of four values for each of the pre-ceding 14 measures. The mean and range of each of these14 measures, averaged over the four values, comprise theset of 28 features which can be used as inputs to theclassifier. In this set of 28 features some of the features arestrongly correlated with each other. A feature-selectionprocedure may be applied to select a subset or linearcombinations of the 28 features.

APPENDIX IIEXAMPLES OF THE SIGNIFICANCE OF SoME TEXTURAL

FEATURES

The problem "What do the textural features represent?"from a human perception point of view can be a subject fora thorough experiment. There are some intuitive expecta-tions as to properties represented by some features. Forexample, one might expect the entropy feature to take highervalues for more complex images. One might expect to beable to notice some linear dependencies in images with highvalues of the correlation feature. As a beginning for aninvestigation of this problem we used an aerial photographydata set that consisted of 12 categories, 6 samples ineach [17].We ordered the categories in the following manner. We

computed the range and the mode of values that eachfeature takes for each category. The categories were thenordered for each feature according to the modes, and theranges were plotted. The prospective of this Appendix is tocomment on the ordering of categories by some of thefeatures. Figs. 8-10 show plots of the ranges of three of thefeatures, each accompanied by three pictures. These pic-tures are of units that have small, medium, and large valuesof the respective feature. The order of categories of theaverage angular moment feature (ANGMOM) in Fig. 8 isalmost the reverse of the order of categories of the averageentropy (ENTROP) in Fig. 9. The three representativepictures show that in both figures the units were orderedaccording to the complexity of the image. Images with moregray levels have lower average ANGMOM and higher

619

mEEE TRANSACTIONS ON sYSTEMs, MAN, AND cYBERNETIcs, NOVEmBER 1973

RAIL 1-1

RSOLD 1-1

SWAMP I--I

ORCHR I---- I

RSN'W 1------1

URBAN I---____1

DROAD I------- I

MARSH I-----------------I

SCRUB I------------I

TWATR I------------------------ I

H wOO I------------- I

SWATR I-------------------- I

0111104711111111111111111111 1111111 270111111 -14llIlII ll

6.047 6.156 6.276 e.3s4

RAIL 4

0.037SCRUB 10.102

SWATR 40.395

Fig. 8. Range plots and representative pictures for average secondangular moment.

SWAMP I-- .-__________-I

H woo I .----------------- I

SWATR I------------------------I

TWATR I.-- --- --- --- -- --- --- --- -- --- --- --- -

SCRUB I .

MARSH

RAIL

ORCHR

URBAr

RSOLD

RSSEW

DROAD

-------------------------------------

----------. --------

6.366 6~~.530 0.702 R.675

SWATR 40.418

RAIL 60.602

DROAD 30.892

Fig. 10. Range plots and representative pictures for average correla-tion.

,.,

.I,

I.,

,.I

,-.

I.,

---- ------

, ,

1.9852.519 3.6g13.644

SWATR 6

1.900SCRUB 22.781

RAIL 63.700

Fig. 9. Range plots and representative pictures for average entropy.

l-F(qk_,)

F(qki~i1-F(qk-1)r-C

l F(qk-1)

Fig. 11. Quantizing algorithm. At kth iteration, F(qk- 1) probabilityhas already been allocated to k - 1 levels and 1 - F(qk - 1)

probability remains to be allocated. If 1 - F(qk - 1) prob-ability is split up equally among remaining K - k + I quan-tizing levels to be allocated, each level would get (I - F(qk.,))/(K - k + 1). Since F is a step function, there is no guarantee thata q, can be found and that F(qk) = F(qk-l) + (1 -F(qk,))l(K - k + 1). Hence we look for a qk which is closest to satisfyingthe equality.

APPENDix IIIEQUAL-PROBABILrrY QUANTIZING

Let X be a random variable with cumulative probabilityfunction Fx. Let Q1, the K-level equal-probability quantizingfunction for X, be defined by

average ENTROP. The average ratio (RATIO) in Fig. 10is lower for natural scenes and higher for man-made scenes.

The three representative pictures in Fig. 10 show corre-

spondence between the average RATIO values and thelinear dependency of gray levels in the images. These com-

ments reflect our subjective perception. Much more ex-

perimentation and analysis should be done in this subject.

Q (x) = k, if and only if

lub (w Fx(W) = kK < x < lub (w Fx(w) = K)

where lub denotes least upper bound.For any strictly monotonic function g, define the random

variable Y by Y = g(X). Let Q2, the K-level equal-prob-

620

SWATRH WOO

TWATR

SCRUB

DROAD

URBAN

BSNREW

MARSH

ORCUR

RSOt-D

SWAnrP

RAIL


ability quantizing function for Y, be defined by let qkbe the smallest number such that

Q2(Y) = k, if and only if 1-Fx(qk-) + Fx(qk)-Fx(qk)K ) ( k I k K-k I

lub{w IFy(w)=k} .y <lub w IFy(w) = -j. I ~

The following lemma states that the equal-probabilityquantization of X produces a random variable which isidentical to the equal-probability quantization of Y.Lemma: Q1(X) = Q2(Y)-

Proof: Q1(X) = k, if and only if

lub x Fx(x) = K-) < X< lub x Fx(x) = A.) (9)

Since g is strictly monotonic, (9) holds if and only if

g (lub x Fx(x) = k-1)) (X)

< g (lub (x Fx(x) = K

(10)Since g is strictly monotonic, we may reverse the order ofg and lub so that (10) holds if and only if

lub (g(x) Fx(x) = <g(X)

< lub (g(x) I Fx(x) =K

(11)However,

Fx(x) = P(X . x) = P(g(X) . g(x))= P(Y < g(x)) = Fy(g(x)).

Hence, (11) holds if and only if

lub(g(x) Fy(g(x)) = k 9(

< lub (g(x) I Fy(g(x)) k)

(12)Finally, (12) is equivalent to

lub y F(Y)= K) < Y < lub y IFy(y) = k)

(13)so that Q2(Y) = k.Equal Probability Quantizing Algorithm: Let X be a non-

negative random variable with cumulative probability func-tion Fx. Let Q, the K-level equal-probability quantizingfunction for X, be defined by Q(x) = k if and only ifqk-1 <x < qk. We define qO,ql,q2,q,qk in an iterativemanner. Let qo= 0. Suppose qk-1has been defined. Then

' Is +Lr. -I+ iX(qk-1) - P(q) , torallrealq.

Fig. 11 illustrates the equal-probability quantizing algorithm.

REFERENCES

[1] Special Issue on Digital Picture Processing, Proc. IEEE, vol. 60,pp. 763-922, July 1972.

[2] H. C. Andrews, A. G. Tescher, and R. P. Kruger, "Image pro-cessing by digital computer," IEEE Spectrum, vol. 9, pp. 20-32,July 1972.

[3] H. Kaizer, "A quantification of textures on aerial photographs,"Boston Univ. Res. Lab., Boston, Mass., Tech. Note 121, 1955,AD 69484.

[4] R. Chevallier, A. Fontanel, G. Grau, and M. Guy, "Applicationdu filtrage optique a l'etude des photographies aeriennes,"presented at the 11th Congr. Int. Photogrammetric, July 1968.

[5] R. Bixby, G. Elerding, V. Fish, J. Hawkins, and R. Loewe,"Natural image computer," Aeronutronic Division, Philco-FordCorp., Newport Beach, Calif., Final Tech. Rep., vol. 1, Pub].C-4035, May 1967.

[6] E. M. Darling and R. D. Joseph, "Pattern recognition fromsatellite altitudes," IEEE Trans. Syst. Sci. Cybern., vol. SSC-4,pp. 3847, Mar. 1968.

[7] A. Rosenfeld and E. Troy, "Visual texture analysis," Comput.Sci. Cent., Univ. Maryland, College Park, Tech. Rep. 70-116,June 1970.

[8] A. Rosenfeld and M. Thurston, "Visual texture analysis, 2,"Comput. Sci. Cent., Univ. Maryland, College Park, Tech. Rep.70-129, Sept. 1970.

[9] E. B. Troy, E. S. Deutsch, and A. Rosenfeld, "Gray-level manip-ulation experiments for texture analysis," IEEE Trans. Syst.,Man, Cybern., vol. SMC-3, pp. 91-98, Jan. 1973.

[10] Proc. Symp. Computer Image Processing and Recognition, Univ.Missouri, Columbia, Aug. 24-26, 1972.

[11] R. M. Pickett, "Visual analysis of texture in the detection andrecognition of objects," in Picture Processing and Psychopictorics,B. S. Lipkin and A. Rosenfeld, Eds. New York: AcademicPress, 1970, pp. 289-308.

[12] A. Rosenfeld and B. S. Lipkin, "Texture synthesis," in PictureProcessing and Psychopictorics, B. S. Lipkin and A. Rosenfeld,Eds. New York: Academic Press, 1970, pp. 309-345.

[13] P. Brodatz, Textures. New York: Dover, 1966.[14] R. M. Haralick, K. Shanmugam, and I. Dinstein, "On some

quickly computable features for texture," in Proc. Symp. Com-puter Image Processing and Recognition, Univ. Missouri, Colum-bia, vol. 2, pp. 12-2-1-12-2-8, Aug. 1972.

[15] E. E. Hall et al., "A survey of preprocessing and feature extractiontechniques for radiographic images," IEEE Trans. Comput., vol.C-20, pp. 1032-1044, Sept. 1971.

[16] R. M. Haralick and D. Anderson, "Texture-tone study withapplications to digitized imagery," Univ. Kansas Center forResearch, Inc., Lawrence, CRES Tech. Rep. 182-2, Nov. 1971.

[17] R. M. Haralick, I. Dinstein, K. Shanmugam, and D. Goel,"Texture-tone study with applications to digitized imagery,"Univ. Kansas Center for Research, Inc., Lawrence, CRES Tech.Rep. 182-4, Dec. 1972.

[18] R. M. Haralick and K. Shanmugam, "Computer classificationof reservoir sandstones," IEEE Trans. Geosci. Electron., vol.GE-11, pp. 171-177, Oct. 1973.

[19] K. Fukunaga, Introduction to Statistical Pattern Recognition.New York: Academic Press, 1972.

[20] K. S. Fu and J. M. Mendel, Adaptive Learning and Pattern Recog-nition Systems. New York: Academic Press, 1972.

[21] W. Miesel, Computter Oriented Approaches to Pattern Recognition.New York: Academic Press, 1972.

[22] N. J. Nilsson, Learning Machines. New York: McGraw-Hill,1965.

[23] E. H. Linfoot, "An information measure of correlation," Inform.Contr., vol. 1, pp. 85-89, 1957.

[24] C. B. Bell, "Mutual information and maximal correlation mea-sures of dependence," Ann. Math. Statist., vol. 43, pp. 587-595,1962.

[25] P. N. Anderson et al., "An automated image processing system-IDECS," Ph.D. project, Univ. Kansas, Lawrence, 1972.

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