statistical and structural approaches to texture

8/8/2019 Statistical and Structural Approaches to Texture

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786 PROCEEDINGS OF THEEEE, VOL. 67 , NO. , MAY 1979

Statistical and Structural Approaches to TextureROBERT M.HAWLICK, SENIOR MEMBER, IEEE

A bm t - I n this survey we review the impge processing literature onthe various approaches and models investigators have uaed for texture.These includest.tbticrl pproachesof autocordation function, opticaltransforms, digital h d o n n s , textural edgeness, structural element,gray tone cooccuaence, run lensuls, and auo modela Wediscuss and generalize some s t r u c t u r a l approachesto texture based onmore omplex primitives than gray tone. We cwdude with omeniquestothestnrcturplpn'mitipeastrudud-~atktidenenliution~which apply tfie stntistial tech-

I. INTRODUCTIONTXTURE is an important characteristic for the analysisof many types of mages. It can be seen in all imagesfrommultispectralscanner images obtained rom air-craftorsatelliteplatforms which theremote sensingcom-munity analyzes) to microscopic images of cell cultures ortissue samples (which the biomedical community analyzes).Despite its importance and ubiquity in image data, a formalapproach or precise definition of texture does not exist. Thetexture discriminationechniques re, forhe most art,ad hoc. In this paper, we survey, unify, and generalize someof the extraction techniques and models which investigatorshave been using t o measure textural properties.The image texture we consider is nonfigurative and cellular.We think of thiskind of texture as anorganized area p h a

granulation, randomness, lineation, o r being motled, irregu-lar, or hummocky. Eachof these adjectives translates intosome property of the tonal primitives and the spatial nter-actionetween theonal primitives. Unfortunately, fewexperiments have been done ttempting to map semanticmeaning into precise properties of tonal primitives and theirspatial distributional properties.To objectively use the tone and textural pattern elements,the concepts of tonal and textural feature must be explicitlyde fi ed . With anexplicitdefinition, wediscover that oneand texture are not independent oncepts.They bear aninextricablerelationship to oneanother very much ike therelation between a particle and a wave. There really is noth-ing that is solely particle or soley wave.Whatever existshas both particle and wave properties and depending on thesituation, he particle or wave properties may predominate.Similarly, in the image context, tone and texture are alwaysthere, lthough at times ne roperty can dominateheother and we tend to speak of only one or only exture.Hence,whenwemake n explicitdefinition of tone andtexture, we are not defining two concepts: wearedefiningone tone-texture concept.The basic interrelationships in the ton etexture concept arethe following When a small-area patch of an image has litt le


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HARALICK: TO TEXTURE I8 1

emphasize one or the otheraspect and tends not to treat eachaspect equally.11. REVIEW F THE LITERATUREN TEXTURE ODELSThere have been eight statistical approaches to the measure-

mentandcharacterization of image texture:autocorrelationfunctions,pticalransforms, digital transforms, texturaledgeness, structural elements, spatial gray tone cooccurrenceprobabilities, gray tone run lengths, and autoregressive models.An early reviewof some of these approaches is given byHawkins [ 361. The first three of these approaches are relatedin tha t they all measure spatial frequency directly or indirectly.Spatial frequency is related to exture because fine texturesare rich nhigh spatial frequencies while coarse textures arerich in low spatial frequencies.An alternative to viewing texture as spatial frequency distri-bution is to view texture as amount ofedgeper unit area.Coarse textures have a small number of edges per unit area.Fine textures have a high number of edges per unit area.The structural element approach f Serra [781 and Matheron[ 4 9 ] uses a matching procedure to detect the spatial egularityof shapes called structural elements in a binary image. Whenthe structural elements themselves are single resolution cells,the information provided by this approach is the autocorrela-tion function of the binary image. By using arger and morecomplex shapes, a more generalized autocorrelation canbecomputed.The gray tone spatial dependenceapproach characterizestexture by the cooccurrence of its gray tones. Coarse texturesare those for which the distribution changes only slightly withdistance and fine textures are those for which the distribution

The power of the autoregression linear estimator approachis that it s easy o use the estimatorn a mode which synthesizestextures rom ny initially given linear estimator. In thissense, the autoregressive approach is sufficient to captureeverything about a texture. Its weakness is that the textures itcan characterize are likely to consist mostly of microtextures.A . The Autocorrelation Function and Texture

From one point of view, texture relates to thespatial size ofthe onal primitives on an mage. Tonal primitives of largersize are indicative of coarser textures; onal primitives ofsmaller size are indicative of finer textures. The autocorrela-tionfunction is a feature which ells about he size of thetonal primitives.We describe the autocorrelation function with the help ofa thought experiment. Consider two image transparencieswhich are exact copies of oneanother. Overlay one trans-parency on top of the other and with a uniformsource oflight, measure the average light transmitted through the doubletransparency. Now, translate one transparency relative to theother and measure only the average light transmitted throughthe portion of the image where one transparency overlaps theother. A graph of these measurements as a function of the

(x, y ) ranslated positions and normalized with respect to the(0, 0) translation depicts the two-dimensional autocorrelationfunction of the image transparency.Let I ( u , u ) denote the transmission of an image transparencyat position ( u , u ) . We assume thatoutside some boundedrectangular region 0 < u < L x and 0 < u


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HARALICK: APPROACHES TO TEXTURE 18 9

aerial or satellite imagery. Lendaris and Stanley [ 4 5 ] , 4 6 ]illuminated smallircular sections of low-altitude aerialphotography and used theFraunhofer iffraction atternas features for identifying the sections. The circular sectionsrepresented a circular area on he ground of 7 50 ft.Themajor category distinction hey were interested n makingwas man-made versus nonman-made. They further subdividedthe man-made category into roads, road intersections, build-ings, and orchards.The pattern vectors they used from the diffraction patternconsisted of 4 0 components.wentyomponents wereaverages of the energy in annular rings of the diffraction pat-tern and 20 were averages of the energy in 9 wedges of thediffraction pattern. They obtained over 90 percent identifica-tion accuracy.Egbert etal . [ 171 used anoptical processing system toexamine theextureon LANDSATmagery verKansas.They used circular areas corresponding to a ground diameterof about 23 mi and looked at the diffraction patterns for theareas when they were snow covered and when they were notsnow covered. They used a Recognition System diffractionpattern sampling unit having 32 sector wedges and 3 2 annularrings to sample and measure thediffractionpatterns. Theywere able to interpret the resulting angular orientation graphsin terms of dominant drainage patterns and roads, but werenot able to nterpret he spatial frequency graphs which allseem to have had the same character: he higher the spatialfrequency, the less the energy in that frequency band.Honeywell Systems and ResearchDivisionhas done workusing optical processing on aerial images t o identify species oftrees. Using imagery obtained from Itasca State Park in north-

17324-5, spatial frequencies larger than 3.5 cycles/km andsmaller than 5.9 cycles/km contain most of the informationneeded to discriminate between terrain types. His terrainclasses were: clouds, water, desert, farms, mountains, urban,riverbed, and cloud shadows. He achieved an over& identifica-tion accuracy of 87 percent.Homing and Smith [37 1 have done work similar o Gramenop-oulos, but with aerial multispectral scanner imagery instead ofLANDSAT imagery.Kirvida andohnson [43 ] compared the fast Fourier,Hadamard, and Slant Transforms forextural features onLANDSAT mageryoverMinnesota. They used 8 X 8 s u bimages and five categories: Hardwoods, Conifers, Open, City,Water.Using only spectral information,hey obtained 74percent orrect identification accuracy. When they addedtexturalnformation,hey increased theirdentificationaccuracy to 99 percent. They found little difference betweenthe different transform methods. (See also Kirvida [ 4 2 ] .)Maurer [ 51 obtained encouraging results classifying cropsfrom low-altitude colorphotography on he basis of a one-dimensional Fourier series taken in a direction orthogonal tothe rows.Bajcsy and Lieberman [ 31, [41 divided the image into squarewindows and used the two-dimensional power spectrum ofeach window. They expressed the power spectrum in a polarcoordinate system of radius r versus ngle @, reating hepower spectrum as two independent one-dimensional func-tions of r and @. Directional textures tend to have peaks inthe power spectrum as a function of 4. Bloblike textures tendto have peaks in the power spectrum as a function of r . Theyshowed that texture gradients can be measured by locating thetrends of relative maxima of r or @ as a function of the position


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790 PROCEEDINGS OF THEEEE, VOL. 67, NO. , MAY 1979r- r- is defined by:F e H = { ( m , n ) E Z X Z I H ( m , n ) C F } .

The eroded image J obtained by eroding I with structuralH = H(O.0)(0.1) H(0.2) H ( 0 . 3 ) element His definedy:E T I U O J ( i , j ) = l i f a n d o n l y i f ( i , j ) E F e H .The number of elements in the erosion F eH is proportionalto the area of the binary 1 figures in the image. An interestingtheoretical property of the erosion is that any operation which

is antiextensive, increasing, and dempotent must be madeH = ~ ~ O , O ~ , ~ O , l ~ , ~ O , ~ ~ , ~ l , ~ ~ ~ upfrosions [44], [ 501, [791.Fii. 2. Set Hand some of its t d a t e s . Texturalroperties can be obtainedromherosion processby appropriatelyparameterizing the structuralelement and

H ( 3 . 0 ) H ( 3 , 4 ) H ( - l ,O) H ( 9 . 9 )

Sutton and Hall applied this textural measure in a pulmonarydisease identification experiment and obtained dentificationaccuracy in the 80 percentile range for discriminating betweennormal and abnormal ungs when using a 128 X 128 subimage.Triendl [go] measuresdegreeofedgenessby filtering heimage witha3 X 3 averaging filter and a3 X 3 Laplacianfilter. The wo resulting filtered images are thensmoothedwith an 11 X 11 smoothing filter. The two values of averagetone and roughness obtained from the ow- and high-frequencyfiltered image can be used as textural features.Hsu [38] determines texturaledgeness by computinggradient-like measures for the gray tones in a neighborhood. I f N de-notes he set of resolution cells inaneighborhood about apixel, and g, is the gray tone of the center pixel, p is themean gray tone in the neighborhood, and p is a metric, thenHsu suggests that

determining the number of elements of the erosion as a func-tion of the parameter. For example, in Fig 3 we consider aseries of structural elements each of tworesolution cells inthe same ineandseparatedbydistances of 0 through 19.The image in Fig. 3 is then eroded by each of these structuralelements producing the eroded images of Fig. 3. In Fig. 4, weillustrate a graph showing the area of the erosion as a func-tion of the distance separating the two resolution cells of thestructural elements. A function such as that graphed in Fig. 4is called the covariance function. Notice how t has relativemaxima at distances which are multiples of about 5 5 resolu-tion cells. This implies that in the horizontal direction thereis a strong periodic component in the original image of about5 3 resolution cells.The generalizedcovariance function can use more compli-cated structural elements andsummarizes the texture informa-tion in the image. If H ( d ) is a structural element having two


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ICI.llj/j l ]F]j.l).

Eroded Images

O r i g i n a l l m a q e

ErodedmagesS t r u c t u r a l l e m e n t s

' I 1 1I

I I 1-4 7 ' 1

I It r u c c r a l l a n e n t sl o Il 2 Il 3 I


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792 PROCEEDINGS OF THE EEE, VOL. 67 , NO. 5, MAY 1979

4 8 12 16 20Fig. 4. The covariance function in thehorizontaldirection or heimage of Fii.3.

0" 900

Fa. . The spatial cooccurrence calculations [331.

Uniformity or energy 'ij(Related t o t h e variance of i , j{ P i l , ..., j " ' 'P"NHEntropy

H a x i m w probability max Pi j Li


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HARALICK: TO TEXTURE 79 3

pair has gray tone 2 and the second resolution cell of the pairhas gray tone1. In Figs. 6(c) hrough6(f), we calculate allfour distance 1 ray tone spatial dependencematrices.Using features calculated from the cooccurrence matrix (seeFig. 7), Haralick et a2. [281 performed a number of identifica-tion experiments. On a set of aerial imagery and eight terrainclasses (oldresidential, new residential, ake,swamp, marsh,urban, railroad yard, scrub, or wooded), an 82 percent correctidentification was obtained. On a LANDSAT Monterey Bay,CA, image, an 84 percent correct identification was obtainedusing 64 X 6 4 subimages andboth spectral nd texturalfeatures on even terrain classes: coastal orest,woodlands,annual grasslands, urban areas, large irrigated fields, smallirrigated fields, and water. On a set of sandstonephoto-micrographs, an 89 percent correct identificationwas obtainedon five sandstone classes: Dexter-L, Dexter-H, St. eter,Upper Muddy, andGaskel.The wide class of images on which they found that spatialgray tonedependence carries much of the exture nforma-tion is probably indicative of the power and generality of thisapproach.The approximate two dozen cooccurrence features times thenumber of distance angle relationships theooccurrencematrices can be computed for lead to a potentially large num-ber of dependent eatures. Tou andChang [ 881 discuss aneigenvector-based feature xtractionpproach to help al-leviate this problem.Theexperiments ofWeszka et 02. [ 9 2 ] suggest that hespatial frequency features and, therefore, the autocorrelationfeature are not as good measures of texture as he cooccurrencefeatures. We suspecthathe reason why cooccurrenceprobabilities have so much more information than the auto-

probabilities at one distancedetermine heautocorrelationfunction at many distances.Because theonditionalooccurrencerobabilitiesrebased on a directed distance rather han he undirected dis-tances ypically used in thesymmetriccooccurrence probabilities, some valuable informationmay be lostn thesymmetric approach. The xtent to which suchnforma-tion is lost has not beenextensively studied [ l l .C. A Textural Transform

We wish to construct an image J such that the gray toneJ(i, ) at resolution cell (i , j ) in imageJ indicates how commonthe texture pattern is in and around resolution cell (i, j ) ofimage I . We call the image J the textural transform f I [251.For analysis of the microtexture, the gray tone J( i , i) can bea function of the gray tone I(i, ) and its nearest neighbors.J ( i , j )=f lI ( i - 1 , j - l ) , I ( i - l , j ) , I ( i - l , j+ l) ,Z( i , j - 11,

- I ( i , j ) , I ( i , j + l),Z(i+ 1, j - l ) , I ( i+ 1 , jh. I ( i + l , j +1)).

Let us assume that this function f is an additiveeffect ofhorizontal, right diagonal, vertical, and left diagonal relation-ships. ThenJ(i, i) = f l i , - 11,I(i,i),10, + 1)) (horizontal)

+f2(I( i+ 1,j- l ) , I ( i , j ) , I ( i - l , j + 1))(right diagonal)

+f 3 10- 1,i), IC, ), I( i + 1,i)) (vertical)


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796 PROCEEDMGS OF THE IEEE, VOL. 67 , NO. , MAY 1979


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HARALICK: TEXTURE 191

for all components not indexedby J. In this manner,under nclude:(*, x2,. * ,XN ) where means any value. Formally, for anyA C G N , we define the order #J cylinderperator \ k ~y: i=1 j = 1the \k {2,. . . N } operator, the N-tuple ( X I , *

The cylinder operator is used t o generalize the samples ofobserved texture from each textureclass by creating a minimalcover of that class against all other classes. A cover for class kis a collection of subsets of G N each of which has nonempty

(short run emphasisinverse moments)(long run mphasismoments)(gray levelnonuniformity)(runengthnonuniformity )

m 2 ksubsets of G N , each subset in the collection generalizing an N-tuple in Sk by an order-M or less cylinderoperator. e={ A C G N I for some (XI, . . ,X N )E Sk and ndex set J,# J < M A = \ ~ J ( X ~. . . ,X ~ ) a n d A m , = $ ~ , m f k } .It is clear that when the observed samplesets Sk are dis-joint, it is always possible to find a cover of S k since we cantake the order M = N making @ contain precisely the single-ton sets whose members are elements of s k . Hence, for largeenough M, it is alwayspossible to make$ atisfy:

sk c U A C U SI .A $? 1 (1)I# kWe will call an o r d e r 4 cover minimal if by using cylinderoperators only of order less than M equation (1) cannot besatisfied.The labeling of neighborhoods by texture class can proceed

Using these five measures for each of 4 directions, and oneof Haralick's data sets, Galloway illustrated that about 83 per-cent identification could be made f the six categories: swamp,lake railroad, orchard, scrub, and suburb.J.Autoregression Models

The linear dependence one pixel of an image has on anotheris well known and can be illustrated by he autocorrelationfunction. This linear dependence is exploited by heauto-regression modelorexture which was fmt usedyMcCormick and Jayaramamurthy [ 521 to synthesize textures.McCormick andJayaramamurthyused the Box and Jenkins[ 6 ] time series seasonal analysis method to estimate the pa-rameters of a given texture.They hen used the estimatedparameters and a given set of starting values to illustrate that


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798 PROCEEDINGS O F THE IEEE, VOL. 67 , NO. , MAY 1979

D p i x e l s1

Randomlyeneratedoise Image Synt hesi zed ImageI ( 1 1. - 1

aN+l a L& 'k aN - k + E - 0 ' Q b N - l l- -Auto-Regressive k v i n g AverageTerms TermsFig. 12 . Illustrationof how from a andomlygeneratednoise imageand a @en start ing sequence a i , . . . K, representing the initialboundary conditions, all values in a texture image can be synthesizedby a one-dimensional autoregressive model.

1

b ( i , j )Order D Neighborhood o f Randomly


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value of the gray tone atresolution cell ( i , ) by:

(See Fig. 14.)( i , ) has texture category if:Assuming a uniform prior distribution, we can decide pixel

and l a ( i , j ) - a k ( i , j ) I Q 8.if l a ( i , ) - a&, j ) I > 8, then decide pixel ( i , ) is a boundarypixel.

Those readers interested in general two-dimensional estima-tion procedures for imageswill frnd Woods [941 of interest.K. Mosa ic T ex ture Mode b

Mosaic texture models tessellate a picture into regions andassign a gray level to the regon ccording to a specified proba-bilitydensity unction [ 1001. Among the kinds of mosaicmodels are the Occupancy Model [ 1011 , the Johnson-MehlModel [ 1021, thePoisson Line Model [ 1031, and theBombingModel [ 1041.The mosaic texture models seem particularlyamenable to statistical analysis. It is not known how generalthesemodels really are nd they arementionedhere orcompleteness.

In . STRUCTURAL APPROACHESO TEXTUREMODELSPure structural models of texture are based on theiew thattextures are made up of primitives which appear in near regu-

We classify textures as being weak textures, or strong tex-tures. Weak textures rehose which have weak spatial-interaction between primitives. To distinguish between themit may be sufficient to determine the frequency with whichthe variety of primitive kinds occur in some local neighbor-hood. Hence, weak texture measures account for many of thestatistical exturalfeatures.Strong exturesare hose whichhave nonrandom spatial interactions. To distinguish betweenthem it may be sufficient to determine, for each pair of primi-tives, the frequency with which the primitives cooccur n aspecified spatial relationship. Thus our discussion will centeron the variety of ways in which primitivescan be defined andthe ways in which spatial relationships between primitivescanbe defined.A . PrimitivesA primitive is a connected set of resolution cells character-ized by a list of attributes. The simplest primitive is the pixelwith its gray tone attribute. Sometimes it is useful to workwith primitives which are maximally COMeCted sets of resolu-tion cells having a particular property. An example of such aprimitive is a maximally connected set of pixels all having thesame gray tone orall having the same edge direction.Gray tones and local properties are not the only attributeswhich primitives may have. Other attributes include measuresof shape of connectedregionandhomogeneity of its localproperty. For example, a connected set of resolution cells canbe associated with its length or elongation of its shape or thevariance of its local property.Many kinds of primitives can be generated or constructedfrom image data by one or more applicationsof neighborhoodoperators. Includedin thisclass of primitives are: 1) connected


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800 PROCEEDINGS OF TH E IEEE, VOL. 7, NO. , MA Y 1979

primitives. Associated with each primitive is a list of proper-ties such as sue and shape. Then hey make a histogram ofsize property or shape propertyver all primitives in the scene.If the scene can be decomposed into two or more regions ofhomogeneous exture, hehistogram will bemultimodal. fthis is the case, each primitive in the scene can be tagged withthe mode in he histogram it belongs to. A region growing/cleaning process on the tagged primitives yields the homoge-neous texturalregion segmentation.If the initial histogram modes overlap too much, a completesegmentation may not result. In this case, the entire processcan be repeated with each of the then so far found homoge-neous exture region segments. If each of the homogeneoustexture regions consists of mixtures of more than one type ofprimitive, then heproceduremay not work at all. In thiscase, the echnique of cooccurrence of primitivepropertieswould have to be used.Zucker e t a l . [991 used a form of this technique by filteringa scene with a spot detector. Nonmaxima pixels on the filteredscene were thrown out. If a scene has many different homoge-neous texture regions, the histogram of the relative max spotdetectorilteredscene will bemultimodal. Tagging themaxima with the modes they belong to and region growing/cleaning thus produced the segmented cene.The idea of theconstant gray-level regions of Tsuji andTomita or the spots of Zucker e t a l . can be generalized to re-gions which are peaks, pits, ridges, ravines, hillsides, passes,breaks, flats, and slopes [631, 1861. In fact, he possibilitiesare numerous nough that investigators doing experiments

will have a ong working periodbeforeunderstanding willexhaust he possibilities. Thenext hreesubsections reviewingreaterdetailsomespecificapproaches and suggest some

I f

I IS i z e 7

Fig. 1 5 . Illustration of ho w the height and size properties of a valleyare defined.

diameter. Maleson [48] has done some work related to maxi-mal homogeneous sets andweak textures.3) RelativeExtremaDensity: Rosenfeld ndTroy [ 7 7 ]suggest the number of extremaperunit area for a exturemeasure. They suggest d e f i i g extremanonedimensiononly along a horizontal scan in the following way: in any rowof pixels, a pixel i is a relative minimum if its gray tone g ( i )satisfies:

g ( i ) < g ( i + 1) and g(i) < g ( i - 1). (2)A pixel i is a relative maximum if:g ( i )2 ( i + 1) and g(i)2 ( i - 1).

Note that with this definition each pixel in the interior of anyconstant gray tone run of pixels is considered simultaneouslya relative minimum and relative maximum. This is so even if


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two-dimensional sense is by the iterated use of some recursiveneighborhood operators propagating extrema values in an ap-propriate way. Maximally connected areas of relative extremamay be areas of single pixelsormay be plateausofmanypixels. We can mark each pixel in a relative extrema region ofsize N with the value h indicating that it is part of a relativeextrema having height h or mark it with the value h / N indi-cating itsontribution to the relative extrema area. Al-ternatively, we can mark the most centrally located pixel inthe relative extrema region with the value h . Pixels not markedcan be given the value 0. Then orany pecified windowcentered on a given pixel, we can add up he values of allpixels in the window. This sum divided by the window size isthe average height of extrema n he area. Alternatively wecould set h to 1 and the sum would be the number of relativeextrema per unit area to be associated with the given pixel.Going beyond he simple counting of relative extrema, wecan associateproperties to each elative xtrema.For x-ample, given a relative maxima, we can determine the set of allpixels reachable only by the given relative maxima and not byany other relative maxima by monotonically decreasing paths.This set of reachable pixels is a connected region and forms amountain. Its border pixels may be relative minima or saddlepixels.

The relative heightof the mountain is the difference betweenits elative maxima and the highest of itsexteriorborderpixels. Its size is the number of pixels which constitute it. Itsshape can be characterized by featuressuch as elongation,circularity, and symmetric axis. Elongation can be defined asthe ratio of the larger to small eigenvalue of the 2 X 2 secondmomentmatrixobtained rom the ($) coordinates of theborderpixels [2], [201.Circularitycan be defined as the

14 16

31

Fig. 16. A waveform.

maximum and the smallest relative minimum in the segment.Thesegmentcontrast extural eature can be he mean orvariance of segment contrast aken over the set of segmentscomprising the given function at a specified level of the tree.Another textural featurecan be the variance of segment length.D. Strong T exture Measures and Generalized Cooccurrence

Strong texture measures take into account the cooccurrencebetween exture primitives. On the basis of Julesz [401 it isprobably the case that the most important interaction betweentexture primitives occurs as a two-way interaction. Textureswith identical second- and lower order interactions but withdifferent higher order interactions tend o be visually similar,The simplest texture primitive is the pixel with its gray toneproperty. Gray tone cooccurrence between neighboring pixels


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802 PROCEEDINGS OF THE IEEE, VOL. 67, NO. 5, MAY 1979

I I

Fig. 17. EM ch and Foiths relational tree for the waveform of f ig . 16.The fvst number in each node is the lowest valley point. The secondnumber is the highest peak point for the egment.

pixel with a special label c for common. We call the regionsso formed thedescending components of the image.Cooccurrencebetweenproperties of the descending com-ponents can be based on the spatial relationship of adjacency.For example, if the property is size, the coOccurrence matrixcould tell us how often a descending component of sizesi oc-curs adjacent to or nearby to a descending component of sizes2 or of label c.

CONCLUSIONWe have surveyed the image processing literatureon hevarious approaches and models investigatorshave used for tex-tures. For microtextures, hestatisticalapproach seems toworkwen. The tatistical pproaches have included a u t ecorrelation unctions,optical ransforms, digital tr an sf om,textural edgeness, structural element, gray tone cooccurrence,and autoregressive models. Purestructuralapproaches based


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[ l o ] Y.P. Chien and K. S. Fu, Recognition of X-ray pictu re pat-237, Princeton University, Princeton, NJ, Jan. 1978.terns, IEEE Trans.Syst.. Man, Cybern., vol. SMC-4, pp. 145-156, Mar. 1974.[ 1 1 1 R W. Conners and C. k Harlow, Some theoretical consider-ations concerning texture analysis of radiographic images, pre-sented at R o c . 1976 ZEEE Con6on DeciPionand Control,1976.[ 121 L. J. Cutrona, E.N. Leith , C. J. Palermo, and k. J. Porcello,Inform. Theory,vol. 15 , no. 6, pp. 386-400, June 1969.Optical data processing and filteringystems, IRE Trans.[ 131 E. M. Darling and R. D. Joseph, Pattern recognition from satel-lite altitudes, IEEE Tnans. Syst., Man, Cybern., vol. SMC-4,pp. 30-47, Mar. 1968.[ 141 L. Davis ,% Johns, and J. K. Agganval, Texture analysis usingnition nd Image ProcessingConfi (Chicago, IL), May 31-generalized co-occurrence matrices, presented at Pattern Recog-June 2 ,1978 .[ 151 K. Deguchi and I. Moriahita. Te xture characterization ndtexture-based image partitioning using two-dimensional linearestimation echniques,presented at U.S.Japan CoopemtiveScience Pmgmm Seminar on Imge Processingn Remote

[ 161 C. Dyer and A. Rosenfeld, Courier texture featu res: suppres-Seming (Washington, DC), Nov. 1-5, 1976.sionofaperature effects, ZEEE T mn sSyst . , Man, Cybern.,[ 171 D. Egbert, J. McCauley, and J. McNaughton, Ground patternanalysis in the Great Plains, Semi-Annual ERTS A Investiga-tion Rep., Remote Sensing Laboratory, University of Kansas,Lawrence, KS, Aug. 1973.[ 181 Roger Ehrich and J. P. Foith , Representation of random wave-forms by relational trees, ZEEE T ran s C ompu t , vol. C-25 , pp.[ 191 -, Topology and semantics of intens ity arrays, ComputerVision, Hanson and Riseman (Eds). New York: AcademicPress, 1978.[ 201 Y. S. Frolov, Measuring the shape of geographical phenomena:A history of the issue, Sov. Geog.:R ev . T r a n s l a , vol. XVI, no.[21 ] M. Galloway, Texture analysis using gray level run lengths,[22 ] J. W Goodman, Infroduction to Fourier Optics. New York:Comput Graphics Image Proce8saizg, vol. 4 , pp. 172-199,1974.McGraw-Hill Book Co., 1968.[23] N. Gramenopoulos, Terrain type recognition using ER TSl

VOI.SMC-6, pp. 703-705, OCt. 1976.

725-736, July 1976.

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361 J. K. Hawkins, Texturalproperties forpattern recognition,Picture Procesping and Psychopictorics, Bernic Sacks Lipkm and37) R. J. Homing and J. A. Smith, Application of Fourier analysisAzriel Rosenfeld (EDS). New York: Academic Press, 1969.to multispectral/spatial recognition, presented at Managementand Utilization of Remote Sensing Data ASP Symposium, SiouxFalls. SD, Oct. 1973.381 S. Hsu, A texture-tone analysis for au tomated landuse mapping

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