JWeszka76-A Comparative Study of Texture Measures for Terrain Classification

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. SMC-6, NO. 4, APRIL 1976 269

[18] C. K. Chow, "On optimum recognition error and reject tradeoff," [20] R. Deutsch, Estimation Theory. Englewood Cliffs: Prentice-IEEE Trans. Inform. Theory, vol. IT-16, pp. 41-46, Jan. 1970. Hall, 1965, ch. 10.

[19] P. W. Cooper, "Hyperplanes, hyperspheres, and hyperquadrics as [21] M. Ichino and K. Hiramatsu, "Suboptimum linear feature selec-decision boundaries," in Computer and Information Sciences, tion in multiclass problem," IEEE Trans. Syst., Man, Cybern.,J. T. Tou, Ed. Washington, D.C.: Spartan, 1964, ch. 4. vol. SMC-4, pp. 28-33, Jan. 1974.

A Comparative Study of Texture Measures forTerrain Classification

JOAN S. WESZKA, CHARLES R. DYER, AND AZRIEL ROSENFELD, FELLOW, IEEE

Abstract-Three standard approaches to automatic texture classifica- II. FEATURES USEDtion make use of features based on the Fourier power spectrum, onsecond-order gray level statistics, and on first-order statistics of gray This section describes the classes of features that werelevel differences, respectively. Feature sets of these types, all designed used.analogously, were used to classify two sets of terrain samples. It wasfound that the Fourier features generally performed more poorly, while A. Fourier Power Spectrumthe other feature sets all performned comparably. The Fourier transform of a picturef(x,y) is defined by

00

H. INTRODUCTION j4 27r1 (ux+VY

T HE PROBLEM of automatic texture classification has F(u,v) dx dyJ been studied for at least 15 years. One of the earliest -

applications to be investigated was that of terrain analysis. and the Fourier power spectrum is IF2 - FF* (where *A recent review of work on texture classification can be denotes the complex conjugate).found in Haralick et al. [1]. It is well known that the radial distribution of values inA number of approaches to the texture classification IFl2 is sensitive to texture coarseness inf A coarse texture

problem have been developed over the years. One approach will have high values of 122concentrated near the origin,makes use of features derived from the texture's Fourier while in a fine texture the values of IFl2 will be more spreadpower spectrum. Another is based on gray level co-occur- out. Thus if one wishes to analyze texture coarseness, arences, i.e., on joint probability densities of pairs of gray set of features that should be useful are the averages oflevels. A third approach uses statistics derived from the IF12 taken over ring-shaped regions centered at the origin,probability densities of values of various local properties i.e., features of the formmeasured on the texture. 2x

In this paper, feature sets of these three types were used Or J IF(r,=)12 dOto classify two sets of terrain samples. An attempt wasmade to equalize the feature sets with respect to their for various values of r, the ring radius.orientation and size sensitivity. The feature sets and clas- Similarly, it is well known that the angular distributionsification scheme used are described in Section II. Section III of values in IFl2 is sensitive to the directionality of thereports on pilot studies using a set of 54 aerial photographic texture in f A texture with many edges or lines in a giventerrain samples belonging to nine land use classes. Section direction 0 will have high values of IFl2 concentrated aroundIV describes a larger-scale study, using 180 LANDSAT the perpendicular direction 0 + (7/2), while in a non-imagery samples belonging to three geological terrain types. directional texture, IFl2 should also be nondirectional.

Thus a good set of features for analyzing texture direction-ality should be the averages of IFl2 taken over wedge-shaped

Manuscript received July 16, 1975; revised September 10, 1975 and regions entered at the origin, i.e., features of the formNovember 4, 1975. This work was supported in part by the U.S. AirForce Office of Scientific Research under Contract F44620-72C-0062 rand in part by the Division of Engineering, National Science Founda- <>-- F(,) drtion, under Grant ENG74-22006.JoThe authors are with the Computer Science Center, University offovaiuvlesf0,tewdelp.

Maryland, College Park, MD 20742.frvrosvle f ,tewdesoe

270 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, APRIL 1976

For n-by-n digital pictures, instead of the continuous the picture isFourier transform defined above, one uses the discrete 01123transform defined by 00233

-I~ f(i,I)e2~~V1(iu+Jv01223F(u,v) = 2 j)e (iu) 12322

n i,j= o 223320 < u, v < n- 1.

and (Ax,Ay) = (1,0), then these numbers are given by theThis transform, however, treats the input picture f(i,j) as matrixperiodic. If, in fact, it is not, the transform is affected by the 0 1 2 3discontinuities that exist between one edge of f and the _opposite edge. These have the effect of introducing spurious 0 1 2 1 0horizontal and vertical directionality, so that high values are 1 0 1 3 0present in IF12 along the u and v axes. 2 0 0 3 5The standard set of texture features based on ring- 3 0 0 2 2

shaped samples of the discrete Fourier power spectrum areof the form where the entry in row i and column] is the number of

times gray level i occurs immediately to the left of gray= E IF(u,v)12 levelj. [Note that for (Ax,Ay) = (1,0), this entry is related

rl2<U2+v2<r22 to the transition probability from level i to level j when thepicture is scanned row by row.] A matrix of this form is

for various values of the inner and outer ring radii r1 and sometimes called a gray level co-occurrence matrix. It isr2. Similarly, the features based on wedge-shaped samples sometimes convenient to use a symmetric matrix in whichare of the form pairs of gray levels at separation either 6 or -6 are counted;

we shall denote this matrix by M,.+8182= E 1lF(u,v)12. If a texture is coarse, and ( is small compared to the sizes

Oi <tan -l(VIU)<02 of the texture elements, the pairs of points at separation (O<u,v.n- 1

should usually have similar gray levels. This means that theNote that in this last set of features, the "DC value" high values in the matrix MA should be concentrated on or(u,v) = (0,0) has been omitted, since it is common to all near its main diagonal. Conversely, for a fine texture, if (the wedges. is comparable to the texture element size, then the gray

These standard features are sensitive to size (spatial levels of points separated by ( should often be quite different,frequency) only, or to orientation only, but not to both. so that the values in M6 should be spread out relativelyOn the other hand, the other two classes of features, to be uniformly. Thus a good way to analyze texture coarsenessdescribed below, are all sensitive to both size and orientation. would be to compute, for various values of the magnitudeIn order to obtain comparable feature sets, it was therefore of 6, some measure of the scatter of the M6 values around thedecided to use Fourier features-based on intersections of main diagonal.rings and wedges. The rings used in most of the experiments Similarly, if a texture is directional, i.e., coarser in one(except for the first pilot study) were [2,4), [4,8), [8,16), direction than another, then the degree of spread of theand [16,31). Their upper frequency limits correspond, for a values about the main diagonal in Mal should vary with the64-by-64 picture, to object sizes 8 (4 objects and 4 spaces direction of (5 (assuming that the (5 magnitude is in theacross the picture), 4, 2, and 1, respectively. The wedges proper range). Thus texture directionality can be analyzedused were 450 wide, centered at 00, 450, 90°, and 135°. by comparing spread measures of the M,6 for various

directions of (.B. Second-Order Gray Level Statistics Haralick [1] has proposed a variety of measures that

Let ( = (Ax,Ay) be a vector in the (x,y) plane. For any can be employed to extract useful textural informationsuch vector and for any picturef(x,y), we can compute the from Ma6 matrices. Only four of these, which he regards as

joint probability density of the pairs of gray levels that occur particularly useful, will be defined here. In what follows,at pairs of points separated by (. If there are only finitely p(i,j) is the (i,j)th element of the given matrix (which hasmany gray levels (e.g., 0, . ,63), this joint density takes the size m by m), divided by the sum of all the matrix elements.form of an array ha, where h,(i,j) is the probability of the 1) Contrast: CON _ ((-j])2p(i,]). This is essentiallypair of gray levels (i,j) occurring at separation (5. This array the moment of inertia of the matrix around its mainis mn by mn, where mn is the number of possible gray levels, diagonal; it is a natural measure of the degree of spread of

If the picture f is discrete, it is easy to compute the h6) the matrix values.array for f, where Ax and Ay are integers, by counting the 2) Angular Second Moment: ASM-E p(i,j)2. Thisnumber oftimes each pair ofgray levels occur at separation measure is smallest when the p(i,j) are all as equal as(5 =(Ax,Ay) in the picture. As a very simple example, if possible; it is large when some values are high and others

WESZKA et al.: TEXTURE MEASURES FOR TERRAIN CLASSIFICATION 271

are low, as is true, for example, when the values are clustered concentrated near i = 0. Conversely, for a fine texture,near the main diagonal. with 6 comparable to the element size, the gray levels of

3) Entropy: ENT - E p(i,j) log p(i,j). This measure is points 6 should often be quite different, so that f,(x,y) willlargest for equal p(i,j) and small when they are very unequal. often be large, i.e., the values in p, should be more spread

4) Correlation: COR - [ijp(i,j) -p,u yJ(o.,y), where out. Thus a good way to analyze texture coarseness would,- and r, are the mean and standard deviation of the row be to compute, for various magnitudes of 6, some measuresums of matrix Ma, and jy and ay are analogous statistics of the spread of values in pa away from the origin. Fourof the column sums. This measures the degree to which the such measures might be the following.rows (or columns) of the matrix resemble each other. It is 1) Contrast: CON _ i2p6(i). This is the secondhigh when the values are uniformly distributed in the matrix, moment of pb, i.e., its moment of inertia about the origin.and low otherwise (e.g., when the values off the diagonal 2) Angular Second Moment: ASM -E p(i)2. This isare small). smallest when the p6(i) are all as equal as possible and large

In our experiments (except for Sections 111-A and IV-D), when some values are high and others low, e.g., when theonly the CON feature was used; the displacements were values are concentrated near the origin.

6 (Ax,Ay) 3) Entropy: ENT -Z-p(i) log p.(i). This is largest forequal p6(i) and small when they are very unequal.

= (1,O),(0,1),(2,O),(0,2),(4,0),(0,4),(8,0),(0,8) 4) MEAN (1/rm) Z ip6(i). This is small when the p6(i)(1,1),(l,- 1),(2,2),(2,-2),(3,3),(3,-3),(6,6),(6,-6). are concentrated near the origin and large when they are

far from the origin. (There is no simple analog of Haralick'sThe first eight of these are in the horizontal and vertical COR measure for the p6 nor would the MEAN measure bedirections at distances 1, 2, 4, 8. The remaining eight are useful for the M,.)in the diagonal directions at distances /2, 2-12, 312 _ 4, If a texture is directional, the degree of spread of theand 61/2 _ 8. values in p6 should vary with the direction of 6 (if itsAnother approach to defining features of this class is to magnitude is in the proper range). Thus texture direction-

use matrices Ma based on pairs of average gray levels, ality can be analyzed by comparing spread measures oftaken over neighborhoods whose centers are 6 apart, the p6 for various directions of 6. In our experiments (exceptrather than on pairs of gray levels of single points. In the for the first pilot study) the 6 used were the same as inmain study reported in Section IV, features based on both Section II-B. In all of the pilot studies, only the MEANM, and M6 matrices were used. The same 6 were used for feature was used; in the main study, both the MEAN andboth sets of features. The averaging neighborhoods were the CON features.square and were of the same size as the displacements 6-in Another approach to defining features of this type isother words, for distances 1, 2, 4, and 8, we used averaging to use vectors P- based on differences between pairs ofneighborhoods of sizes 1 by 1 (i.e., no averaging), 2 by 2, average gray levels, taken over neighborhoods whose4 by 4, and 8 by 8, respectively. Note that for sizes 4 and 8 centers are 6 apart, rather than using pairs of gray levels ofin the diagonal directions, this implies that the neighbor- single points. In the pilot studies, only average gray levelshoods overlap slightly. were used; in the main study, we used both single points

and averages. When averaging was used, the averagingC. Gray Level Diffierence Statistics neighborhoods were square and were of the same size asA third useful class of picture properties that can be the displacements 6, as in Section II-B.

employed for texture analysis are (first-order) statistics It should be pointed out that there is a close relationshipof local property values, i.e., the means, variances, etc., between the vectors p, and the matrices M65. If we sumof the values of various local picture properties computed the elements of Ma along lines parallel to its main diagonal,at every point of the given picture. In particular, we consider we obtain total numbers of point pairs having a given grayhere a class of local properties based on absolute differences level difference (ji - j1 = k), up to a proportionality con-between pairs of gray levels or of average gray levels. stant. Thus features derived from M, matrices will be quite

For any given displacement 6 =(Ax,Ay), let f,(x,y) = similar to features derived from pa vectors; in fact, thelf(x,y) - f(x + Ax, y + Ay)j. Let p6 be the probability CON feature should be essentially the same for both.density of f6(x,y). If there are m gray levels, this has theform of an rn-dimensional vector whose ith component is D Lthe probability that f6(x,y) will have value i. If the picture A set of features based on gray level run lengths was alsofis discrete, it is easy to computep by counting the number employed in the first pilot study. If we examine the pointsof times each value off,(x,y) occurs, where Ax and Ay are of the picture that lie along some given line, we will oc-integers, casionally find runs of consecutive points that all have the

If a texture is coarse, and 6i is small compared to the same gray level. In a coarse texture, we would expect thattexture element size, the pairs of points at separation 6i relatively long runs would occur relatively often, whereas ashould usually have similar gray levels, so that f6(x,y) fine texture should contain primarily short runs. In ashould usually be small, i.e., the values in p6 should be directional texture, the run lengths that occur along a given

272 IEEE TRANSACTIONS ON SYSrEMS, MAN, AND CYBERNETICS, APRIL 1976

_Urban - Suburb

- S | Woods

* - ~~Scrub * Railroad

_ ~~~Swamp _ Mar,h

||CliF|CEOrchard

Fig. 1. Terrain samples.

line should depend on the direction of the line. The run The set of features measured on a picture is treated as alength features used were defined as follows [2]. Let p(i,j) feature vector Z. Suppose we are given a pair of classes C,be the number of runs of length j, in some direction 0, and Cj and a set of feature vectors Zil,Zi2,'-- ,Zik, andconsisting of points whose gray levels lie in the ith range (we Zjl,Zj2, ,Zjk2 obtained from pictures belonging to C,used the ranges (0,7),(8,15), * *,(56,63)). Then we can define and Cj, respectively. Let the sample means and the samplethe following features. covariances be p,,pj and i,Y_j, respectively. A linear dis-

1) Long Runs Emphasis: LRE = Ej2p(i,j) p(i,j). This criminant direction a is obtained such that when we projectgives greater weight to long runs, of any gray level. the feature vectors on this direction, (pi-_ j)2/(ai2 + oj2)

2) Gray Level Distribution: GLD = Yi (j p(i,j))2/ is maximized, where pi and uj are the mean values of thep(i,j). This is smallest when runs are evenly distributed projected samples from classes C, and Cj, and ai,2 and aj2

over the gray levels. are their variances. It can easily be shown that the optimal3) Run Length Distribution: RLD = yj (i p(i,j))2/ linear direction o is given by

X p(i,j). This is smallest when the run lengths are evenly a = (£, + X)-'(p - P).distributed.

4) Run Percentage: RPC = Y_p(i,])/N2 where N2 is To decide the class to which a sample Z belongs, wethe number of points in the picture. This is largest when the compute a.Z and compare it against (p,iaj + 1ujai)/runs are all short. (uf + aj). The Fisher linear classifier so constructed is theThe directions used were 0 = 00, 450, 900, and 1350. optimal linear classifier and yields minimum error prob-

ability classification if both classes have a multivariateE. Classification Schieme Used normal distribution with equal covariances. (It should be

The Fisher linear discriminant technique was used to pointed out that the classifications obtained in this way areclassify the pictures based on their measured feature values. not necessarily maximum likelihood classifications.)


TABLE INUMBERS OF PICTURES CORRECTLY CLASSIFIED USING EACH OF THE 64 SINGLE FEATURES

Number Number Number Run Num,berFourier correctly Second-order correctly Difference correctly length correctly

features classified statistics classified statistics classified features classified

Ring (1,1) 15 CON(1,0) 17 (1,0) 19 LRE(0) 19

Ring (1,2) 16 ASM(1,0) 14 (2,0) 16 GLD(0) 11

Ring (2,4) 20 ENT(1,0) 17 (3,0) 20 RLD(0) 14

Ring (4,8) 11 COR(1,0) 18 (4,0) 16 RPC(0) 14

Ring (8,12) 18 CON(0,1) 18 (5,0) 19 LRE(90) 15

Ring (12,16) 21 ASM (0,1) 17 (6, 0) 19 GLD(90) 14

Ring (16,31) 19 ENT(0,1) 16 (7, 0) 17 RLD(90) 12

Wedge (0,20) 11 COR(0,1) 17 ( 8, 0) 16 RPC(90) 16

Wedge (20,40) 10 CON(l,l) 15 ( 0,1) 19 LRE(45) 19

Wedge (40,60) 15 ASM(l,l) 16 (0,2) 18 GLD(45) 17

Wedge (60,80) 10 ENT(l,l) 14 (0,3) 20 RLD(45) 17

Wedge (80,100) 13 COR(l,l) 14 (0, 4) 13 RPC(45) 17

Wedge (100,120) 15 CON(l,-l) 19 (0, 5) 11 LRE(135) 19

Wedge (120,140) 13 ASM(l,-l) 22 (0, 6) 13 GLD(135) 18

Wedge (140,160) 8 ENT(l,-l) 19 ( 0, 7) 12 RLD(135) 17

Wedge (160,180) 13 COR(l,-l) 18 ( 0,8) 11 RPC(135) 19

When we have more than two classes, let us say C,, ,C,, II-A-II-C as well as the run length features of Section II-D.we can use a voting scheme to classify a given measurement These feature sets were not equalized with respect to orienta-Z. For each pair of classes Ci,Cj, we project Z on the tion and size sensitivity. Using the notation of Section II,appropriate line and classify it as described above. This the feature sets, each of which consisted of 16 features,gives us t(t - 1)/2 different classifications of Z. Finally, were as follows.we assign Z to the class that received the most votes. 1) Fourier Power Spectrum Features: 1-7) SOrlr29 forSuppose, for example, that Z comes from class Ch; then (r,,r2) = (1,1), (1,2), (2,4), (4,8), (8,12), (12,16), and (16,31).most of the votes between Ch and the other classes Ck 8-16) 04,o2, for (01,02) = (0,20), (20,40), (40,60), (60,80),should be in favor of Ch. On the other hand, the votes (80,100), (100,120), (120,140), (140,160), and (160,180).between classes Ci and Cj, with i,j both different from h, 2) Second-Order Gray Level Statistics: CON, ASM,should be essentially random. Thus class Ch should normally ENT, and COR of M,6, for 3 _ (Ax,Ay) = (1,0), (0,1),receive the greatest number of votes. (1,1), and (1,- 1).

3) Gray Level Difference Statistics: MEAN of pa, forIII. PILOT STUDIES 3 = (2,0),(3,0), - -,(9,0) and (0,2),(0,3), -,(0,9); here (in

The terrain samples used in the pilot studies, which were this study only) the neighborhood sizes were I less than theprovided by Prof. R. M. Haralick of the University of separations, i.e., the sizes were 1,2,-- *,8, respectively.Kansas, are shown in Fig. 1. These samples are 64-by-64 4) Gray Level Run Lengths: LRE, GLD, RLD, and RPC,arrays whose elements have 64 possible gray levels (0, - * *,63). for directions 0°, 45°, 90°, and 135°.The samples have been subjected to a gray-scale "histogram Note that in set 1) there are seven sizes (spatial frequencies)flattening" transformation to make each gray level occur and nine directions; in set 2), essentially only one size (1 or

equally often. This was done in order to remove the effects /2) and four directions; in set 3), eight sizes and only twoof unequal overall brightness and contrast in the original directions; and in set 4), four directions.images; these effects might otherwise have dominated the The Fisher classification scheme described in Section II-Emeasured feature values. A discussion of histogram flatten- was used to classify the 54 terrain samples of Fig. 1 intoing transformations can be found in [1] . the nine classes shown there, using each of these 64 individual

features. The results are shown in Table I. Only a fewA. PrliminryStdy Usng Unqualied Feturesfeatures in each class correctly classified 20 or more of the

A preliminary study was conducted (by Eileen J. Carton 54 samples, so that the results are rather poor. Nevertheless,of our laboratory') using sets of commonly employed the results are far above chance, since there are nine classes,features of each of the three classes described in Sections and one would expect a picture to be classified correctly

by chance only 1/9 of the time, i.e., only six of the classifica-

' Now with D;igital Equipment Corp. tions should have been correct.


TABLE II one exception) pairs of rings, one of which is the largestBEST-PERFORMING PAIRS OF FEATURES ring (corresponding to the highest spatial frequency, or

Nurrmber finest detail). Similarly, the best pairs of difference statisticscorrectly

Feature set Feature pair classified are always both horizontal or both vertical, and alwaysFourier Ring (2,4) and ring (16,31) 37 involve small sizes (0 or 1, with 0 best); they never involve

Ring (8,12) and ring (16,31) 37 the very large sizes. These results again imply that coarse-Ring (1,2) and ring (16,31) 35 ness is important for classifying our set of features; theRing (12,16) and ring (16,31) 35 eight best pairs involve comparing a fine-detail featureRing (12,16) and wedge (100,120) 35 (ring (16,31), or a difference of size 0 or 1) with a coarser

feature. The reason that the second-order statistics didSecond-order ENT(1,0) and ENT(1,-1) 34 poorly is probably that they involved almost no size varia-statistics ASM(1,-1) and ENT(1,-1) tion; all the 5 used were based on nearest-neighbor point

COR(1,0) and CON(1,-1) 33 pairs, i.e., distances of 1 or 2. The run length features didCON(1,0) and CON(1,-l) 33 generally more poorly than the other feature types, in both

Tables I and II, possibly because these features are moreDifference (H,0) and (H,2) 40 sensitive to noise than the other types. For this reason, runstatistics

(V,0) and (V,1) 39 length features were not used in the remaining studies.(V,1) and (V,3) 38 Since size or coarseness appears to be important in the(H,1) and (H,3) 38 classification of our texture samples, it is evidently unfair

to use feature sets that do not have comparable size sen-Run length RPC(135) and RPC(90) 31 sitivity. For this reason, in the subsequent studies feature

RPC(135) and RPC(0) 31 sets that were equalized in orientation and size sensitivityGLD(135) and GLD(0) 30 were used..LD (135) and RLD (0) 30 B. Study Using Equalized Features

In this study, the feature sets used all involved four sizesSubstantially better results are obtained when we use (or spatial frequency bands) and four directions, as described

pairs of features values. This was done for each of the 120 in Sections II-A-Il-C: four rings intersected with fourpairs of features belonging to each of the four classes. Here wedges; the CON feature for M., and the MEAN featureagain, each picture was then classified using the Fisher for pj, with distances 1, 2, 4, 8 in four directions. Thuscriteria computed from the entire set of pictures. The results there were again 16 features in each set.are not given here in full, but Table II shows the four Each of the 48 features just described was measured forfeature pairs in each class (or more, in case of a tie) which each of the 54 pictures in Fig. 1, and classifications werescored highest. Here the performance is much better; one obtained using the Fisher voting scheme of Section II-E.feature pair did as well as 40 out of 54 correct, i.e., nearly The single-feature results are shown in Table III. They are75 percent. not very different from the results in Table I, except thatA few comments can be made about the results shown in one Fourier feature does remarkably well (25 correct out of

Tables I and II. For the single features, the second-order 54).gray level statistics did best; of these, the (1,- 1) direction The pairs of features yield much better results, as shownwas consistently best for all four features. This may reflect in Table IV, which gives the feature pairs in each set havingthe presence of some diagonal structure in the pictures. the top four scores. (For the detailed scores see Table 4 ofFor gray level differences, the vertical results were con- [3].) The Fourier features do slightly better than thesistently poor for large amounts of averaging (k . 3), but results in Table IL (the top four scores are 38, 37, 36, 34,the horizontal results were not; this could be due to unequal rather than 37's and 35's); the difference statistics do some-sampling in the two directions. For the Fourier features, the what better (43, 42, 41, 39 rather than 40, 39, and 38's);wedges did substantially worse than the rings, indicating and the second-order statistics do substantially better (40,that coarseness is more important than directionality for 39, and 38's rather than 34's and 33's). The improvementthese pictures. in performance of the second-order statistics is very likelyFor the pairs of features shown in Table II, the features due to the fact that more than one distance is used in the

based on difference statistics seem to have done significantly new features. The best score, 43 out of 54 (for differencebetter than the Fourier features, and these in turn seem statistics (2, 135°) and (4, 135°)), is nearly 80 percent correct,significantly better than the second-order statistics and run which is quite good for a nine-class problem using only twolength features. (No attempt will be made here to quantify features.these remarks, since the present study used such a small The pairs of second-order and difference statistics seemnumber of pictures.) Here again, for the second-order to do systematically better than the Fourier feature pairs.statistics, one of the features in each best pair was always This can be seen if we look at histograms of the scoresa 135° feature. The best Fourier feature pairs are (with obtained using the three feature sets; the Fourier pair


TABLE IIINUMBERS OF PICTURES CORRECTLY CLASSIFIED USING EQUALIZED SINGLE FEATURES

Feature Fourier features Number Second-order statistics Number Difference statistics NumberNo. correctly correctly correctly

Ring n) Wedge classified Distance Direction classified Size Direction classified

1 (16,31) 0 10 1 0 17 1 0 19

2 (16,31) 45 19 45 15 1 45 18

3 (16,31) 90 14 1 90 18 1 90 15

4 (16,31) 135 25 v2 135 19 1 135 20

5 (8,16) 0 9 2 0 18 2 0 15

6 (8,16) 45 17 2/2 45 15 2 45 14

7 (8,16) 90 14 2 90 17 2 90 16

8 (8,16) 135 20 2/2 135 20 2 135 17

9 (4,8) 0 12 4 0 22 4 0 17

10 (4,8) 45 15 3v/2 45 20 4 45 16

11 (4,8) 90 15 4 90 17 4 90 12

12 (4,8) 135 17 3/2 135 18 4 135 20

13 (2,4) 0 7 8 0 9 8 0 11

14 (2,4) 45 17 6/2 45 18 8 45 18

15 (2,4) 90 13 8 90 20 8 90 13

16 (2,4) 135 13 6/2 135 16 8 135 19

TABLE IVBEST-PERFORMING PAIRS OF EQUALIZED FEATURES

Numbercorrectly

Feature set Feature pair classified

Fourier Ring (8,16) n Wedge 45 and Ring (16,32) n Wedge 45 38

Ring (8,16) n Wedge 45 and Ring (16,32) C Wedge 135 37

Ring (8,16) n Wedge 135 and Ring (16,32) fl Wedge 135 36

Ring (4,8) fl Wedge 135 and Ring (16,32) n Wedge 135 34

Ring (2,4) fl Wedge 135 and Ring (16,32) n Wedge 135 34

Second-order Dist /2, Dir 135 and Dist 6/2, Dir 135 40statistics

Dist /2, Dir 135 and Dist 3/E, Dir 135 39

Dist 1, Dir 90 and Dist 6/2, Dir 45 38

Dist /2, Dir 45 and Dist 2/2, Dir 45 38

Dist 1, Dir 0 and Dist 4, Dir 0 38




Difference Size 2, Dir 135 and Size 4, Dir 135 43statistics

Size 1, Dir 135 and Size 2, Dir 135 42




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grams,the x axis repreentrten recobandDiffey iial frteote etrenets n ftedsacso

axis, the number of feature pairs. which yielded that score. sizes is always small (1, \/2, or 2).The single features of all three types do about equally These results suggest that we could also do well if we

well (with the exception of an unusually good F;ourier used certain combinations of our features as single, "high-er-feature, already mentioned). There appears to be a bias order" features. For example, suppose that we computedin favor of diagonal directions in the best performing the mean over the four directions, for each size or distance,features (three out of four best difference statistics are the and used these means as features, then feature pairs con-135° directio'n; the top Fourier features are all in the 45° itn of a small-size mean and a large-size mean shouldand 135° directions, with the unusually good one at 135°), do well. On the other hand, if we computed means over thewhich may be due to the fact that the distances in the four sizes for each direction a-nd used these means asdiagonal directions are 'not quite the same as those in the features, we should not expect to do well. A supplementaryhorizontal and vertical directions. The horizontal direction study, based on such composite features, will now beis consistentlypoor for the Fourier features, and the vertical described. This method of combining features was alsodirection is not very good either, perhaps du'e to the spurious used by Haralick in [1].high values in those directions (resulting from the non-periodicity of the pictures), which may mask the real textural C td sn opst etrdifferences. For each of the three sets of features used in SectionAmong the good feature pairs shown in Table IV, only III-B, a set of composite features was computed. This

the diagonal directions appear, for the Fourier features and was done by taking the mean and standard deviation over

difrec sttsis an h etcldrcinapasol he ordrcin,frecOie(rdsac,o ptaonce The* twIetrsi ahpi r sal ntesm reunybn) n h enadsadr eito

direction,~ ~ ~ ~ ~ ~ ~~~~~~~~siniatnonc agi*htcasns smr vrtefu ie,frec ieto.I htfloshim- ran0ha dietonlt for diciiaigtee faue*fScinIIBwl erfre oa h rw0atcua tetues Not tha eve whe the 41etosfaue,i otatwt tecmoiefaue eie eedifer*h size als *41*r41hteFuirfaue,oe h lsiiainrslsfr h igecmoiefaueo th pair1 is alay*from *41*ihspta rqec r hw nTbl .I sse,b oprsnwt alban (1,3) corsodn *toth4mletsieo1itne;1I*htte4obndFuie1etrsd*wreta h


TABLE VNUMBERS OF PICTURES CORRECTLY CLASSIFIED USING COMPOSITE SINGLE FEATURES

Feature Fourier Second-order Difference

No.

1 Mean over sizes in direction 0 8 16 17

2 45 13 19 13

3 90 9 17 16

4 135 14 22 23

5 S.D. over sizes in direction 0 9 14 17

6 45 16 19 23

7 90 13 20 18

8 135 14 16 12

9 Mean over directions Ring (16,31): 18 Distance 1 or /2: 16 Size 1: 17

10 Ring (8,16): 21 Distance 2 or2/2: 17 Size 2: 16

11 Ring (4,8): 14 Distance 4 or 3/2: 21 Size 4: 18


13 S.D. over directions Ring (16,31): 8 Distance 1 or /2: 16 Size 1: 17

14 Ring (8,16): 9 Distance 2 or2/2: 19 Size 2: 15



raw features, while the combined second-order statistics sets. In fact, inspection of the pictures in Fig. 1 indicatesdo about as well as, and the combined difference statistics that this result should not be surprising, since some of theslightly better than, the corresponding raw features. For pictures do not closely resemble the other pictures in theirthe latter two sets, the mean over sizes does surprisingly classes. For example, the last picture in the urban class haswell, particularly in the 135° direction. Note that the com-. more detail in it than the other five pictures, the last twobined mean Fourier features are similar to the Fourier marsh pictures are more finely textured than the first four,features that were used in the first pilot study of Section and so on.III-A except that the wedges used are wider. A detailed analysis of how the individual pictures wereThe results for pairs of composite features are given in misclassified is beyond the scope of this paper. For a list of

Table 7 of [3]; the best few pairs in each feature set are pictures most often misclassified by the best feature pairs seeshown for convenience in Table VI. Here the combined [3], Table 9. Appendix A of [3] explores how well theFourier features and difference statistics both do somewhat pictures in each class are clustered. This was investigatedworse than the corresponding raw features, while the by plotting, for each class, a one-parameter family of featurecombined second-order statistics do slightly better than the values (specifically, the Fourier ring features for ringsraw features. Histograms of the feature pair performances (1,1),(2,2), ,(33,33)) for each picture in the class; cluster-are shown in Fig. 3. It can be concluded that for the com- ing or dispersedness is more apparent for these plottedbined features too, the Fourier set is substantially worse curves than it would be for single-point feature values.than the other two sets.

It will be noted that in the best feature pairs, one feature E. Discussionis almost always a mean over directions, confirming once The studies described in this section involved a veryagain that size is more important than direction. Moreover, small data set, which was used because similar pictures hadone of the sizes in each best feature pair is always the smallest previously been analyzed by Haralick (see [1]). Unfor-or next smallest size that was used. When a mean or standard tunately, the smallness of the data set makes any con-deviation (SD) over sizes is present, the direction is always clusions drawn from these studies tentative at best. Sincediagona!, as before. These conclusions are similar to those there were only six samples in each of the nine classes, nodiscussed in Section Ill-B. There is no apparent advantage attempt was made to use more than two features at a time.in using combined rather than raw features. (Even with only two features, it is possible that the results

are influenced by artifacts in the samples; e.g., why is 1350D. Analysis of the Errors generally better than 45°?) For similar reasons, it seemed

In many cases, the errors made in classifying the pictures inappropriate to use a higher-order classifier than theshow consistent patterns; a particular picture is often Fisher linear discriminant. Division into test and trainingmisclassified in the same way by many different feature sets would not have been reasonable, and the computational


TABLE VIBEST-PERFORMING PAIRS OF COMPOSITE FEATURES

Numbercorrectlv

Feature set Feature pair alasified

Fourier Mean over dirs.,ring (2,4), and mean over 34dirs., ring (16,31)

mean over dirs.,ring (8,16), and mean over 33sizes, dir. 45

mean over dirs.,ring (4,8), and mean over 32dirs., ring (16,31)

Mean over dirs.,ring (8,16), and mean over 31dirs., ring (16,31)

Mean over dirs.,ring (8,16), and mean over 31sizes, dir. 135

Mean over dirs.,ring (8,16), and S.D. over 31sizes, dir. 135

Mean over dirs.,ring (16,31), and S.D. over 31sizes, dir. 45

Second- Mean over dirs., dist. 2 or 217, and mean 42order over dirs., dist. 4 or 317

Mean over dirs., dist. 1 or 17, and mean 41over dire., diet 8 or 6/1 Fig. 4. LANDSAT image used in main study, with regions outlined.

Mean over dists. ,dir. 45, and man over 40 A-Mississippian limestone and shale. B-Lower Pcnnsylvaniandire., diet. 1 or 17 shale. C-Pennsylvanian sandstonc and shale.

S.D. over dists., dir 45, and mean over dirs., 39dist. 1 or 17

S.D. over dists., dir. 135, and S.D. over 39dirs., dist. 1 or 17 two of the classes, scrub and woods. In our study, we used

Mean over dirs., dist. 1 or 17, and mean over 39 only 16 features (of each type), and obtained nearly 80 per-dire., diet. 4 or 317 cent correct classifications with the best pairs of those,S.D. over dirs., dist. 1 or 17, and S.D. over 39dirs., dist. 2 or 217 using all nine classes. It is difficult to estimate how much

worse our results would have been if we had used a leave-Difference Mean over dirs., size 1, and S.D. over dirs., 40size 1 one-out testing scheme; but under the circumstances, our

Meaniover dirs., size 1, and man over dirs. 39 results can be regarded as reasonably good.

Mean over sizes, dir. 135, and mean over dirs., 38 IV. MAIN STUDYsize 1 I.M I TD

Mean over sizes, dir. 45, and mean over dirs., 38 A. Data and Features Usedsize 1

Mean ov-r dirs., size 1, and mean over dire., 38 The terrain samples used in the main study were selectedsize 2 from a LANDSAT-1 image of Eastern Kentucky (frame

Mean over dire., size 2, and mean over dire., 38 E 1354-15424, band 6), which was made available to us by

the Earth Satellite Corporation; see Fig. 4. A geologist,Dr. John R. Everett of EarthSat, demarcated a set of

cost of a leave-one-out testing scheme would have been regions on this image, as shown on Fig. 4, and identifiedprohibitive. these regions as having three geological terrain types:

In spite of these inadequacies, the comparative results Mississippian limestone and shale; Lower Pennsylvanianobtained from these studies may still be of some value. shale; and Pennsylvanian sandstone and shale (labeledThese results suggest the following tentative conclusions. A, B, C on Fig. 4). A set of 60 windows, each 64 by 64

1) Fourier features do not do as well as second-order pixels, was selected from each of the three regions. Theor difference statistics (except on the first pilot study.)2 image gray-scale was modified to cover just 64 gray levels,

2) Difference statistics do about as well as second-order and histogram flattening was performed on each of thesestatistics (better, on the first pilot study). 180 windows. The resulting normalized windows are shown

3) Composite features seem to do no better than raw in Figs. 5-7.features. Seven sets of 16 features each, equalized in size andThe first two conclusions are substantiated by the results orientation sensitivity, were used. Each set involved four

of the main study, which is described in Section IV. sizes (or displacements, or spatial frequency bands), andIn [1], using 170 terrain samples of the same types and a four directions, just as in Section III-B; these are listed,

leave-one-out test procedure, Haralick obtained 82.3 percent for convenience, in Table VII. The Fourier feature set wascorrect classifications; but he used 33 composite features the same as in Section III-B. There were two feature sets in-(means, ranges, and standard deviations over the four volving second-order statistics, using the CON feature fordirections, derived from an initial set of 44 second-order both the Ma and the M. Finally, there were four featurestatistics, II in each direction at distance 1). He also merged sets involving difference statistics; these used the CON

and MEAN features for the pj and for the pi. Note that fordistance 1, the MJ and Ma features are the same, and the

2The second-order and difference statistics are also less costly to p, and j5, features are the same. The Fisher classificationcompute than the Fourier features, which is a further argument in their s m wa u afavor. scheme was used, just as in Section 111.


Windows 1-16 Windows 17-32

Windows 1-16 windows 17-32

Windows 33-48 Windows 49-60

Fig. 5. Windows of terrain type A (Mississippian limestone and shale).Windows 33-48 Windows 49-60

Fig. 7. Windows of terrain type C (Pennsylvanian sandstone andshale).

TABLE VIIFEATURE NUMBERING

Size, displa;cement,No. or spatial frqecy band Direction

1 1 ~~~~~~~~~~~~~02 1 45

3 1 90Windows 1-16 Windows 17-32

-~~~~~~~~~~~~~~~~1- 135

5 2 0

6 2 45

7 ~~~~2 90

8 2 135

9 4 0

10 4 45

11 4 90

12 4 135

13 8 0

Windows 33-48 Windows 49-60 14 8 45

Fig. 6. Windows of terrain type B (Lower Pennsylvanian shale). 15 8 90

16 8 135

B. Resuilts Notes: Sizes 1, 2, 4, 8 and displacements 1, 2, 4, 8 (or V/7,2_2, 3r2, 6/2) correspond to spatial frequency bands

The 180 terrain samples shown in Figs. 5-7 were classified (r , r2 ) = (16, 31), (8, 16), (4, 8), and (2, 4).

into the three classes, using each of the 16 individual Directions 0, 45, 90, 135 are the centers of thefeatures in each set, and also using each of the 120 pairs spatial frequency sectors.

of features in each set. The numbers of samples classifiedcorrectly by the individual features are shown in Table VIII,


TABLE VIIINUMBERS OF SAMPLES CORRECTLY CLASSIFIED USING INDIVIDUAL FEATURES

FEATURE SET

Feature Fourier Second-order Second-orda Difference (points) Difference (averages)No. (points) (averages) MEAN CON MEAN CON

1 130 131 131 130 132 130 132

2 117 123 123 122 123 122 123

3 116 136 136 135 136 135 136

4 133 128 128 128 128 128 128

5 108 126 101 133 126 105 101

6 81 110 86 108 110 106 87

7 92 126 112 128 126 116 112

8 102 119 89 120 119 123 91

9 94 99 116 99 99 115 117

10 94 92 106 97 92 105 106

11 111 113 117 108 113 108 116

12 101 99 112 100 99 109 112

13 77 99 107 100 99 107 10714 95 68 117 71 68 108 11715 90 82 116 79 82 108 11616 86 80 107 77 80 103 108

and the numbers correctly classified by the best feature pairs samples misclassified by one pair were often misclassifiedare shown, for each feature set, in Table IX. (See Tables by other pairs as well. Often, but not always, these samples3-9 of [4] for the details.) The following remarks can be did appear to differ visually from the general appearance ofmade about these results. their classes.

1) The best results obtained using each feature set A geologist and a naive subject were asked to classifyalways come from feature pairs involving small sizes the 180 samples, presented in random order and out of

(1, 12, or 2). Feature pair (1,3), i.e., size 1, horizontal context, into three classes. The geologist got 143 of the 180direction, paired with size 1, vertical, occurs as one of the correct, while the naive subject got 145 correct. (The errors

three best-scoring pairs for each of the seven sets. made by each of them are listed in Table 13 of [4]). There2) The Fourier features do not do quite as well as the was only partial overlap among the misclassifications made

other types of feature pairs. See Section IV-E for a dis- by the features, the naive subject, and the geologist. Note,cussion of possible reasons for this. however, that both subjects made about 20 percent errors,

3) Statistical features (MEAN or CON) based on average which is poorer performance than that of even the goodgray levels (Ma or p) do better, especially for large sizes, Fourier feature pairs.than those based on single points (M, or p.); see Tables3-9 of [4]. D. Supplemental Study

4) The MEAN features, derived from the pa, do at As a check on the results of the main study, a supplementalleast as well as the CON features derived either from the study was conducted using the ASM and ENT featurespa or the Ma. Since these MEAN features are computation- (see Sections Il-B and II-C) for the same set of Ma and Maally cheapest to implement, they would seem to be the cooccurrence matrices, and p6 and p,, difference histograms.preferred choice for the present classification problem. Another feature proposed by Haralick [I], the "Inverse

All of the statistical features did about equally well; Difference Moment" IDM - p(i,)/((i - j)2 + 1)-orthe best single feature in each set correctly classified 135 E p6(k)/(k2 + 1), for the difference histograms-was alsoor 136 of the 180 samples (about 75 percent), while the best tested.feature pair in each set correctly classified 165, 166, or 167 These twelve sets of features were computed for the sameof the samples (about 93 percent). These results were not 16 values of 5 indicated in Table VII, and the classificationverified by independent testing (i.e., the classifier was scheme of Section Il-E was used, as in the main study, todesigned and tested on the same sample set), but since such classify the 180 terrain samples into the three classes, usinga large number of training samples was used ((samples per each single feature and each pair of features in each set.class)/(number of features) = 30), this should make little The single-feature classification results are given in Table X.difference. The feature pairs giving the best scores are listed in Table

XI; for the detailed scores of the feature pairs see [5,C. Analysis ofthe Errors Tables 2-13]. For convenience, the maximum, mean,

The errors made by the highest-scoring feature pairs median, and minimum scores of the single features in allin each set are given in Tables 10-12 of [4]; the details 18 feature sets (the 12 new sets, plus the six non-Fourierare beyond the scope of this paper. It was found that the sets used in the main study) are summarized in Table XII,


TABLE IXBEST-PERFORMING PAIRS OF FOURIER, CON, AND MEAN FEATURES

Numbercorrectly


Fourier Ring (16,31) n Wedge 0 and Ring (16,31) n Wedge 135 158

Ring (16,31) n Wedge 0 and Ring (16,31) n Wedge 90 153

Ring (16,31) n Wedge 45 and Ring ( 8,16) n Wedge 90 151

Second-order Dist /2, Dir 45 and Dist 2, Dir 0 166CON, singlepoints Dist 1, Dir 90 and Dist /4, Dir 135 166

Dist 1, Dir 0 and Dist /2, Dir 45 163


Dist 1, Dir 90 and Dist 2, Dir 0 16.0

Second-order Size 1, Dir 90 and Size 1, Dir 135 166CON, averages




Difference CON, Dist /2, Dir 45 and Dist 2, Dir 0 166single points





Difference CON, Size 1, Dir 90 and Size 1, Dir 135 166averages




Difference Dist /1, Dir 45 and Dist 2, Dir 0 167MEAN, singlepoints Dist 1, Dir 0 and Dist 1, Dir 90 165


Dist 1, Dir 90 and Dist /r, Dir 135 164

Difference Size 1, Dir 0 and Size 1, Dir 45 165MEAN, averages



and a similar summary for the feature pairs is given in nearly zero differences, will always tend to be higher thanTable XIII. The following may be seen from these tables. those for unequal pairs or large differences. The distinction

1) Like the CON features of [1], the best-scoring pairs between busy and coarse textures will be more apparentof IDM and ENT features do about as well when measured at the very unequal or large difference end of the scale.for the difference histograms as when measured for the This end is emphasized by the CON features, but it iscooccurrence matrices; while the best ASM features (singles deemphasized by the IDM features. This suggests that inand pairs) do even better on the histograms than on the many cases the CON features will perform better than thematrices. 1DM features.

2) The 1DM features do more poorly than the other sets. 3) The worst features based on average gray levels doThis may be because the 1DM features place greatest weight better than the worst features based on single-point grayon pairs of gray levels (or averages) that are (nearly) equal, levels for both single features and pairs, as already observedand least on pairs that are very unequal. Even in "busy" in Section LV-B.textures (short of pure "noise" textures), there will be some It was not surprising in the main study that the CONredundancy between the gray levels of nearby points; thus features based on difference histograms did as well as thosethe matrix or histogram values for nearly equal pairs, or based on cooccurrence matrices, since the CON feature for a


TABLE XNUMBERS OF SAMPLES CORRECTLY CLASSIFIED USING INDIVIDUAL ENT, ASM, AND IDM FEATURES

SECOND-ORDER STATISTICS

FEATURE ENT ENT ASM ASM IDM IDMNO. (poits) (averages) (points) (averages) (Points) (averages)

1 130 130 124 124 113 113

2 118 118 125 125 112 112

3 136 136 126 126 113 113

4 124 124 127 127 123 123

5 120 99 113 91 120 110

6 111 86 115 82 98 97

7 116 95 113 90 106 106

8 113 99 115 95 99 98

9 75 124 78 126 81 94

10 91 133 91 129 84 81

11 95 135 104 131 84 84

12 87 131 93 127 86 87

13 68 116 67 111 75 102

14 74 113 74 110 63 101

15 79 110 78 118 69 85

16 71 113 69 111 59 93

DIFFERE1NCE STATISTICS

FEATURE ENT ENT ASM ASM IDM IDMNO. (plt) (averages) (pit) (averages) (pit) (averages)

1 127 127 127 127 113 113

2 126 126 124 124 112 112

3 133 133 137 137 113 113

4 127 127 126 126 123 123

5 127 97 130 106 121 103

6 108 85 107 94 99 87

7 127 109 129 112 99 99

8 118 90 115 105 106 93

9 93 117 101 118 85 106

10 96 108 103 109 89 72

11 110 115 109 104 81 78

12 99 112 102 111 88 85

13 97 111 104 108 77 94

14 69 114 71 115 66 99

15 79 119 77 110 72 85

16 74 109 76 109 62 94

matrix depends only on the spread of its values away from III-E (except for the conclusion about composite features,the main diagonal; but it is interesting that the same results which were not used in the main study).were obtained for the ASM and ENT features. 1) Good classification results (over 90 percent correct)

were obtained on terrain samples representing three geo-F. Conclusions logical classes. This confirms the general usefulness ofThe following conclusions can be drawn from the main texture features, even in the absence of spectral information,

study; they confirm the tentative conclusions of Section for terrain classification [6].


TABLE XIBEST-PERFORMING PAIRS OF ENT, ASM, AND IDM FEATURES

Numbercorrectly


Second-order Dist 1, Dir 0 and Dist 1, Dir 90 163ENT, singlepoints Dist 1, Dir 0 and Dist /T, Dir 45 160

Dist 1, Dir 90 and Dist /T, Dir 135 156

Second-order Size 1, Dir 0 and Size 1, Dir 90 163ENT, averages



Difference ENT, Dist 1, Dir 90 and Dist VT, Dir 135 164single points

Dist 1, Dir 0 and Dist /, Dir 45 163

Dist 1, Dir I and Dist 1, Dir 90 163

Dist /2, Dir 45 and Dist 2, Dir 0 163


Difference ENT, Size 1, Dir 90 and Size 1, Dir 135 164averages

Size 1, Dir 0 and Size 1, Dir 45. 163





Second-order Dist 1, Dir 0 and Dist VT, Dir 45 158ASM, singlepoints Dist 1, Dir 0 and Dist 1, Dir 90 158



Second-order Size 1, Dir 0 and Size 1, Dir 45 158ASM, averages





Difference ASM, Dist /, Dir 45 and Dist 2, Dir 0 167single points






Difference ASM, Size 1, Dir 0 and Size 1, Dir 45 165averages




Second-order Dist 1, Dir 0 and Dist 1, Dir 90 140IDM, singlepoints Dist 1, Dir 90 and Dist 2, Dir 0 140


Dist 1, Dir 90 and Dist 2/F, Dir 135 133


Dist 1, Dir 90 and Dist /f, Dir 135 132


Second-order Size 1, Dir 0 and Size 1, Dir 90 140IDM, averages





Difference IDM, Dist 1, Dir 90 and Dist 2, Dir 0 141single points

Dist 1, Dir 0 and Diet 1, Dir 90 140

Dist */2, Dir 45 and Dist 2, Dir 0 135

Difference 1DM, Size 1, Dir 0 and Size 1, Dir 90 140averages




TABLE XIIMAXIMUM, MEAN, MEDIAN, AND MINIMUM SCORES FOR THE 16 SINGLE FEATURES IN EACH SET

The four scores in SECOND-ORDER DIFFERENCEeach box are the STATISTICS STATISTICSmaximum, mean, median,and minimum scores for Single Averages Single Averagesthat set of single Points Pointsfeatures

136 136 133 133

ENT 100 116 107 11295 116 108 11268 86 69 85

127 131 137 137101 114 109 113

ASM 104 118 107 110

67 82 71 94

123 123 123 12393 100 94 97

1DM 86 98 89 94

59 81 62 72

136 136 136 136

CON 108 113 108 113CON ~~~~110 112 110 11268 86 68 87

135 135108 114

MEAN 108 10871 103

TABLE XIIIMAXIMUM, MEAN, MEDIAN, AND MINIMUM SCORES FOR THE 120 PAIRS OF FEATURES IN EACH SET

The four scores in each SECOND-ORDER DIFFERENCEbox are the maximum, STATISTICS STATISTICSmean, median, and mini- Single Averages Singlemum scores for that set Points Pointsof feature pairs

163 163 164 164ENT 119 138 129 134ENT ~~~~~123 138 129 134

74 105 79 99

158 158 167 165118 133 131 133

ASM 122 134 131 13170 97 80 108

140 140 141 140IDM ~~~~~109 115 111 1131DM 113 115 114 114

62 82 69 82

166 166 166 166130 134 130 134

CON 129 134 130n134_ 72 96 72 96

167 165MEAN 131 135

131 13373 115


2) Features based on second-order and difference statistics analysis exist, e.g., Bajcsy's [7] Fourier-based features.do about equally well (except for IDM) and perform some- However, it was felt that in a comparative study, it waswhat better than Fourier features. Two reasons can be given desirable to use equalized feature sets. It is hoped that ourfor the poorer performance of the Fourier features. results will encourage others to carry out further comparative

a) The discrete Fourier transform treats a picture as studies, which should lead to an increased understandingthough it is periodic, even if, in fact, it is not. Thus the of the nature of visual texture and the choice of features fortransforms of the terrain samples contain spurious high texture classification.values in the horizontal and vertical directions, arisingfrom "discontinuities" between the left and right columns, ACKNOWLEDGMENTSand the top and bottom rows, of the pictures. The presenceof these spurious values may degrade the Fourier features. The authors wish to thank Prof. R. M. Haralick of the

b) The textures of the terrain samples may be more University of Kansas for providing the aerial photographicappropriately modeled statistically in the space domain terrain samples; Mr. R. Michael Hord and Dr. John R.(e.g., as random fields with specified autocorrelations), Everett of the Earth Satellite Corp., for providing andrather than as sums of sinusoids. Thus our statistical classifying the LANDSAT data; Prof. A. K. Agrawala offeatures may capture the essential differences among the the University of Maryland, for providing the Fishersamples more effectively than do the Fourier features. classification program; Eileen J. Carton, Robert L. Kirby,

3) Statistics based on gray level averages gave better and Jeffrey M. Mohr, for conducting some of the classifica-performance for larger sizes and distances than statistics tion studies; and Donald Kent, Andrew Pilipchuk, andbased on single gray levels. This is presumably because at Shelly Rowe, for their help in preparing this paper.large distances, the single gray levels are relatively uncor-related, so that the data become noisy; whereas the averages REFERENCESremain correlated, since they arise from adjacent

[1] R. M. Haralick, K. Shanmugam, and I. Dinstein, "Texturalneighborhoods. features for image classification," IEEE Trans. Syst., M7an, Cybern.,

4) The MEANs of the difference histograms pa3 did about vol. SMC-3, pp. 610-621, Nov. 1973.as well as the other statistical features (CON, ENT, ASM) [2] M. M. Galloway, "Texture classification using gray level runlengths," Computer Graphics and Image Processing, vol. 4, pp.measured on either the j,5 or the Mb. For the best feature 172-179, June 1975.pairs,thesttisticbaseonsinlepoitsdidabou[3] J. S. Weszka and A. Rosenfeld, "A comparative study of texturepairs, the statistics based on single points did about as well measures for terrain classification," Computer Science Center,as those based on averages.3 Thus it seems that there Univ. Md., College Park, Tech. Rep. TR-361, Mar. 1975.should be no loss in classification power if one uses the [4] C. R. Dyer, J. S. Weszka, and A. Rosenfeld, "Experiments in

terrain classification on LANDSAT imagery by texture analysis,"computationally cheapest of the statistical features, namely, Computer Science Center, Univ. Md., College Park, Tech. Rep.the EANsof the single-point difference histograms. TR-383, June 1975.the MEANs of the single-point difference histograms. [5] C. R. Dyer, J. S. Weszka, and A. Rosenfeld, "Further experiments

The feature sets used in these studies were not necessarily in terrain classification by texture analysis," Computer Sciencethe best ones of each class. Other approaches to texture Center, Univ. Md., College Park, Tech. Rep. TR-417, Sept. 1975.6]R. M. Haralick and R. Bosley,_ "Spectral and textural processing

of ERTS imagery," in Proc. 3rd ERTS-1 Symp., vol. I, pp. 1929-1969, Dec. 1973.

3This is because the best pairs almost always involved small dis- [7] R. Bajcsy, "Computer description of textured surfaces," in Proc.placements, for which little or no averaging was done. 3rd Int. Joint Conf. Artificial Intelligence, Aug. 1973, pp. 572-579.

JWeszka76-A Comparative Study of Texture Measures for Terrain Classification

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