U.P.B. Sci. Bull., Series C, Vol. 70, Iss. 4, 008 ISSN 454-34x STATISTICA TEXTURE ANAYSIS OF ROAD FOR MOVING OBJECTIVES Dan POPESCU, Rau DOBRESCU, Nicoleta ANGEESCU 3 Obiectivul articolului este acela e a ientifica şi e a localiza regiunile importante in imaginile cu textură pentru navigaţia obiectivelor mobile. Sunt analizate ouă tipuri e trăsături. Primul tip sunt histogramele şi ensităţile e pixeli e contur. Trăsăturile e al oilea tip erivă in matricele e co-ocurenţă meii, noţiune ce a fost introusă e autori. Algoritmii au fost implementaţi în MATAB. Asfaltul este consierat textură e urmărit (referinţa) iar pietrişul şi iarba sunt consierate texturi e evitat. Rezultatele experimentale au reliefat faptul că trăsăturile ce erivă in matricele e coocurenţă meii prezintă putere e iscriminare mare, atât pentru clasificarea, cât şi pentru localizarea regiunilor. The paper objective is to ientify an localize significant regions in texture images for navigating an autonomous agent. Two types of statistic texture features are use. The first type features are the histograms, an the ege ensity. The secon type features erive from the meium co-occurrence matrices, which is a notion introuce by the authors. The algorithms are implemente in MATAB. The basic texture is consiere the asphalt an the ifferent textures are consiere the grass an the pebble. The experimental results inicate that the features, which erive from meium co-occurrence matrices, have a goo iscriminating power both for texture classification an region localization. Keywors: texture, statistic features, meium co-occurrence matrix, ege ensities, grey level histogram. Introuction Image texture, efine as a function of the spatial variation in pixel intensities (gray values), is useful in a variety of applications an has been a subject of intense stuy by many researchers. It is very har to efine rigorously the texture into an image. The texture can be consiere like a structure which is compose of many similar elements (patterns) name textons or texels, in some regular or continual relationship. Texture analysis has been stuie using various approaches, like statistical type (characteristics associable with grey level histogram, grey level image ifference histogram, grey level co-occurrence matrices an the features extracte from them, autocorrelation base features, Prof., Faculty of Control an Computers, University POITEHNICA of Bucharest, Romania ecturer, Faculty of Electrical Engineering, Valahia University of Târgovişte, Romania 3 ecturer, Faculty of Electrical Engineering, Valahia University of Târgovişte, Romania
76 Dan Popescu, Rau Dobrescu, Nicoleta Angelescu power spectrum, ege ensity per unit of area, etc.), fractal type (box counting fractal imension), an structural type. In the last case, the textures are compose of primitives, an an image escription is prouce by the placement of these primitives accoring to certain placement rules. The structural approach is suitable to analyze textures with more regularity in the placement of texture elements. The statistical approach utilizes features to characterize the stochastic properties of grey level istribution in the image. There are two important categories of problems that texture analysis research attempts to solve: texture segmentation an texture classification. Another problem, texture synthesis is often use for image compression application. The process, calle texture segmentation, consists of similar texture region ientification an ifferent texture region separation. Texture classification involves eciing what texture class an observe image belongs to. Thus, one nees to have an a priori knowlege of the classes to be recognize. The major focus of this paper is the route analysis for moving objectives, base on statistical features (especially erive from meium co-occurrence matrix). For the purpose of algorithm valiation, two experimental stuies have been conucte. The first stuy is focuse on region classification an localization of texture images compose of asphalt an pebble (Fig., Image I ), an the secon stuy is focuse on route ientification an localization form texture images compose of asphalt an grass (Fig., Image I ). Fig.. Analyze images I an I. With this en in view, the whole image is partitione in sixteen equivalent regions (Fig. ). Different texture regions are compare, base on minimum istance between measure features, which are erive from meium cooccurrence matrices (contrast, energy, entropy, homogeneity, an variance). Other texture features, like grey level histograms or contour pixel ensities, are also iscusse. Image region I (), which contains asphalt texture, is consiere the reference texture template. If a region contains another texture or mixe textures, then it is a efect region.
Statistical texture analysis of roa for moving objectives 77 I() I() I(3) I(4) I(5) I(6) I(7) I(8) I(9) I(0) I() I() I(3) I(4) I(5) I(6) Fig.. Sixteen regions image partition. The experimental results inicate that the five features selecte from meium co-occurrence matrices have a goo iscriminating power, both in texture classification applications an in efect region etection an localization.. Statistical methos to texture analysis The statistical approach to texture analysis is more useful than the structural one. The simplest statistical features, like the mean () an stanar eviation (3), can be compute inirectly in terms of the image histogram h. Thus, K μ = x h i ( x i ), () N N = N i= i= K i= h( ), () x i K σ = ( x μ) h( ) (3) i x i N = n n is the image imension, an K is the number of grey levels. The shape of an image histogram provies many clues to characterize the image, but sometimes it is inaequate to iscriminate textures (it is not possible to inicate local intensity ifferences). Another simple statistic features is the ege ensity per unit of area, Den e (4). The ensity of eges, etecte by a local binary ege etector, can be use to istinguish between fine an coarse texture, like in Fig.3. Den e can be evaluate by the ratio between the pixel number of extracte eges (which must be tinne one pixel thickness) an image area (pixel number of image region): N Den = e e A (4) In (4), N e represents the number of ege pixels (tinne eges, with one pixel thickness) an A is the region area.
78 Dan Popescu, Rau Dobrescu, Nicoleta Angelescu In orer to characterize texture images, connecte pixels must be analyze. For this reason, correlation function (5), ifference image (6) in certain irection = (Δx, Δy), an co-occurrence matrices (9), must be consiere: R n n u = 0 v = 0 ( x, y ) = n n I ( u, v ) I ( u + x, v + y ) u = 0 v = 0 I ( u, v ) I (x,y) = I(x,y) I(x+Δx, y+δy) (6) (5) From the histogram of the ifference image h, one can extract the mean (7) an stanar eviation (8): K μ = x h ( x ) (7) K i N i= i σ = ( x μ ) h ( x ) (8) N i= The most powerful statistical metho for texture image analysis is base on features extracte from the Grey-evel Co-occurrence Matrix (GCM), propose by Haralick in 973 []. GCM is a secon orer statistical measure of image variation an it gives the joint probability of occurrence of grey levels of two pixels, separate spatially by a fixe vector istance = (Δx, Δy). Smooth texture gives co-occurrence matrix with high values along iagonals for small. The range of grey level values within a given image etermines the imensions of a co-occurrence matrix. Thus, 4 bits grey level images give 6x6 co-occurrence matrices. The elements of a co-occurrence matrix C epen upon isplacement =(Δx, Δy): C (i,j) = Car{((x,y),(t,v))/I(x,y) = i, I(t,v) = j, i (x,y), (t,v) N x N, (t,v) = (x+ Δ x, y+ Δ y)} (9) From a co-occurrence matrix C one can raw out some important statistical features for texture classification. These features, which have a goo iscriminating power, were propose by Haralick: contrast (), energy (), entropy (3), homogeneity (4), variance (5). The contrast measures the coarseness of texture. arge values of contrast correspon to large local variation of the grey level. The entropy measures the egree of isorer or nonhomogeneity. arge values of entropy correspon to uniform GCM. The energy is a measure of homogeneity. i
Statistical texture analysis of roa for moving objectives 79 3. ocal features erive from mean co-occurrence matrix For each pixel we consier increasing (+)x(+) symmetric neighborhoos, =,, 3,...,5. Insie each neighborhoo there are 8 principal irections:,, 3, 4, 5, 6, 7, 8 (Fig. 3) an we evaluate the co-occurrence matrices C,k corresponing to vector istances etermine by the central point an the neighborhoo ege point in the k irection (k =,,...,8). With a view to obtain statistical feature insensitive relatively to texture rotate, we introuce the mean co-occurrence matrix notion. For each neighborhoo type, the mean cooccurrence matrix C m is calculate by averaging the eight co-occurrence matrices (0): C m =/8(C, +C, +C,3 +C,4 +C,5 +C,6 +C,7 C,8 ), =,,...,0 (0) Thus, for 3x3 neighborhoo, = ; for 5x5 neighborhoo, = ; for 7x7 neighborhoo, = 3; for 9x9 neighborhoo, = 4, an so on. 4 3 5 6 8 7 Fig.3. The principal irections for co-occurrence matrix calculus. In orer to quantify the spatial epenence of the gray level values from the average co-occurrence matrices C m, =,,..., 0, it is necessary to compute various textural features like Contrast Con (), Energy Ene (), Entropy Ent (3), Homogeneity Omo (4) an Variance Var (5). Con = ( i j ) C ( i, j ) () i = j = Ene = C i= j= ( i, j) () Ent = C i= j= ( i, j) log( C ( i, j)) (3)
80 Dan Popescu, Rau Dobrescu, Nicoleta Angelescu Omo C ( i, j) = i= j = + i j (4) Var = [ C i= j= ( i, j) C ( i, j)] (5) In the preceing relations, x represents the imension of co-occurrence matrices. 4. Experimental Results for Texture Classification an Route Ientification by Statistical Features For algorithm testing an program valiation we use two texture images I an I (Fig. ), each partitione into sixteen regions I i (), I i (),..., I i (5), I i (6), i=,. The consiere regions have 8 x 8 pixels, an 6 grey levels. Fig. 4. Selecte regions from I an I. From these images we chosen five regions for I image: I () reference texture, asphalt; I (5) teste region, asphalt; I (4) teste region, pebble; I (8) teste region, pebble I (3) teste region, asphalt an pebble, an three regions
Statistical texture analysis of roa for moving objectives 8 for I image: I (4) teste region, grass; I (8) teste region, grass; I (3) teste region, asphalt an grass (Fig. 4). Firstly, the analysis of the simple grey level histograms (Fig. 5) emonstrates that the regions can be iscriminate with the ai of the vectors of the histogram values. The istance between the histogram vectors of the regions I () an I (5) is smaller than the istance between the histogram vectors of the regions I () an I (3) or between the histogram vectors of the regions I () an I (3). Fig.5. Grey level histogram It was also teste the efficiency of the grey level image ifference histogram in texture classification an efect region etection. With that en in view, we have consiere the same images I (), I (5), I (3), I (3). The image ifference histograms in the isplacement x = 0, y = 0 are presente in Fig. 6. In the graphical histogram representation, the value for gray level 0 is too high an irrelevant comparing with the others. Therefore it is neglecte. One can observe that the ifference image histogram has a better behavior referring to texture classification than to efect region etection an localization. Fig.6. Grey level ifference histogram Seconly, supposing that the histograms are not so ifferent, another set of statistical texture features makes possible the region classification. Thus, we can consier the co-occurrence matrices an the features erive from them. Textural
8 Dan Popescu, Rau Dobrescu, Nicoleta Angelescu features like Con, Ene, Ent, Omo, an Var are calculate from average cooccurrence matrices for ifferent istances. The normalize results are presente in Table, for = 0. The normalize characteristics are necessary because the ranges of initial characteristics can iffer too much for efficient Eucliian istance calculation. For the purpose of the evaluation of the iscriminating power of the selecte features, we have calculate the Eucliian istances between regions with similar texture:, D{I (),I (5)}, an the Eucliian istances between regions with ifferent textures: D{I (),I (4)}, D{I (),I (3)}, D{I (),I (4)}, D{I (),I (3)}. Statistical texture features for = 0 Region Ent Ene Con Omo Var Inex I ().07 4.976 0.34.30.39 I (3).693.005.547 0.973.596 I (4).706 0.843.699 0.86.50 I (5).03 4.876 0.35.33.40 I (3).849.54 0.898.86.69 I (4).867.543.83.07.04 I (8).847.37.79.03.0 Table The Eucliian istance D{I, I } between two images I an I, which are characterize by the feature vectors [C,E,Et,O,V ] T an [C,E,Et,O,V ] T, is expresse by the following relation:, I ) ( C C ) + ( E E ) + ( Et Et ) + ( O O ) + ( V ) D ( I V = (6) where: C = Con, E = Ene, Et = Ent, O = Omo, V = Var. The results of the mentione istances calculus are presente in Table. Eucliian istances between template I () an ifferent regions D{I (),I (5)} D{I (),I (4)} D{I (),I (3)} D{I (),I (4)} D{I (),I (3)} 5 0.0 5.050 4.69 4.00 3.773 0 0.05 4.563 4.57 3.577 3.448 5 0. 4.7 3.99 3.83 3.04 Table
Statistical texture analysis of roa for moving objectives 83 One can observe that the istances between two ifferent regions, like D{I (),I (4)}, D{I (),I (3)},D{I (),I (4)},D{I (),I (3)},are greater than the istances between two similar regions, like D{I (),I (5)}. In orer to evaluate the efficiency of the presente algorithm, we analyze the most unfavorable cases, namely the minimum istance between two regions coming from ifferent textures, an the maximum istance between two regions coming from the same texture. Thus, the minimum value for issimilar textures, min{d{i (),I (3),D{I (),I (4)},D{I (),I (4)},D{I (),I (3)}} = 3.04, is greater than the maximum value for similar textures, max{d{i (),I (5)}} = 0., in the large neighborhoo case ( = 5,0,5). To ameliorate the classification accuracy, a evelopment of the recognition algorithm, consisting in the attachment of new textural features, like ege point ensity per unit of area, is analyze. Thus, we consiere an ege extraction algorithm, base on binary image an logical function [], which gives tinne eges (Fig. 7). Unfortunately, the ege ensities for the analyze regions I (5), I (3), I (4), I (3), an I (4) show that this feature has not a goo iscriminating power (Table 4). The combination with the previous secon orer type statistical features will give better results in texture classification. Another isavantage of this algorithm is the epenence of the results on the threshol level for ege extraction. Fig. 0. Contour image for some regions. Ege ensities for some regions Region I (5) I (4) I (3) I (4) I (3) Den e 0.40 0.88 0.95 0.300 0.99 Table 4.
84 Dan Popescu, Rau Dobrescu, Nicoleta Angelescu 5. Concluing remarks Because it is an average co-occurrence matrix, the presente algorithm is relatively insensitive to image translation an rotation. The results confirm that the statistic secon orer features, extracte from meium co-occurrence matrices, in the case = 5, 0, 5, offer a goo iscriminating power both in the texture ientification process an in the efect region etection an ientification. The main application of the algorithm consists in roa (asphalt) ientification an efect region etection (pebble or grass) in texture images (like images from fixe camera or images from vieo camera of intelligent vehicles). The aitional features, like ifference image histograms an ege pixel ensity per unit of area, can increase the power of iscrimination for texture ientification an classification. The efficiency of the route following an efect region etection an localization epens upon the range of image partition. R E F E R E N C E S []. R.M. Haralick et al. - Textural Features for Image Classification, IEEE Trans. on Systems, Man An Cybernetics, vol. SMC-3, no.6, pp. 60-6, nov.973. []. R.M. Haralick,.G. Shapiro - Computer an Robot Vision, A.-Wesley, Pub. Co., 99. [3]. H. Tamura, S. Mori, T. Yamawaki - Texture features corresponing to visual perception, IEEE Trans. On Systems, Man an Cybernetics. vol. 6(4), pp. 460-473, 976. [4]. W. Niblack et al. - The QBIC Project: Querying Images by Content Using Color, Texture an Shape, Proc. of the Conference Storage an Retrieval for Image an Vieo Databases, SPIE, pp. 73-87, 993. [5]. F. iu, R.W. Picar - Perioicity, irectionality an ranomness: Worl features for image moeling an retrieval, IEEE Transactions on Pattern Analysis an Machine Intelligence, vol. 8, pp. 7-733, 996. [6]. B.S. Manjunath, W.Y. Ma - Texture features for browsing an retrieval of large image ata, IEEE Transactions on Pattern Analysis an Machine Intelligence, (Special Issue on Digital ibraries), Vol. 8 (8), pp. 837-84, August 996. [7]..M. Kaplan et al. - Fast texture atabase retrieval using extene fractal features, in Storage an Retrieval for Image an Vieo Databases VI, (Sethi, I K an Jain, R C, es.), Proc SPIE 33, pp.6-73, 998. [8]. J. Smith - Integrate Spatial an Feature Image System: Retrieval, Analysis an Compression, Ph. D. Thesis, Columbia University, 997. [9]. Y. Deng, - A Region Representation for Image an Vieo Retrieval, Ph. D. thesis, University of California, Santa Barbara, 999. [0]. W.Y. Ma, - Netra: A Toolbox for Navigating arge Image Databases, Ph. D. thesis, University of California, Santa Barbara, 997. []. D. Popescu, R.. Dobrescu, V. Avram, St. Mocanu Deicate Primary Image Processors For Mobile Robots, WSEAS Trans. on Systems, Issue 8, Vol.5, pp. 93-939, August 006.