Brachiaria species identification using imaging techniques based on fractal descriptors
João Batista Florindo, Núbia Rosa da Silva, Liliane Maria Romualdo, Fernanda de Fátima da Silva, Pedro Henrique de Cerqueira Luz, Valdo Rodrigues Herling, Odemir Martinez Bruno
BBrachiaria species identification using imaging techniques based on fractal descriptors
Jo˜ao Batista Florindo ∗ N´ubia Rosa da Silva † Institute of Mathematics and Computer Science, University of S˜ao Paulo (USP),Avenida Trabalhador s˜ao-carlense, 400 13566-590 S˜ao Carlos, S˜ao Paulo, Brazil
Liliane Maria Romualdo, ‡ Fernanda de Ftima da Silva, § PedroHenrique de Cerqueira Luz, ¶ and Valdo Rodrigues Herling ∗∗ Faculdade de Zootecnia e Engenharia de Alimentos,Universidade de S˜ao Paulo (USP), Pirassunuga, S˜ao Paulo, Brazil
Odemir Martinez Bruno †† (Dated: December 30, 2014)The use of a rapid and accurate method in diagnosis and classification of species and/or cultivarsof forage has practical relevance, scientific and trade in various areas of study. Thus, leaf samples offodder plant species Brachiaria were previously identified, collected and scanned to be treated bymeans of artificial vision to make the database and be used in subsequent classifications. Forage cropsused were:
Brachiaria decumbens cv. IPEAN;
Brachiaria ruziziensis
Germain & Evrard;
BrachiariaBrizantha (Hochst. ex. A. Rich.) Stapf;
Brachiaria arrecta (Hack.) Stent. and
Brachiaria spp .The images were analyzed by the fractal descriptors method, where a set of measures are obtainedfrom the values of the fractal dimension at different scales. Therefore such values are used as inputsfor a state-of-the-art classifier, the Support Vector Machine, which finally discriminates the imagesaccording to the respective species.
I. INTRODUCTION
The knowledge and understanding of functional prop-erties of plants make possible to develop advances in sev-eral areas like medicine to cure diseases, produce andimprove species to feed people and animals [1]. Involvingthis last topic, the analysis of consumption by animalsis very important because the animal production can beimproved from grazed pastures. Specifically, ruminantshave their amount of feeding directly linked with the pro-cesses of particle-size reduction during the feeding. Dueto the physical strength of grasses, ruminant animals con-sume larger quantities of forages with lower resistance tobreakdown [2]. Since the grass is extremely importantfor animal food, it becomes the object of study here be-ing one of the main forms of ruminant feeding is throughgrazing
Brachiaria .The genus Brachiaria consists of herbaceous, perennialor annual, erect or decumbent. Belonging to the grass ∗ jbfl[email protected] † [email protected] ‡ [email protected] § [email protected] ¶ [email protected] ∗∗ [email protected] †† [email protected] family, it presents approximately one hundred species,and therefore their correct classification is of great im-portance for the genetic improvement of forage speciesand purity of the species in the field of seed production[3–5]. Grouping plants into genus is a way of facilitatingthe understanding of the diversity of the grasses, accord-ing to the particularities of each species [3].The classification of grasses is mainly based on thecharacters of the spikelet structure and its arrangement.The main taxonomic feature of the genus Brachiaria , de-spite not being present in many species, is the reversedor adaxial position of the spikelet and of ligule. Thisspikelet is relatively large, oval or oblong and it is ar-ranged regularly in a row along one side of the rachis.However, the taxonomy of this genus is not satisfactory,both in terms of species composition and in their inter-relationship with other genus. Problems related to incor-rect classifications often occur among Brachiaria speciescommonly used in pastures, as well as among accessionsof germplasm collections.Since there is a great variability among natural speciesof
Brachiaria , to identify really discriminant charactersbecomes a difficult task so that seeking for techniquesthat improve the identification will contribute to studieswithin this theme, as well as provide a reasonable sys-tem of classification, since there is no such system for thegenus
Brachiaria . Thus, the objective of this study was a r X i v : . [ c s . C V ] D ec to take the volumetric Bouligand-Minkowski and Prob-ability fractal descriptors associated with the PrincipalComponent Analysis transform to classify samples fromfive species of Brachiaria cultivars. This methodologyprovides a set of coefficients for each image that will char-acterize it. The tests were performed in a large databasewith almost ten thousand of samples including the supe-rior and inferior face of leaves obtaining 92.84% of cor-rectness rate in the classification (of all leaves).The text in this paper is organized as follows. In Sec-tions II, III and IV the theory of the methods is ex-plained. In Section V the description of the methodBouligand-Minkowski with probability dimension ap-plyed to texture characterization. Section VI shows theexperiments in a database of
Brachiaria leaves and inSection VII the results are analysed. The paper is con-cluded in Section VIII.
II. FRACTAL GEOMETRY
Fractal geometry [6] is the area of Mathematics whichdeals with fractal objects. These are gometrical struc-tures characterized by two main properties: the infiniteself-similarity and infinite complexity. In other words,these elements are recursively composed by similar struc-tures. In addition, they exhibit a high level of detail onarbitrarily small scales.In the same way as in the Euclidean geometry, frac-tal objects are described by numerical measures. Themost widespread of such measures is the fractal dimen-sion. Given a geometrical set X (set of points in the N -dimensional space), the fractal dimension of D ( X ) isexpressed in the following equation: D ( X ) = N − lim (cid:15) → log( M ( (cid:15) ))log( (cid:15) ) , where M is a fractality measure and (cid:15) is the scale param-eter. The literature presents various definitions for thefractality measure [7, 8]. The following sections describetwo of such approaches. A. Bouligand-Minkowski
One of the best-known methods for estimating the frac-tal dimension of an object is the Bouligand-Minkowskiapproach [7]. In this solution, the grayscale image I :[1 : M ] × [1 : N ] is mapped onto a surface S , using thefollowing relation: S = { ( i, j, k ) | ( i, j ) ∈ [1 : M ] × [1 : N ] , k = I ( i, j ) } . Then, each point having co-ordinates ( x, y, z ) is dilatedby a sphere with variable radius r . Therefore, the di-lation volume V ( r ) may be computed by the followingexpression: V ( r ) = (cid:88) χ D ( r ) [( i, j, k )] , where ( i, j, k ) are points in the surface S , χ is the char-acteristic function and D ( r ) refers to the following set: D ( r ) = { ( x, y, z ) | [( x − P x ) +( y − P y ) +( z − P z ) ] / ≤ r } , in which ( P x , P y , P z ) ∈ S . In practice, the EuclideanDistance Transform [9] is used to determine the value of V ( r ).Finally, the fractal dimension D BM itself is given by: D BM = 3 − lim r → log( V ( r ))log( r ) . The limit in the above expression is calculated by plottingthe values of V ( r ) against r , in log − log scale, and thelimit is the slope of a straight line fitting the log − logcurve. The Figure 1 exemplify the process. (a) (b)(c) (d) Figure 1. Bouligand-Minkowski dilation process. a) Gray-level image. b) Surface with radius 1. c) Surface with radius2. d) Surface with radius 3.
III. PROBABILITY DIMENSION
Also refered to as Voss dimension, this method obtainsthe fractal dimension from the statistical distribution ofpixel intensities within the image [10].Like in the Bouligand-Minkowski method, the imageanalyzed is converted into a three-dimensional surface S . Hence, the surface is surrounded by a grid of cubeswith side δ . By varying the value of δ , the informationfunction N P is provided through: N P ( δ ) = N (cid:88) m =1 m p m ( δ ) , where N is the maximum possible number of pointswithin a single cube and p m is the probability of m pointsin S belonging to the same cube.Finally, the fractal dimension D is estimated by thefollowing relation: D = − lim δ → ln N P ln δ . (1)As with the Bouligand-Minkowski approach, the limit iscomputed by a least squares fit. IV. FRACTAL DESCRIPTORS
Fractal descriptors are a methodology that extractsmeaningful information of an object of interest by meansof an extension of the fractal dimension definition [11–13].Instead of using the dimension for describing the object,the fractal descriptors u use the entire set of values inthe fractality curve: u : log( (cid:15) ) → log( M ) . (2)The values of u can be used directly to compose the fea-ture vector [12] or after some sort of transform [13]. Inthe present work, we use the raw data of log( M .The fractal descriptors extract significant informationfrom the object at different scales. The values of thefractality for larger radii measure the global aspect ofthe structure. In the case of plant leaves like those an-alyzed here, these data concern important informationregarding the general aspect of the nervure distribution.On the other hand, the smallest radii provide essential in-formation on the variability of the pixel intensities insidea local neighborhood. Biologically, these micro-patternsare tightly related to the constitution of the plant tissue. V. PROPOSED METHOD
The proposed methodology combines the previouslydescribed approaches to compose a precise and robusttool to identify plant species from an image of the leafof
Brachiaria . The feature vector is obtained by con-catenating the Bouligand-Minkowski and Probability de-scriptors and then applying a dimensionality reductionprocedure to the merged descriptors.Let the Bouligand-Minkowski descriptors be repre-sented by the vector (cid:126)D : (cid:126)D = { x , x , ..., x n } and the Probaility features expressed through (cid:126)D : (cid:126)D = { y , y , ..., y n } . Then, in a problem of species discrimination over adatabase of leaf images, we can define two feature matri-ces, M (1) m × n and M (2) m × n , one for each descriptor, where the rows correspond to the descriptor vectors for each im-age to be analyzed. After that, the matrices are concate-nated horizontally, giving rise to the matrix M . Next,this matrix is transformed into one matrix ˜ M :˜ M = M inter M − intra , (3)where M intra and M inter are, respectively, the inter andintra-class matrix. The intra-class matrix is defined by: S intra = K (cid:88) i =1 (cid:88) i ∈ C i ( X ( i, . ) − C i )( X ( i, . ) − C i ) T , (4)where C i is the i th class in M , K is the total number ofclasses, M ( i, . ) expresses the i th row (sample) of M and C i is a row vector representing the average descriptorsof each class C i . On its turn, the inter-class matrix isprovided by the following expression: S inter = K (cid:88) i =1 N i ( C i − M )( C i − M ) T , (5)in which N i is the number of samples of the i th class.The concatenation process ensures that the resultingdescriptors emphasize the best discriminative propertiesof each fractal approach. In this case, both descriptorsprovide a different perspective of the object. While theBouligand-Minkowski capture a multiscale mapping ofthe texture morphology, the Probability method gives adetailed description of the statistical distribution of thepixels along the gray-level image. The sum of these view-points makes possible a detailed description of the pat-terns within the image, at different scales.In the present study, the cancatenated descriptors areobtained from the windows extracted from the scannedimage of the analyzed grass. The Figure 2 illustrates theprocess involved in computing the descriptors, since theoriginal image until the descriptors themselves. VI. EXPERIMENTS
The leaf samples were collected in the agrostologic fieldat the Faculdade de Zootecnia e Engenharia de Alimen-tos (FZEA-USP), which is located in Pirassununga cityat state of S˜ao Paulo, Brazil. The leaf images were col-lected manually, directly from live plants, with extremecarefulness in not damaging the leaf surface. All plantsgrew with ideal conditions of nutrients and lighting. Inthis study, five species were took:
Brachiaria decum-bens
Stapf. cv. Ipean
Brachiaria ruziziensis
Germain& Evrard,
Brachiaria brizantha (Hochst. ex. A. Rich.)Stapf.,
Brachiaria arrecta (Hack.) Stent. and
Brachiariaspp. .After collecting the leaves, they were submitted to ascanning procedure, where the superior and inferior faceof the leaf was scanned in 1200 dpi ( dots-per-inch ) reso-lution and saved in a lossless image format with no com-pression. It was obtained 5 sheets with 10 different tillers, log(V(1)) log(V(1)) ... log(V(r))Boulgand-Minkowski ProbabilityCanonical transformlog(NP(1)) log(NP(1)) ... log(NP(r))
Figure 2. A diagram illustrating the steps to obtain the proposed descriptors. totalling 100 samples (50 images from the superior facesof the leaves and 50 images from the inferior faces).As the leaves were scanned manually, they were notproperly aligned. Therefore, the images were veticallyaligned according to the central axis using the Radontransform [14]. Subsequently, for mounting the database,it were randomly obtained about 20 sub-images of 200 ×
200 pixels without overlapping and considering all theleaf surface, avoiding stains margins and allowing thecentral vein (Figure 3). At Figure 3 it can also be seenthe preparation of the signature for each sample. Themethod is applied to each sub-image from the sample(superior and inferior face of the leaf) to obtain a fea-ture vector F with features { F , F , F , ..., F n } where n is the number of features. Afterward, the signaturefrom the superior face of the image is concatenaded withthe signature from the inferior face to generate the finalsignature of the sample. Therefore, the final databaseis composed by 9832 images, 4916 images from superiorface and 4916 from inferior face of leaves. Figure 4 showssome samples for each class of the database.The proposed method is applied to compute descrip-tors from the images of the analyzed grass species. There-fore, the obtained descriptors are used as the input of aclassifier, in this case, the Suport Vector Machine method[15]. The classification is carried out in a 10-fold cross-validation scheme [15]. VII. RESULTS
The graph in the Figure 5 shows the success rate ofeach compared texture descriptors when the number ofdescriptors is varied. We notice that even with only 4 el- ements, the proposed method achieves a correctness rateclose to 90%. Gabor and Fourier have a close behav-ior, while the fractal descriptors presents an outstandingperformance for any number of elements greater than 3.The Table I shows the best success rate achieved byeach method by using an optimal number of descriptors.The success rate is accompanied by other important mea-sures related to the performance of each approach appliedto discriminate the grass species. In this table,
N D is thenumber of descriptors, CR is the correctness rate, κ is the κ index and AE AE Method ND CR (%) κ AE1 AE2Fourier 30 89.79 0.88 0.10 0.10Gabor 21 88.02 0.86 0.12 0.12Proposed method 30 92.84 0.91 0.07 0.07Table I. Success rate for different approaches.
The tables II, III and IV exhibit the confusion matricesfor each compared descriptor. These tables are helpful todescribe either the correctly classified samples as well asthe false negatives and false positives, outside the maindiagonal. We observe that, despite some minor differ-ences among the methods, the methodology developed
Figure 3. Samples acquisition. Sub-images of 200 ×
200 pixels size obtained from samples. A signature F = { F , F , F , ..., F n } is extracted for each sub-image and, afterward, the signature from the superior and inferior face of the leaf are concatenatedto obtain the final signature. in the present study demonstrated to be the most reli-able solution to identify the grass samples. Reinforcingthe values on the Table I, the type 1 and 2 errors are verysimilar, expressing the homogeneity of the distinguishedclasses.
913 7 20 6 1412 888 19 8 7325 15 925 6 53 14 2 952 920 80 4 10 886Table II. Confusion matrix for the proposed method. 882 21 22 2 3320 884 22 16 5822 24 877 34 1914 20 21 919 652 74 12 10 852Table III. Confusion matrix for the Fourier method.
The great performance achieved by the proposed frac-tal descriptors is due to the nature of the fractal model-ing, as mathematical fractals and natural objects have agreat deal in common. The similarities are related to thehigh complexity usually found in the nature as well as the (a) (b)
Figure 4. Samples of final database. Each row represents samples of the same specie, from top to bottom:
Brachiaria decumbens , Brachiaria ruziziensis , Brachiaria brizantha , Brachiaria arrecta and
Brachiaria spp. . (a) Face superior and (b) face inferior ofleaf. S u cc e ss r a t e ( % ) ProposedGaborFourier
Figure 5. Graph of the success rate as function of the numberof descriptors. 891 35 2 9 2333 829 13 59 660 2 958 15 140 55 19 813 5337 102 5 20 836Table IV. Confusion matrix for the Gabor method. self-similarity property, which also appears often in partsof plants, like leaves, flowers, etc. Actually, the fractaldescriptors are tightly related to important physical at-tributes of the leaf, such as roughness, reflectance anddistribution of colors and brightness levels. In turn, thisset of properties is capable of identify plant species faith-fully, using their digital image representation, as demon-strated in [11]. The present study confirms such reliabil-ity and robustness of fractal descriptors and shows thatthis is a powerful tool for the species categorization ofthe grasses analyzed here.
VIII. CONCLUSIONS
The present study proposed a combination of fractaldescriptor approaches to discriminate among species of
Brachiaria grass, based on the digital images from theirleaves. The proposed solution achieved a high successrate even using a low number of features. Such resultconfirms the effectiveness and reliability of fractal de-scriptors in this kind of task.This result is also remarkable from a biological perspec-tive, as
Brachiaria grasses are one of the most importantfoods for animals that are used for the labor and hu-man consumption. The precise discrimination of speciesmakes possible to better understand the distribution ofspecies in a region and, as a consequence, to optimize thenecessary attention for that region.Despite the importance of this study, the literatureshows very few works on
Brachiaria classification andthe present is the first to obtain such a great effective-ness. Such so good results suggest the use of fractal de-scriptors as a powerfull method to identify these speciesand markedly help the taxonomy specialist.
ACKNOWLEDGMENTS