LBP maps for improving fractal based texture classification

Neurocomputing 266 (2017) 1–7

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Neurocomputing journal homepage: www.elsevier.com/locate/neucom

LBP maps for improving fractal based texture classification André Ricardo Backes a,∗, Jarbas Joaci de Mesquita Sá Junior b a

Faculdade de Computação, Universidade Federal de Uberlândia, Av. João Naves de Ávila, 2121, Uberlândia CEP: 38408-100, Minas Gerais, Brasil Curso de Engenharia de Computação Campus de Sobral, Universidade Federal do Ceará, Rua Estanislau Frota, S/N, Centro, Sobral CEP: 62010-560, Ceará, Brasil

b

a r t i c l e

i n f o

Article history: Received 13 November 2016 Revised 7 March 2017 Accepted 9 May 2017 Available online 17 May 2017 Communicated by Dr. Y Gu Keywords: Texture recognition Image analysis Fractal dimension Local Binary Pattern

a b s t r a c t This paper presents an innovative manner of obtaining discriminative texture signatures by using the LBP approach to extract additional sources of information from an input image and by using fractal dimension to calculate features from these sources. Four strategies, called Min, Max, Diff Min and Diff Max, were tested, and the best success rates were obtained when all of them were employed together, resulting in an accuracy of 99.25%, 72.50% and 86.52% for the Brodatz, UIUC and USPTex databases, respectively, using Linear Discriminant Analysis. These results surpassed all the compared methods in almost all the tests and, therefore, confirm that the proposed approach is an effective tool for texture analysis.

1. Introduction Since the studies of Julesz [23], texture analysis has been a focus of intensive research. Texture is an excellent descriptor of object’s appearance and plays a key role in computer vision and pattern recognition applications [2,11,13,40]. Nevertheless, it is a term that has a great variety of definitions. Some authors describe texture as a repetition of sub-patterns (in its exactly form or with small variations) over the image area [5,36,43]. Such definition is adequate for texture patterns representing man-made materials. However, a large scope of natural textures (e.g., images of leaf surface, bark, smoke etc.) does not fit in this description as they present a persistent stochastic patterns with cloud-like appearance [24]. Usually, a set of descriptors is extracted from a texture sample for characterization purposes. Then, two sets of descriptors (from test and target images) are compared using a similarity measure in a matching scheme. To accomplish good texture description and classification, a texture descriptor must be able to represent satisfactorily the texture and compensate variations that may distort its original appearance, such as variation in illumination, rotation, scale and viewpoint [25]. Describing a texture pattern can be quite challenging and it has motivated intense research over the years, as well as a great va-

∗

Corresponding author. E-mail addresses: [email protected] (A.R. Backes), [email protected] (J.J. de Mesquita Sá Junior). http://dx.doi.org/10.1016/j.neucom.2017.05.020 0925-2312/© 2017 Elsevier B.V. All rights reserved.

© 2017 Elsevier B.V. All rights reserved.

riety of texture analysis methods. Texture descriptors can be obtained by using agent-based methods that explore the relation among pixels in a certain region of the image [8]. Image patches of predefined shape and size may be used to create a feature space of histograms of equivalent patterns (HEP) [14]. In [36], the authors propose the use of local binary patterns (LBP) as an approach to achieve rotation invariant texture descriptors. This motivated the development of other approaches that aimed to improve the original LBP [9,20,44]. In [37], the authors propose a globally multiscale LBP descriptor that encodes the correlation between scales. Global appearance and local structure of images can be combined into a spectral histogram that encodes the distributions of a bank of filters responses [29]. In [28], micro-structures present in the texture are the object of analysis. In [7], texture is modeled as a complex network and topological properties of this network are used as texture descriptors. Fractal dimension and invariant filter response are combined into a single texture descriptor in [38]. In [34], the authors investigate sets of texture descriptors to be extracted from co-occurrence matrices. In a more restrict context, a line of research in texture analysis has focused on pre-processing approaches that improve the descriptors of a determined method. For instance, in [33], the authors propose preprocessing techniques in order to improve the descriptors extracted from co-occurrence matrices. The paper [30] presents a face recognition system in which an input face image is preprocessed by several approaches and different descriptors are obtained from the resulting images. In [39], pixels in a texture image are modeled as a gravitational system in collapsing process.

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A.R. Backes, J.J. de Mesquita Sá Junior / Neurocomputing 266 (2017) 1–7

Fig. 1. Example of calculus of the LBP code using a 3 × 3 rectangular neighborhood. Table 1 Evaluation of the combination of different sets of descriptors using LDA. Patterns combined Original

Min

Max

X X X X X X X

X X X

X

Diff Max

X X X X

X

Diff Min

X

X X X

X X X

After this preprocessing step, the Bouligand–Minkowski fractal dimension is obtained from each resulting image (collapsing stage) in order to construct a texture signature. In this paper, we propose a hybrid approach that obtains LBP maps from an original input image and extracts descriptors from them by using the Bouligand-Minkowski fractal dimension. To describe this method, the remaining of this paper is organized as follows: Section 2 reviews the concepts used in local binary patterns (LBP) while Section 3 describes the fractal dimension (FD) method used. In Section 4 we show how to combine LBP and FD into an approach that improves texture discrimination. Texture image datasets and experiments are described in Section 5. Results are presented and discussed in Section 6, while Section 7 concludes the paper. 2. Local binary patterns Recently, local binary patterns (LBP) have been proposed as a new tool for discriminating texture images [36]. LBP constitutes a very discriminative source of information for different texture patterns. Their advantages led to the development of many variation approaches, each one exploring and extending a different aspect of the original method [16,20]. The method is based on the analysis of the differences among the intensities of a central pixel and its neighboring pixels. The variations in intensities and positions of these differences generate a pattern code that is associated to the central pixel. Letting gc be the gray level in a central pixel and gp , p = 1, . . . , P, be the gray level in its P neighbors, we compute the LBP pattern code as

LBPP,R =

P−1 

s ( g p − g c )2 p

(1)

p=0

with

s (x ) =



1 0

x≥0 x<0

(2)

where R is the radius of the neighborhood. Different approaches can be used to select the neighboring pixels, as a circular or the

No of

Success rate (%)

descriptors

Brodatz

UIUC

USPTex

24 24 24 24 24 24 40

99.50 99.00 98.75 99.25 99.50 99.25 99.25

68.40 68.40 65.60 67.80 68.50 68.30 72.50

84.60 84.77 83.29 83.07 83.99 83.81 86.52

traditional 3 × 3 rectangular (Fig. 1) neighborhood. Neighboring pixels are visited in clockwise order and their gray levels are compared to the central pixel. If the intensity of the neighboring pixel is greater than the central pixel, we assign value 1 to it; otherwise, we assign value 0. As a result, we obtain a binary sequence that is converted into a decimal value. This value is the LBP code associated to the central pixel. By computing the LBP code for each pixel, we obtain the LBP map of the image, which can be used to compute a histogram representing the texture pattern.

3. Bouligand–Minkowski fractal dimension Introduced by Benoit Mandelbrot in 1970s, fractals are objects that exhibit a repeating pattern at different scales. Another remarkable characteristic of fractals is their non-integer dimension, called fractal dimension, which measures the self-similarity of the fractal through the scales. Fractal dimension also enables us to describe an object in terms of space occupation, a property related to its complexity [35,31,15]. Even though fractals are purely mathematical objects and do not exist in the real world, the fact that the fractal dimension is a measure of complexity based on space occupation enables its use in real world objects, such as images. This has motivated the development of different approaches to compute fractal descriptors from images, with special attention to texture analysis applications [5,17,18]. Among the many approaches in the literature, Bouligand– Minkowski fractal dimension is considered one of the most accurate [15,17,41]. Initially proposed for shape and later extended to texture analysis, Bouligand–Minkowski method considers the influence volume of a texture pattern in order to compute its fractal dimension. This influence volume is very sensitive to structural changes in the texture (such as changes in pixels values and positions) and it can be easily computed through the dilation of the texture pattern using spheres of radius r. Let f: I → C be a function that maps a graylevel image I to a point cloud C ∈ R3 , so that,

C = {(x, y, z )|I (x, y ) = z}.

(3)

A.R. Backes, J.J. de Mesquita Sá Junior / Neurocomputing 266 (2017) 1–7

3

Once we converted the image into a cloud point, we use a sphere of radius r to simultaneously dilate each point of the cloud, c ∈ C. As a result, the dilation process generates the volume in the space in which the cloud point has influence, i.e., the influence volume V(r). Basically, the influence volume of a texture pattern is the sum of the points in the space whose distance from its respective cloud point is not larger than r. Mathematically, the influence volume V(r) is defined as









V (r ) = c ∈ R3 |∃c ∈ C : c − c  ≤ r .

(4)

The main reason why the influence volume V(r) is sensitive to structural changes lies in the fact that spheres produced by different points interfere to each other as the dilation radius r increases. For smaller radii, each point is able to freely dilate and the influence volume is similar to the sum of the volume of the spheres. However, as the radius increases, nearby spheres start to intersect to each other, changing how the influence volume increases. The amount of intersections among spheres depends on the texture pattern evaluated. Thus, using different radius values, fractal descriptors can be computed directly from influence volume V(r) [15,17] or by computing the fractal dimension D as

D = 3 − lim r→0

log V (r ) , log (r )

Fig. 2. Depending on the initial point, it is possible to generate 8 different LBP masks.

(5)

where the limit can be easily computed as the slope α of the line that approximates the log–log curve log (r) × log V(r), thus resulting in

D = 3 − α.

(6)

4. Proposed approach In order to compute the LBP method, the approach described in Section 2 must be applied to all the pixels of the image. This procedure results in a map of LBP codes associated to the texture pattern. From this map, we are able to compute a histogram, which is commonly used as descriptors for the original texture. One possible flaw in such approach lies in the fact that histograms are only capable of describing the frequency of each pattern, they do not give us any clue about the spatial distribution of such patterns. That means that textures with equal frequency but different spatial distribution of patterns would appear as the same for the method. Moreover, one must consider that the calculus of the LBP code depends on the initial point used to generate the binary code in Fig. 1. By considering the traditional 3 × 3 rectangular neighborhood, we have 8 possible choices of neighboring pixels to be used as initial points. Each initial point results in a different LBP mask (Fig. 2) and generates a different LBP map for the same image, as shown in Fig. 3. Although each LBP map is not able to provide spatial information of the image, their combinations give clues about the spatial distribution and organization of the pixels. Among the many possible ways to combine different maps, we propose using the minimum and maximum values at each pixel to build two new code maps, LBPmin and LBPmax

LBPmin (x, y ) = min LBPi (x, y ),

(7)

LBPmax (x, y ) = max LBPi (x, y ),

(8)

i=1,...,8

i=1,...,8

where LBPi represents a LBP map computed for a specific initial point i = 1, . . . , 8. From the minimum and maximum code maps, we are also able to build code maps that represent the sum of the differences among the maps

LBPdi f f min (x, y ) =

8  i=1

(LBPi (x, y ) − LBPmin (x, y )),

(9)

Fig. 3. Lena image and LBP maps computed, respectively, for each LBP mask in Fig. 2.

and

LBPdi f f max (x, y ) =

8 

(LBPmax (x, y ) − LBPi (x, y )).

(10)

i=1

These two maps, LBPdiffmin and LBPdiffmax , are normalized to the interval [0, . . . , 255], so that the range of values of them is the same for any LBP map. These four maps (LBPmin , LBPmax , LBPdiffmin and LBPdiffmax ) represent not only the distribution of LBP codes, but also how spatially they are deposited, as shown in Fig. 4. By estimating the fractal dimension (Section 3), we are able to measure the amount of irregularity (how homogeneous/heterogeneous it is) present in a LBP map. Fractal dimension can also be used to describe the original image. Since image patterns (such as LBP maps) have finite size and limited resolution, fractal dimension is a

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Fig. 4. Lena image and the four proposed code maps.

multi-scale measure, i.e., its value changes as we vary the dilation radius r. Thus, the following feature vector is used to describe an image pattern in terms of the relation between fractal dimension D(r) and dilation radius r

ψ (rmin , rmax ) = [D(rmin ), D(rmin + 1 ), . . . , D(rmax )],

(11)

where r = {rmin , rmin + 1, . . . , rmax } is the set of dilation radii used.  (r , rmax ) can be used to describe both the origThe vector ψ min inal image or any of the proposed LBP maps (LBPmin , LBPmax , LBPdiffmin and LBPdiffmax ). By using concatenation, we are able to combine descriptors from different patterns p1 , p2 . . . , pN into a  single feature vector ϕ

  ϕ p1 ,...,pN (rmin , rmax ) = ψ p1 (rmin , rmax ), . . . , ψ pN (rmin , rmax ) .

(12)

5. Experiments To evaluate our method’s accuracy, we used three wellestablished benchmark image databases. They are: • Brodatz [10]: we used 40 classes (10 images per class) from the original Brodatz dataset. Each image is 20 0 × 20 0 pixel size with 256 gray levels. • UIUC [27]: the original database is composed of 25 classes (40 images per class and each image is 640 × 480 pixel size). We used the whole dataset, but each used sample is an image 200 × 200 pixel size cropped from the upper-left side of each original image. This approach was used to decrease the computational cost. Again, each image has 256 gray levels. • USPTex [1,6]: this is a color database composed of 191 classes (12 images per class) representing scenes of everyday life, such as seeds, roads, walls, vegetation etc. The images are 128 × 128 pixel size and were converted into grayscale (only luminance was considered). For classification, we used the Linear Discriminant Analysis (LDA) [19]. This is a statistical classifier based on the Bayes theory

and that considers that all the samples have the same covariance matrix. We chose this classifier because it is robust, deterministic and do not present the common problems of the non-linear methods, such as underfitting, overfitting or a high number of parameter values to choose. As validation strategy, we adopted the leave-one-out cross-validation. In this approach one sample is used for testing and the remainder for training and this procedure is repeated until all the samples are used for testing. The performance measure was the mean of all the accuracies. We also adopted a Support Vector Machine (SVM) for a second classification experiment. For this purpose, we used LIBSVM [12], which is a public library for SVMs. We adopted a linear SVM with the default parameter values of this library. The approach used for our multi-class problems was “one-against-one”. As validation strategy, we adopted the 5-fold approach (the dataset is divided into 5 subsets, one for testing and the remainder for training). Once again, our performance measure is the mean of the accuracies. Finally, because 5-fold is non-deterministic, we performed 101 runs per experiment and adopted the median value as our definite accuracy. To assess the accuracy of our method, we compared it to other texture analysis methods. They are: • Fourier descriptors [42]: a Fourier transform was applied over the input image and a shifting operation was performed to centralize the low frequencies. Next, the spectral image was divided into Isd /2 − 1 (Isd is the smallest dimension of the image) radial distances equally distributed. In this way, each attribute of the feature vector is the sum of the absolute values of the coefficients between two consecutive radial distances (except for the first descriptor, which is the sum of the absolute values between the first radial distance and the center of the spectral image). • Gabor filters [32]: a Gabor filter is basically a Gaussian modulated by a sinusoid. When an image is convolved with this filter, some image characteristics are emphasized according to

A.R. Backes, J.J. de Mesquita Sá Junior / Neurocomputing 266 (2017) 1–7

•

•

•

•

•

•

the sinusoidal direction and frequency. In this paper we used 24 filters (6 rotations, 4 scales, and minimum and maximum frequencies of 0.04 and 0.5, respectively). Next, we extracted the mean and standard deviation of the magnitude of the coefficients, thus creating a feature vector of 48 attributes. This procedure and parameter values are present in [32] and we also used its mathematical rules to create the other parameter values of the filters. Wavelet descriptors [26]: we performed three 2D-wavelet dyadic decompositions using Daubechies 4 and extracted the energy and entropy from the horizontal, vertical and diagonal details, thus resulting in a signature of 18 features. Tourist walk [8]: this method interprets each pixel as a city. A tourist starts at determined city and visits the next city (among the neighboring pixels) according to the rule of going to the nearest or farthest city, where the distance is the difference (in modulus) between the intensities of the pixels. The tourist has a memory μ that allows it to remember cities previously visited. In this way, according to the memory μ, the tourist’s trajectory has two elements: a path of cities t visited only one time and a cycle p of cities continuously visited. Based on t, p and μ, it is possible to create histograms that provide an image signature. In this paper, we used μ = {0, 1, . . . , 5}, according to [8], thus resulting in a feature vector of 48 attributes. Co-occurrence matrices [22]: this method quantifies pairs of pixels in a determined direction θ and distance d. In this paper we used non-symmetric matrices with θ = {0◦ , 45◦ , 90◦ , 135◦ } and distances d = {1, 2}. The obtained measures were energy and entropy, resulting in a signature of 16 features. LBPV [21]: this is a modified scheme of traditional LBP [36] descriptor that uses the rotation invariant measurement of the local variance. We set the radius = 3, neighborhood = 24 with uniform patterns, totaling 555 features. These are the best parameters in the author’s paper for Outex database. We also used global matching using 2 principal orientations for each image in classification task. This method has its own classification approach. Lacunarity 3D [4]: this technique expands the gliding-box lacunarity concept by gliding the box over the gray level intensity axis of the texture. Then, it computes the number of gaps inside each cubic box of size r × r × r. 39 lacunarity values were obtained by using box sizes from r = 2, . . . , 40. LBP lacunarity [4]: based on the gliding-box lacunarity, this method uses local threshold to enhance local features of the texture pattern. This enables us to compute lacunarity in terms of the local binary patterns that exist in the image. 11 lacunarity values were obtained by using box sizes from r = 2, . . . , 12.

6. Results and discussion Prior to using our approach, one must choose the best interval of radius values, rmin , rmax , to characterize the sample through fractal dimension, where rmin and rmax represent, respectively, the initial and final radius values of the range of dilation radii used to compute the Bouligand–Minkowski fractal dimension used in  . As initial radius, we propose using r the feature vector ψ min = 3. For rmin < 3, the dilation radius is too small and the Bouligand– Minkowski computes a log–log curve with few points, thus resulting in a poor description of the texture pattern. Once defined the initial radius, one must choose the final radius rmax . To accomplish that task, we evaluated the performance (by using LDA) of different values for rmax , as shown in Fig. 5.  feature vectors computed In this experiment, we compared ψ from our four proposed LBP maps (LBPmin , LBPmax , LBPdiffmin and LBPdiffmax ). We also compared the LBP maps to the descriptors computed directly from the original input image. Surprisingly,

5

Table 2 Comparison results for different texture methods using LDA and SVM (except for LBPV, which has its own classification approach). Method

Success rate (%) Brodatz

Fourier descriptors Co-occurrence matrices Gabor filters Wavelet descriptors Tourist walk Fractal dimension LBPV Lacunarity 3D LBP lacunarity Proposed approach

UIUC

USPTex

LDA

SVM

LDA

SVM

LDA

SVM

88.50 93.75 97.00 87.50 95.50 93.75 82.25 95.75 83.50 99.25

83.75 64.00 95.25 79.50 94.00 44.25 82.25 84.25 64.75 96.25

34.10 41.10 56.50 41.00 48.10 48.70 33.70 53.40 34.20 72.50

51.30 34.60 61.80 42.00 54.60 29.60 33.70 59.10 39.50 65.90

61.56 73.69 89.22 68.28 64.66 62.09 39.70 67.23 48.47 86.52

49.30 15.92 85.86 51.70 55.24 18.67 39.70 64.84 33.38 74.43

Fig. 5. Impact of the number of fractal descriptors computed for each LBP patterns in Brodatz dataset.

descriptors computed from the LBP maps presented an inferior performance in comparison to the ones computed from the original image. Such setback should not be interpreted as a failure of our approach but, instead, as an indication that the proposed LBP maps should be used as complementary descriptors and not as the main descriptors of an image. Also, for the final radius rmax , the larger the radius the higher the success rate. However, as the radius increases, the improvement in the discrimination ability of the method decreases and the computation cost involved in the calculus of the influence volume grows. Thus, we propose using rmax = 10 as this value provided a good texture discrimination and an acceptable computation cost. Considering that the proposed LBP maps should be used as complementary descriptors for the main texture pattern, we must evaluate their combination in the feature vector ϕ p1 ,...,pN (rmin , rmax ). Table 1 shows the results (obtained by using LDA) yielded by some combinations of image patterns when using (rmin , rmax ) = (3, 10 ), which results in 8 fractal descriptors for pattern. In order to simplify the analysis, we evaluated pairs of LBP maps in combination with the descriptors from the original texture pattern. Results show that the inclusion of any pair of LBP maps improves the success rate of the original image’s descriptors (Fig. 5) in, at least, 5.00% in the Brodatz dataset. In the UIUC and USPTex datasets, we notice a similar behavior (at least, 16.90% and 20.98%, respectively) when using any pair of LBP maps. Moreover, the use

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A.R. Backes, J.J. de Mesquita Sá Junior / Neurocomputing 266 (2017) 1–7

of the four maps provides an improvement of, at least, 4.00% and 1.75% in the results of the UIUC and USPTex datasets, respectively, when compared to any pair of LBP maps. On the other hand, there was no improvement using the four maps in the Brodatz dataset, which is likely due to the already higher results achieved. We also compared our approach to traditional texture analysis methods. Results for each method are presented in Table 2. For this comparison, we considered the set that results in the general largest success rate for our method in Table 1 (i.e., concatenation of descriptors from the original image and the 4 proposed LBP maps). “Fractal dimension” represents the proposed descriptors computed only for the original image, i.e., without combining with any LBP map. Results show that our approach was able to surpass almost all the compared methods (Except for Gabor filters in USPTex database) using both LDA and SVM. We must emphasize the excellent result yielded in the UIUC dataset, when our approach surpassed the second best method (Gabor filters) with a difference of 16.00% using LDA. Such difference shows the relevance in combining fractal analysis and LBP for improving the description of the image. Moreover, Table 2 shows that our method presents the best results in the Brodatz and UIUC databases, while it is surpassed by Gabor filters in the USPTex dataset. Although we do not have a definite explanation for this behavior, we suppose that the USPTex database have a great number of images with “directional characteristics” that can be better exploited by sinusoidal frequencies and directions in Gabor filters. Also, we notice that LDA is generally better than SVM in our experiments. To account for this fact, one possible explanation is that SVM tends to perform lower than other simpler methods when default parameter values are used, as suggested in [3]. Moreover, both methods find a hyperplane separating the classes but, while LDA assumes that the samples follows a normal distribution, i.e., they are more tightly around the mean of the class (which seems to be the case in our experiments), SVM aims at separating the closest points in different classes. Finally, we believe that it is not possible to establish “a priori” the conditions where our method performs better. Nevertheless, the high success rates in three very different image databases suggest that our signature is suitable for a large range of images. In future research, we intend to apply it in biological and medical images in order to confirm even more its performance. 7. Conclusion This paper presented a powerful hybrid method that extracts additional information from an input image by using LBP maps and computes descriptors from these maps by using fractal dimension. Different combinations of the LBP maps (Min, Max, Diff Min and Diff Max) were tested and all of them presented high performance, with special emphasis for the combination of the four LBP maps, which surpassed almost all the compared methods. This result confirms that the proposed method provides very discriminative signatures and suggests that it can be applied successfully in different domains that require texture analysis. Moreover, our proposed approach opens a line of research to investigate novel different ways of joining LBP and fractal dimension in order to create feature vectors increasingly discriminative. Acknowledgments André R. Backes gratefully acknowledges the financial support of CNPq (National Council for Scientific and Technological Development, Brazil) (Grant #302416/2015-3) and FAPEMIG (Foundation to the Support of Research in Minas Gerais) (Grant #APQ-0343715).

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A.R. Backes, J.J. de Mesquita Sá Junior / Neurocomputing 266 (2017) 1–7 [36] T. Ojala, M. Pietikäinen, T. Mäenpää, Multiresolution gray-scale and rotation invariant texture classification with local binary patterns, IEEE Trans. Pattern Anal. Mach. Intell. 24 (7) (2002) 971–987. [37] X. Qi, L. Shen, G. Zhao, Q. Li, M. Pietikäinen, Globally rotation invariant multiscale co-occurrence local binary pattern, Image Vis. Comput. 43 (2015) 16–26. [38] L.C. Ribas, D.N. Gonçalves, J.P.M. Oruê, W.N. Gonçalves, Fractal dimension of maximum response filters applied to texture analysis, Pattern Recogn. Lett. 65 (2015) 116–123. [39] J.J.M. Sá Junior, A.R. Backes, A simplified gravitational model to analyze texture roughness, Pattern Recogn. 45 (2) (2012) 732–741. [40] G. Tkacik, J.S. Prentice, J.D. Victor, V. Balasubramanian, Local statistics in natural scenes predict the saliency of synthetic textures, Proc. Natl Acad. Sci. 107 (42) (2010) 18149–18154. [41] C. Tricot, Curves and Fractal Dimension, Springer-Verlag, 1995. [42] J.S. Weszka, C.R. Dyer, A. Rosenfeld, A comparative study of texture measures for terrain classification, IEEE Trans. Syst. Man, Cybern. 6 (4) (1976) 269–285. [43] J. Xie, L. Zhang, J. You, S.C.K. Shiu, Effective texture classification by texton encoding induced statistical features, Pattern Recogn. 48 (2) (2015) 447–457. [44] H. Zhou, R. Wang, C. Wang, A novel extended local-binary-pattern operator for texture analysis, Inf. Sci. 178 (22) (2008) 4314–4325. ANDRÉ RICARDO BACKES is a professor at the College of Computing at the Federal University of Uberlndia in Brazil. He received his B.Sc. (2003), M.Sc. (2006). and Ph.D. (2010). in Computer Science at the University of S. Paulo. His fields of interest include Computer Vision, Image Analysis and Pattern Recognition.

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JARBAS JOACI DE MESQUITA SÁ JUNIOR is a professor at the Computer Engineering Course at the Federal University of Cear – Campus Sobral, in Brazil. He received his M.Sc. (2008) in Computer Science at the University of S. Paulo and Ph.D. (2013) in Teleinformatics Engineering at the Federal University of Cear. His fields of interest include Computer Vision, Image Analysis and Pattern Recognition.