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# Melanoma recognition using extended set of descriptors and classifiers

- Michał Kruk
^{1}Email author, - Bartosz Świderski
^{1}, - Stanisław Osowski
^{2, 3}, - Jarosław Kurek
^{1}, - Monika Słowińska
^{4}and - Irena Walecka
^{4}

**2015**:43

https://doi.org/10.1186/s13640-015-0099-9

© Kruk et al. 2015

**Received: **1 May 2015

**Accepted: **23 November 2015

**Published: **14 December 2015

## Abstract

The paper presents a novel method of melanoma recognition on the basis of dermoscopic images. We use color images of skin lesions, advanced image processing, and different classifiers to distinguish melanoma from the other non-melanoma lesions. Different families of descriptors are used for generation of the image diagnostic features for final pattern recognition. To increase the efficiency of the system, we apply different selection procedures to find the best set of features and different solutions of classifier. The numerical results concerning the accuracy of the proposed recognition system have confirmed good accuracy of the proposed method and high sensitivity in melanoma recognition.

## Keywords

## 1 Introduction

Melanoma is a potentially life-threatening neoplasm. It is manifested by the growing, unusual-looking skin lesion, of the odd-shaped, uneven, or uncertain borders and multiple colors in advanced cases. Thin melanomas a few millimeters in diameter can mimic benign nevi and cannot be detected by the “naked eye” examination. The only possibility to diagnose them is using the dermoscopy as a tool. Early recognition and surgical excision can be curative for the patient.

However, the number of yearly deaths from melanoma continues to increase, and the overall melanoma mortality rate is one of the few cancer mortality rates not on the decline [1–3]. These realities combined with increasing evidence of the lack of efficacy of the clinically assessed ABCDE criteria (“A” for “asymmetry,” “B” for “border irregularity,” “C” for “color variation,” “D” for “diameter,” and “E” for “evolving lesions”) have necessitated ongoing efforts to enhance the earlier clinical detection of melanoma [3, 4].

Most approaches to melanoma diagnosis have included emphases on recognition of changing lesions, recognition of outlier (“ugly duckling”) lesions, and specific melanoma features, with the most utilized criteria being the ABCDE descriptors. Some recently published strategies have rejected the diameter criterion as well as abandoned all or portions of the ABCDE mnemonics [3–5]. The additional problems with application of the ABCDE descriptors appear for extensive lesions, for which the borders of lesions are outside the dermoscopic image or there is a smooth transition between the lesions and the healthy skin. Therefore, the development of other diagnostic features well characterizing the skin lesions is needed.

There is a growing interest in developing automatic systems which support the dermatologists in early recognition of melanoma [6]. Such systems include composition of few main steps: (1) image segmentation, (2) feature extraction and selection, and (3) lesion classification. Recently, many approaches to these topics have been proposed. The paper [7] proposed new mathematical descriptors for the border of pigmented skin lesion images, like lesion slope and lesion slope regularity. The other works proposed different approaches to melanoma segmentation and characterization. They include color clustering [6], wavelet analysis [5], Markov tree features [8], use of color texture [9], application of global and dynamic thresholding [10], GVF snakes [10], etc.

Different classifier solutions applying the selected descriptors have been proposed. They include clustering approach, linear discriminant analysis, neural networks, fuzzy and neuro-fuzzy systems, support vector machines (SVM), K-nearest neighbors (KNN), naïve Bayes, random forest, etc. Ganster et al. [6] has achieved a sensitivity of 87 % and a specificity of 92 % for a large data set with more than 5300 dermoscopy images. Recent results show a sensitivity of 83.06 % and specificity of 90.05 % of cascade classifiers in tenfold cross-validation mode for recognition of melanoma in clinical images [11]. The research of melanoma reported in [5] show the accuracy of 91.26 % and area under the curve (AUC) value of 0.937 on the set of 289 dermoscopic images (114 malignant, 175 benign) partitioned into train, validation, and test image sets. The paper [8] has declared the accuracy of SVM classifier varying from 40 to 75 %, depending on the test performed and features used. The paper [12] has reported the sensitivity of 93 % and specificity of 92 %. The work [13] has reported the accuracy rate changing from 69.9 up to 93.7 % depending on the combination of training and testing results. The paper [14] has reported the accuracy of 85 % for recognition of non-invasive melanomas based on the ABCD rule and pattern-recognition image-processing algorithms. The other paper [15] has compared the application of neural and neuro-fuzzy networks to skin cancer recognition, reporting the accuracy rate of 90.67 % for neural and 91.26 % for neuro-fuzzy networks. The recent paper [16] has investigated two systems (global and local) of detection of melanoma and declared the sensitivity of 96 % and specificity of 80 %.

In this paper, we propose the application of different types of image descriptors to characterize the dermoscopy image of the skin lesions. Textural features are based on the standard Haralick descriptors [17], while statistical features apply the segmentation-based fractal texture analysis (SFTA) [18, 19], Kolmogorov–Smirnov distance [20, 21], percolation descriptors [22], and maximum subregion descriptors [20]. The selection procedure based on application of Fisher discrimination measure, feature correlation, and fast correlation-based filter is used to choose the features, which is able to recognize melanoma with the best accuracy. The selected descriptors are used as the input attributes to the system of classifiers, responsible for the final recognition of melanoma.

## 2 Materials

The database of skin lesions used in experiments

Type of lesions | Number of samples | |
---|---|---|

Melanoma | Lentigo maligna melanoma | 69 |

Nodular melanoma | 17 | |

Non-melanoma | Seborrheic keratosis | 4 |

Angioma | 1 | |

Pigmented nevus | 29 | |

Atypical nevus | 59 |

The additional experiments have been performed using the data set PH2 available in the Internet [23]. The dermoscopic images forming the basis were obtained by the Dermatology Service of Hospital Pedro Hispano (Matosinhos, Portugal) using the Tuebinger Mole Analyzer system at the magnification of ×20. They are 8-bit RGB color images of a resolution of 768 × 560 pixels. The database contains 200 dermoscopic images of melanocytic lesions, including 80 common nevi, 80 atypical nevi, and 40 melanomas. The PH2 database includes medical annotation of all the images based on medical segmentation of the lesion, clinical and histological diagnosis, and the assessment of several dermoscopic criteria (colors, pigment network, dots/globules, streaks, regression areas, blue-whitish veil). The assessment of each parameter was performed by an expert dermatologist [23].

## 3 Methods

### 3.1 Image filtering

Image filtering is aimed at removing small structures and artifacts from skin image to reduce future over-segmentation in further processing steps of the image. The artifacts are treated as an impulse noise and are removed by applying median filtering.

### 3.2 Generation of diagnostic features

To create the effective classification system, we have to generate the appropriate set of diagnostic features, which will form the input signals to the classifier. Good features should allow distinguishing different classes with the highest precision. It means that they should assume similar values for the images belonging to the same class and different values for the representatives of the opposite class. In the proposed solution, we will exploit the statistical and textural descriptions of the image. They are divided into few subgroups: the numerical descriptors based on the Kolmogorov–Smirnov (KS) statistical distance [20, 21], maximum subregion principle, percolation theory [22], classical Haralick descriptors [17], and descriptors based on fractal texture analysis [18].

#### 3.2.1 Kolmogorov–Smirnov descriptors

*x*

_{ i }and

*x*

_{ j }belonging to two different rings using the KS test is estimated. The KS statistics determines if the samples of both rings are drawn from the same continuous population characterized by the cumulative distributions

*F*(

*x*

_{ i }) and

*F*(

*x*

_{ j }). The distance between these two populations is defined in the KS test as

over all *x*. This distance is treated as the measure of difference between the distributions of both populations.

The KS distance for all combinations of two rings is calculated. As a result, we get a set of KS statistics corresponding to different levels of such differences. Level 1 corresponds to KS differences of the succeeding rings, i.e., rings 1 and 2, 2 and 3, 3 and 4, etc. Level 2 corresponds to the KS differences of rings distant by 2, for example 1 and 3, 2 and 4, etc. As a result, we collect the KS distances corresponding to the same differences of rings for each level.

*d*

_{KS}for different levels

*l*and its linear regression estimated for the image of Fig. 1b. The measured (known) values of

*d*

_{KS}are given by three square points and a solid line while its linear approximation by the dashed line. The horizontal axis represents the succeeding levels

*l*and the vertical one the average KS distance.

- a)
*d*_{KS}12 (the mean of KS statistics between ring no. 1 and ring no. 2) - b)
*d*_{KS}13 (the mean of KS statistics between ring no. 1 and ring no. 3) - c)
*d*_{KS}14 (the mean of KS statistics between ring no. 1 and ring no. 4) - d)
The ratio

*d*_{KS}13/*d*_{KS}12 - e)
The ratio

*d*_{KS}14/*d*_{KS}12 - f)
The coefficient

*α*_{0}of the approximation line*d*_{KS}=*α*_{0}+*α*_{1}*l*+*ε* - g)
The slope coefficient

*α*_{1}of the approximation line*d*_{KS}=*α*_{0}+*α*_{1}*l*+*ε*

In this way, the total population of KS features is equal to seven.

#### 3.2.2 Maximum subregion descriptors

*th*

_{ a }corresponds to the

*p*th percentile for the grayscale image of the intensity changing from 0 to 255. We scale this threshold value to the range of percentiles from 1 to 99 (to avoid the effect of saturation of black and white colors). For each image, we determine the intensity levels

*f*

_{1}corresponding to the first percentile and the intensity

*f*

_{99}associated with the 99th percentile. Then, the normalized threshold

*nth*

_{ a }is recalculated according to the formula

The value of percentile *p*th and the corresponding normalized threshold *nth*
_{
a
} represent the features. The additional descriptor is the area (in pixels) of the largest subgroup in the image after thresholding. Because of two types of thresholding procedures (the intensity of compact subgroups of pixels higher or lower than the threshold value), the number of these features is duplicated (six features in total).

#### 3.2.3 Percolation descriptors

*q*= 1 up to

*q*= 9. The more jagged image the longer fire duration. For each threshold, we note the duration of fire. As a feature, we define the weighted average indicator

*q*

_{ w }of quantiles

where *q*
_{
i
} is a quantile changing from 0.1 to 0.9 with step equal to 0.1 and *d*
_{
i
} is the duration of fire at the threshold value corresponding to the *i*th decile. The segmentation of the image may be continued on the pixels of the intensity higher or lower than the threshold value. In this way, we can define two features *q*
_{
w
} corresponding to these two percolation processes.

*q*

_{ i }and

*d*

_{ i }represent the deciles and duration of fire, respectively, at the threshold value corresponding to the

*i*th decile, calculated for the regions corresponding to the pixel intensity higher than the threshold value.

The duration of “fire” of the image of Fig. 6 as a function of the threshold values measured in quantiles *q*
_{
i
} changing from 0.1 to 0.9

| 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |

| 31 | 40 | 31 | 30 | 40 | 24 | 29 | 27 | 22 |

In this case, the descriptor *q*
_{
w
} takes the value 0.469.

#### 3.2.4 Haralick descriptors

Haralick (GLCM) descriptors of the texture are based on the co-occurrence matrix concept [17] and focus on the relationships among the intensity levels of the neighboring pixels in the image. In this application, we have limited our considerations to the statistics concerning the local contrast of the image, correlation of pixel pairs, energy representing the occurrence of repeated pairs within an image, and homogeneity coefficient characterizing the distribution of the elements of a GLCM with its diagonal. They have been generated separately for three RGB channels of the color image. Up to 48 features have been defined in this way.

#### 3.2.5 Descriptors based on fractal texture analysis

The next set of image descriptors uses the segmentation-based fractal texture analysis (SFTA) [18]. The input grayscale image is decomposed into a set of binary images by selecting pairs of lower and upper threshold values (multi-level Otsu algorithm) for each region until the desired number *n*
_{
t
} of thresholds is obtained. In this way, the number of the resulting binary images is equal to 2*n*
_{
t
}.

The SFTA feature vector is constructed by representing the resulting binary images through their size, mean gray level, and characterization of boundary fractal dimension through the box-counting method. In this application, we have used six binary images, each described by three abovementioned measures. In this way, 18 SFTA features have been defined.

The total size of image descriptors taken into account in the next steps of processing is equal to 81. The first seven represent the KS features, six represent the maximum subregion descriptors, two represent the percolation descriptors, the next 18 (from 16 to 34) are based on the SFTA approach, and the last 48 are the Haralick features.

### 3.3 Feature selection

A central problem in constructing the efficient classification system is identifying a representative set of features from which to construct a classification model for a particular task. Good feature should take similar values for the representatives of the same class and differ significantly for different classes. Thus, the main problem in the classification process is to find out the features of the highest importance for the problem solution. Elimination of the features of the weakest class discrimination ability (treated as the noise) leads to smaller dimension of the feature space and improvement of the generalization ability of the classifier in the testing mode for the data not taking part in learning.

In our numerical experiments, we have implemented and compared three methods of feature selection: Fisher discriminant measure (FD) [25], correlation feature selection (CFS) [26], and fast correlation-based filter (FCBF) [27].

*f*is measured on the basis of the so-called discrimination coefficient

*S*

_{ ab }

*(f)*. For two classes A and B, it is defined as follows

*c*

_{A}and

*c*

_{B}are the mean values of the feature

*f*in classes A and B, respectively. The variables

*σ*

_{A}and

*σ*

_{B}represent the standard deviations determined for both classes. The larger the value of

*S*

_{AB}(

*f*) the better is the separation ability of the feature

*f*for these two classes. Figure 7 presents the actual values of the Fisher measure of all features generated for the set of images representing the investigated 176 lesions of the skin.

According to the Fisher method, the best discrimination ability possesses the maximum subregion descriptors and KS features. The poorest performance is associated with the Haralick features. By trying different values of threshold levels and checking the maximum classification accuracy on the learning set, we have found the optimum cutoff value of Fisher measure equal to 0.18 (the horizontal continuous line in the figure). It resulted in 21 important features, which are then treated as the elements of the input vector to the classification system. The representative features from all families have been chosen in the selected set: 6—KS, 7—maximum subregions, 1—percolation, 5—SFTA, and 2—Haralick.

where *R*
_{cf} is the estimated total correlation measure between the summed features and class *c*, *N* is the number of components, \( \overline{R_{\mathrm{ci}}} \) is the average of Pearson’s correlations between the set of features and the class, and \( \overline{R_{\mathrm{ii}}} \) is the average inter-correlation between features [26]. This equation is used as a heuristic measure of the “merit” of feature subsets in classification tasks. The set resulting in the highest value of this merit measure is treated as an optimal one.

Application of the CFS method has resulted in the set of 15 features, covering the members of all feature families. The following features have been selected: 1, 2, 4, 6, 8, 9, 11, 12, 13, 14, 24, 27, 31, 32, and 43. The first four belong to KS family, six of them are the maximum subregion descriptors, four represent the SFTA, and only one represents the Haralick feature.

The third selection method investigated in this work is the fast correlation-based filter (FCBF), exploiting the correlation measure based on the information-theoretical concept of entropy, defined for the variable *x* and for variable *x* after observing the variable *y*. The task is to select the features which are important to the class recognition but at the same time not redundant to any of the other relevant features.

The relevance of the feature *x* to class *c* is decided by calculating the symmetrical uncertainty SU(*x*,*c*) measure between each feature and the class and also the values of SU(*x*
_{
i
},*x*
_{
j
}) for pairwise correlations [27]. By assuming proper threshold values for both measures, we eliminate the features below the threshold.

In practical application of this algorithm, we have assumed the threshold SU(*x*,*c*) equal to 0.68 and SU(*x*
_{
i
},*x*
_{
j
}) = 0.50. As a result, we have selected only six features treated as the most important for the class recognition. This set included one feature representing KS family (feature 4), the next two representing the maximum subregion descriptors (features 9 and 12), two of the SFTA (features 24 and 31), and one of the Haralick family (feature 43).

### 3.4 Classification systems

The selected features are used as the input attributes to the classifier system. To get the best possible solution, we compared the performance of two classifiers: support vector machine (SVM) and random forest (RF), both having the opinion of the best. All of them have been implemented in Matlab [28].

The SVM [29, 30] is a linear machine, working in the high-dimensional feature space formed by the non-linear mapping of the *N*-dimensional input vector **x** into an *L*-dimensional feature space (*L > N*) through the use of a kernel function *K*(**x,x**
_{
i
}). The learning problem of SVM is formulated as the task of separating the learning vectors **x**
_{
i
} into two classes of the destination values either *d*
_{
i
} = 1 (one class) or *d*
_{
i
} = −1 (the opposite class), with the maximal separation margin. The SVM of the Gaussian kernel has been used in our application. The hyperparameters (the regularization constant *C* and Gaussian kernel width) have been adjusted by repeating the learning experiments for the set of their predefined values and choosing the best one for the validation data set.

The Breiman random forest (RF) is an ensemble of decision trees for classification [31]. It operates by constructing many decision trees at training time and outputting the class that is the mode of the classes output by individual trees. The generalization property is improved by applying randomness in selecting the learning data and using the limited set of decision variables chosen randomly in each node of the tree. Random forest has the reputation of very high efficiency classification system.

## 4 Results of numerical experiments

Statistical results of accuracy of melanoma recognition in tenfold cross validation

Classifier | All features | FCBF | CFS | Fisher |
---|---|---|---|---|

SVM | 85.47 % | 78.62 % | 89.51 % | 93.76 % |

RF | 85.34 % | 83.15 % | 89.50 % | 91.5 % |

The confusion matrix of melanoma recognition for our base of images

Melanoma | Non-melanoma | |
---|---|---|

Melanoma | 80 | 4 |

Non-melanoma | 7 | 85 |

The confusion matrix illustrates how the cases belonging to two classes (class of melanoma and the class of other skin lesions) have been classified by our system. The columns represent the actual outputs of our system and the rows—the targets. The number in each entry of the 2 × 2 matrix is the total number of the actually recognized classes in testing mode, calculated in five runs of cross-validation experiments. The diagonal entries of this matrix represent the quantity of the properly recognized cases. Each entry outside the diagonal means the number of misclassifications. The entry in the (*i*,*j*)th position of the matrix for *i ≠ j* means false assignment of the case of *i*th class to the *j*th one.

The sensitivity is defined as the ratio of the true positive cases of melanoma to the sum of true positive and false negative cases. The specificity represents the ratio of the true negative cases (class of non-melanoma) to the sum of true negative and false positive cases.

The results show that the best classification system (SVM associated with Fisher selection) is able to recognize the melanoma from the other lesions of the skin with the total accuracy of 93.8 %. The sensitivity in recognition of melanoma is equal to 95.2 % and the specificity 92.4 %. The non-zero class recognition errors are due to the non-unique characteristics of the images in the data sets. The melanoma and other skin lesions images inherently vary greatly from patient to patient according to the type and advancement degree of lesions. Special difficulties in recognition follow from the changing colors of the skin lesions taking part in experiments. Among the processed lesions images, we have found brown, skin-colored, pink, red, purple, and even blue.

The confusion matrix of melanoma recognition for PH2 database

Melanoma | Non-melanoma | |
---|---|---|

Melanoma | 38 | 2 |

Non-melanoma | 19 | 141 |

The sensitivity of the system for this database was equal to 95.0 % and specificity 88.1 %. The results are slightly better than these presented by authors in [16, 23] for the same database. The best reported measures in these works were given for different variants of solution: sensitivity 93 % and specificity 78 % (global method and texture features), sensitivity 90 % and specificity 89 % (global method and color features), sensitivity 96 % and specificity 80 % (global system splitting image into two subregions), or sensitivity 100 % and specificity 75 % (local system).

In general, it is impossible to get at the same time very high sensitivity and specificity. By changing the classification criteria, it is possible to change the balance level between these two quality measures. For example, at application of one-class SVM [30], we have got 100 % sensitivity; however, on the cost of specificity, it has dropped to 79.4 %.

## 5 Conclusions

The paper has presented the research directed to the automatic recognition of melanoma from the other lesions of the skin on the basis of color image of the nevus. The proposed approach uses extended set of diagnostic features describing the image of the skin lesions combined with different solutions of the classifiers. In our solution, we have resigned from the popular ABCD features, trying to find more powerful descriptors of the image, which are able to increase the accuracy of class recognition (melanoma versus non-melanoma lesions).

The applied descriptors rely on the Kolmogorov–Smirnov statistics, maximum subregions statistics, percolation theory, fractal texture analysis, and Haralick texture descriptors. To reduce the number of input attributes applied in classification, we have tried three different selection methods of diagnostic features: standard Fisher discrimination measure, correlation feature selection, and fast correlation-based filter. Each of these methods applies different mechanism of selection, which results in various sets of attributes.

These sets have been confronted with three different classification systems. As the classifiers, we have tried support vector machine and random forest of decision trees. The best accuracy of class recognition on the database of Warsaw Memorial Cancer Center (Poland) has been achieved in the system formed by the SVM classifier supplied by the attributes selected using the Fisher method. The results of numerical experiments show that this classification system is able to recognize the melanoma from the other lesions of the skin with the total accuracy of 93.8 %. The sensitivity in recognition of melanoma is equal to 95.2 % and the specificity 92.4 %.

Additional experiments performed on the publically available PH2 database of Hospital Pedro Hispano (Matosinhos, Portugal) have also shown the superiority of this approach. In this case, the sensitivity in recognition of melanoma was equal to 95.0 % and the specificity 88.1 %. They are of slightly higher quality than the results reported for this database in [23].

These experimental results obtained on these two data bases confirm that an automatic system applying extended set of image descriptors can reach the efficiency close to the dermatologist’ expert results.

## Declarations

### Acknowledgements

This work was supported by The National Centre for Research and Development of Poland under grant TANGO1/266877/NCBR/2015 which is being realized in the years 2015–2018.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

## References

- N. Howlader, A.M. Noone, M. Krapcho, J. Garshell, N. Neyman, S.F. Altekruse, C.L. Kosary, M. Yu, J. Ruhl, Z. Tatalovich, H. Cho, A. Mariotto, D.R. Lewis, H.S. Chen, E.J. Feuer, K.A. Cronin, SEER Cancer Statistics Review, 1975-2010, National Cancer Institute. Bethesda, MD, http://seer.cancer.gov/archive/csr/1975_2010/, based on November 2012 SEER data submission, posted to the SEER web site, April 2013.
- SE Yagerman, A Marghoob, The ABCDs and beyond. Skin Canc. Found. J.
**31**, 61–3 (2013)Google Scholar - SE Yagerman, L Chen, N Jaimes, SW Dusza, AC Halpern, A Marghoob, ‘Do UC the melanoma?’ Recognizing the importance of different lesions displaying unevenness or having a history of change for early melanoma detection. Australas. J. Dermatol.
**55**, 119–24 (2014)View ArticleGoogle Scholar - SM Goldsmith, A unifying approach to the clinical diagnosis of melanoma including “D” for “Dark” in the ABCDE criteria. Dermatol. Pract. Concept.
**4**(4), 75–78 (2014)Google Scholar - R Garnavi, M Aldeen, J BaileyJ, Computer-aided diagnosis of melanoma using border and wavelet-based texture analysis. IEEE Trans. Inf. Technol. Biomed.
**16**(6), 1–13 (2012)View ArticleGoogle Scholar - H Ganster, A Pinz, E Wildling, M Binder, H Kittler, Automated melanoma recognition. IEEE Trans. Med. Imag.
**20**(3), 233–239 (2001)View ArticleGoogle Scholar - C Grana, G Pellacani, R Cucchiara, S Seidenari, A new algorithm for border description of polarized light surface microscopic images of pigmented skin lesions. IEEE Trans. Med. Imag.
**22**(8), 1235–1247 (2003)View ArticleGoogle Scholar - M Duarte, T Matthews, WS Warren, Calderbank,
*Melanoma Classification from Hidden Markov Tree Features. Int. Conf. ICASSP*, 2012, pp. 6865–688Google Scholar - AG Manousaki, AG Manios, EI Tsompanaki, AD Tosca, Use of color texture in determining the nature of melanocytic skin lesions—a qualitative and quantitative approach. Comput. Biol. Med.
**36**, 419–427 (2006)View ArticleGoogle Scholar - M Silveira, JC Nascimento, JS Marques, AR Marcal, T Mendarca, S Yamauchi, J Maeda, J Rozeira, Comparison of segmentation methods for melanoma diagnosis in dermoscopy images. IEEE J. Sel. Top. Sign. Proces.
**3**(1), 35–45 (2009)View ArticleGoogle Scholar - P Sabouri, HH Gholam, T Larsson, J CollinsJ,
*A Cascade Classifier for Diagnosis of Melanoma in Clinical Images. Engineering in Medicine and Biology Society (EMBC) 36th Annual Intern. Conf. of the IEEE, Chicago*, 2014Google Scholar - M Celebi, HA Kingravi, B Uddin, H Iyatomi, Y Aslandogan, W Stoecker, R Moss, A methodological approach to the classification of dermoscopy images. Comput. Med. Imaging Graph.
**32**(6), 362–373 (2007)View ArticleGoogle Scholar - E Zagrouba, W Barhoumi, A preliminary approach for the automated recognition for malignant melanoma. Image Anal. Stereol.
**23**(2), 121–135 (2004)View ArticleGoogle Scholar - AG Isasi, BG Zapirain, AM Zorrilla, Melanomas non-invasive diagnosis application based on the ABCD rule and pattern recognition image processing algorithms. Comput. Biol. Med.
**41**, 742–755 (2011)View ArticleGoogle Scholar - B Salah, M Alshraideh, R Beidas, F Hayajneh, Skin cancer recognition by using a neuro-fuzzy system. Cancer Informat.
**10**, 1–11 (2011). doi:10.4137/CIN.S5950 Google Scholar - C Barata, M Ruela, M Francisco, T Mendonça, J Marques, Two systems for the detection of melanomas in dermoscopy images using texture and color features. IEEE Syst. J.
**8**(3), 965–979 (2013)View ArticleGoogle Scholar - R Haralick, L Shapiro, Image segmentation techniques. Computer Vision Graphics Image Process.
**29**, 100–132 (1985)View ArticleGoogle Scholar - F Costa, GE Humpire-Mamani, AJ Traina, An efficient algorithm for fractal analysis of textures, in
*SIBGRAPI - XXV Conf. Graphics, Patterns and Images, Ouro Preto, Brazil*, 2012, pp. 39–46Google Scholar - M Schroeder,
*Fractals, Chaos, Power Laws*(W.H. Freeman and Company, New York, 2006)MATHGoogle Scholar - GW Corder, DI Foreman,
*Nonparametric Statistics for Non-Statisticians: a Step-by-step Approach*(Wiley, New York, 2009)View ArticleMATHGoogle Scholar - Swiderski, S Osowski, M Kruk, J Kurek, Texture characterization based on the Kolmogorov-Smirnov distance. Expert Syst. Appl.
**42**(1), 503–509 (2015)View ArticleGoogle Scholar - D Stauffer,
*Introduction to Percolation Theory*(Taylor & Francis, London, 1985)View ArticleMATHGoogle Scholar - T Mendonca, P Ferreira, J Marques, AR Marcal, J Rozeira,
*PH2—a Dermoscopic Image Database for Research and Benchmarking, 35th Int. Conf. IEEE Engineering in Medicine and Biology Society, Osaka*, 2013. http://www.fc.up.pt/addi/ph2%20database.html Google Scholar - K Kimia, RS Ahmad, E-shaver: an improved DullRazor for digitally removing dark and light-colored hairs in dermoscopic images. Comput. Biol. Med.
**41**, 139–145 (2011)View ArticleGoogle Scholar - RO Duda, PE Hart, P Stork,
*Pattern Classification and Scene Analysis*(Wiley, New York, 2003)Google Scholar - M Hall,
*Correlation-Based Feature Selection for Discrete and Numeric Class Machine Learning. Proc. 17th Intern. Conf. Machine Learning Morgan Kaufmann Publishers, San Francisco*, 2000, pp. 359–366Google Scholar - H Liu, L Yu,
*Feature Selection for High-Dimensional Data: a Fast Correlation-Based Filter Solution. Proc. 20th Intern. Conf. Machine Leaning (ICML-03), Washington, D.C*, 2003, pp. 856–863Google Scholar - MATLAB (R2012a) (2012) MATLAB user manual, Release 7.14.0. The Math Works, USAGoogle Scholar
- S Haykin,
*Neural Networks, a Comprehensive Foundation*(Macmillan College Publishing Company, New York, 2000)MATHGoogle Scholar - B Schölkopf, A Smola,
*Learning with Kernels*(MIT Press, Cambridge MA., 2002)MATHGoogle Scholar - L Breiman, Random forests. Mach. Learn.
**45**(11), 5–32 (2001)View ArticleMATHGoogle Scholar - PN Tan, M Steinbach, V Kumar,
*Introduction to Data Mining*(Pearson Education Inc, Boston, 2006)Google Scholar