# Fuzzy Color Clustering for Melanoma Diagnosis in Dermoscopy Images

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Dermoscopy Image Data

^{3}or 16,777,216 possible colors in this color space.

#### 2.2. Diagnostic Assessment

#### 2.3. Skin Lesion Border Determination

_{(x,y)}, G

_{(x,y)}, B

_{(x,y)}), where 1 ≤ x ≤ N and 1 ≤ y ≤ M.

#### 2.4. Relative Color

_{rel}(x,y) = (R

_{rel(x,y)},G

_{rel(x,y)},B

_{rel(x,y)}) = (R

_{(x,y)}− R

_{skin},G

_{(x,y)}− G

_{skin},B

_{(x,y)}− B

_{skin}|(x,y) ∈ ROI), where −255 ≤ R

_{rel(x,y)}, G

_{rel(x,y)},B

_{rel(x,y)}≤ 255. R

_{skin}, G

_{skin}and B

_{skin}are the average red, green and blue plane pixel values computed from the surrounding skin. Section 2.5, presents the procedure for finding the surrounding skin.

#### 2.5. Surrounding Skin Color Determination

_{skin}, G

_{skin}, B

_{skin}) pixel values.

#### 2.6. Color Histogram Bin Determination

_{rel}, G

_{rel}and B

_{rel}in the relative color space, defined by subtracting the R, B and B values from the surrounding skin, can take values in the range [−255,255]. Pixels from the entire benign lesion training set thus have 511 possible values on each of the three color axes, resulting in a three-dimensional histogram for counting pixel values; this histogram has 511

^{3}possible values. To increase statistical significance for benign-malignant color separation and reduce computational complexity, these values are quantized by dividing each original relative color value by 4, to create the final relative color histogram with dimensions 128 × 128 × 128. Each final quantized histogram value represents a cube of dimension 4 × 4 × 4 containing up to 64 original lesion color values. Thus each point in the final relative color histogram is a “bin” that counts pixels with up to 64 possible original color values.

_{bin}denote the set of relative color bins, and let C

_{bin(x,y)}denote the relative color bin in which the pixel (x,y) of the skin lesion falls. Since each of the original axes has 511 possible values, quantization by dividing the axis by 4 will result in bins on the edges of the cube that are 4 × 4 × 3 and one bin in the corner of the cube that is 3 × 3 × 3. Upon examining the training set relative color histograms, the bin that contains the relative color −255 (before quantization) will not likely occur in dermoscopy images in the three planes R, G, and B; hence that cube is assigned the smaller dimension (3

^{3}).

#### 2.7. Color Histogram Analysis Technique

#### 2.7.1. Fuzzy Set Description for Trapezoidal Membership Function

**B**represent a fuzzy set [36] having a trapezoidal membership function for relative skin lesion color, for the specified skin lesion class. This study utilizes the same trapezoidal membership function from [25], which is derived using a data-driven process that assigns membership values to skin lesion relative colors based on frequency of occurrence in the training set of skin lesions. The colors within the color histogram bins defined in the Section 2.6 were assigned membership values using the following process: The training set of images for the specified class is used to populate the three-dimensional relative color histogram bins in batch mode; each bin will contain the sum of pixels with relative color mapping to that bin from all skin lesion regions in all the training images. A secondary histogram is defined as a histogram of the three-dimensional relative color histogram. The secondary histogram is a function of bins in the relative color histogram; it will indicate the number of bins containing x pixels in the relative color histogram.

**B**. The secondary histogram of the relative colors is used to assign the membership values. The membership function μ

**(x) denoting the fuzzy set [36] is given as**

_{B}**B**. F is set as the frequency count given that 5% of the secondary histogram of the benign skin lesions have frequency F or greater. Increased bin frequency (up to F) will be reflected as increased membership value in the specified class of skin lesion. Figure 2 shows a representative secondary histogram with the frequency count F labeled in (a) and the trapezoidal membership function generated in (b). The horizontal axis provides the frequency of occurrence (x) that a bin is populated over all benign images of the training set. The vertical axis in Figure 2a gives the number of bins with x “hits” per bin over the training set of benign images.

#### 2.7.2. Color Feature Determination

**B**is given by the fuzzy clustering ratio feature. The fuzzy clustering ratio feature is computed as follows. Let M denote the set of relative color values that map into relative color histogram bins labeled with

**B**and (x,y) contained in the skin lesion. M is given by

_{rel(x,y)}that map into M, formally

_{((x,y),r)}denote the number of 8-connected neighbors within the square neighborhood of radius r for (x,y) ∈ ROI and N

_{(M(x,y),r)}denote the number of neighbors connected within the square neighborhood of radius r that are contained in the lesion region of interest for pixel (x,y) ∈ L, such that r = 0 refers to the pixel (x,y) itself, r = 1 refers to the eight-connected neighborhood of (x,y) and so on. By Equation (6), the neighbors of radius r for a point (x,y) ∈ L are excluded from calculating N

_{(x,y)}and N

_{(M(x,y),r)}if the neighbors lie outside of the lesion ROI. Then,

**B**for the specified lesion class. The fuzzy clustering ratio for a skin lesion is given as

**B**for a given radius r. If

**B**represents the fuzzy set for benign skin lesion relative color as determined from the benign training set of images, then R(α,r) represents the degree to which the clustering of benign colors within square radius r of the skin lesion are the colors perceived to be associated with benign skin lesions. After determining

**B**, the next step is to compute R(α,r) for all benign and melanoma skin lesions from the training data for a specified value of α. A threshold T is automatically determined from the ratios R(α,r) calculated from the training data. The procedure for finding T is presented in the following Section 2.7.3. Skin lesions are categorized as either benign or melanomas for the data set used in this research. A given skin lesion is classified as benign if R(α) > T. Otherwise, the skin lesion is labeled as a melanoma. A similar process is used to determine

**B**, R(α), and T using melanoma skin lesion images as the training set. However, a given skin lesion would be classified as benign if R(α,r) ≤ T.

#### 2.7.3. Threshold Determination Procedure

#### 2.8. Lesion Region Analysis

**B**and μ

**from the training set of images for the specified class, R(α,r) is computed over different skin lesion regions, referenced as boundary area percentages, for skin lesion discrimination. The boundary area percentage is defined as the uniform skin lesion region closest to the boundary that contains a specified percentage of the lesion area. The boundary area region is found using the method developed in [37] with summary in pseudocode:**

_{B}- (1)
- start with the lesion border
- (2)
- compute the distance transform using 8-connected distance to get pixel distance from the lesion boundary inside of the skin lesion
- (3)
- starting with a distance of 0 (lesion boundary), determine the lesion boundary region with distance less than or equal to the current distance
- (4)
- compute the area of the resulting lesion boundary region
- (5)
- retain the lesion boundary region if its area is greater than the boundary area percentage
- (6)
- otherwise, increment the distance by 1 and repeat Steps (2)–(6)

## 3. Experiments Performed

**B**with trapezoidal membership function is determined from the benign training images using the entire skin lesion. Variables are assigned as follows: α = 0.1, 0.2, 0.4, 0.6, 0.8 and 1, r = 0, and 1 and boundary area percentage 10%, 25%, 75%, and 100%; classification of test lesions as melanoma or benign is based upon the optimal threshold T, Section 2.7.3. The entire process is repeated, this time using the melanoma training images to determine

**B**.

## 4. Results and Discussion

**B**is denoted as FCN-Melanoma; (2) the average correct melanoma rate found based on computing R(α,r) using the melanoma training images for determining the fuzzy set

**B**is denoted as FCM-Melanoma; (3) the average correct benign rate found based on computing R(α,r) using the benign training images for determining the fuzzy set

**B**is denoted as FCN-Benign; and (4) the average correct benign rate found based on computing R(α,r) using the melanoma training images for determining the fuzzy set

**B**is denoted as FCM-Benign. Note that other boundary area percentage areas, including 50%, were tested, but the results were not improved over the tables presented in this study.

**B**using the benign training set of images than the rates based on the melanoma training set of images for all boundary area percentage cases examined. In particular, the disparity between the melanoma correct rates for the benign and melanoma training approaches, respectively, for determining R(α,r = 0) increases with the boundary area percentage examined, with the greatest disparity observed for the 100% boundary area percentage case (entire lesion). A similar trend is observed between the benign correct rates for the benign and melanoma approaches, respectively. Using the benign training images to determine

**B**for computing R(α,r = 0) may yield better discrimination capability because relative colors may be more consistent in benign lesions than in melanoma lesions.

**B**. For fuzzy ratio R(α,r) calculations, the numerator S(α,r) and the denominator V(r) are dependent on the training set for the specified class of images used to determine

**B**. Every pixel within every training image of the specified class of images has a nonzero membership in

**B**. Accordingly, V(r) is equal to the lesion area for those training images, and each pixel within every training skin lesion is included in S(α,r) for some range of α > 0. This is not necessarily true for the non-specified class of training images and the melanoma and benign test images. Because the training fuzzy ratios R(α,r) for the specified class of training images are slightly skewed from the test benign fuzzy ratios R(α,r), the threshold T determined from the training set of images may not be as reflective of the test fuzzy ratios for the specified class of images as for the non-specified class of images. A similar trend is observed from Figure 4 and Figure 5 for r = 0 and r = 1 for the true positive (FCM-Melanoma) and true negative (FCM-Benign) rates for all boundary percentage area cases except for the 10% case using the melanoma training images to determine B, where the true positive rate exceeds the true negative rate for α > 0.4. This trend could be attributed to the approach used for deriving the fuzzy set

**B**and the membership function µ

**. There are fewer melanoma images than benign lesion images, and the 10% boundary area cases results in fewer relative color histogram bins being populated, yielding most relative colors as having low membership in**

_{B}**B**. Thus, melanoma and benign lesions have similar R(α,r) for small values of α (α < 0.4), leading to low melanoma discrimination rates.

**B**in the denominator V(r) without taking into account spatial context for feature determination. As a result, there is less variation in R(α,r = 0) for the benign and melanoma images for different values of α. The experiments for computing R(α,r = 1) incorporate only some spatial context for feature calculations which allows for clustering of neighboring pixels with membership values that satisfy the α constraint.

**B**, with the highest true positive rate of 91.29% at α = 0.4 and the highest true negative rate of 86.9% at α = 0.2 and 0.4. The true negative rates using the benign images as the training set of images are consistently higher at the 25% boundary area case for all alpha-cuts than for the other boundary area percentage case. The feature R(α,r) for r = 1 is computed as the sum of the number of eight-connected neighbors that satisfy the alpha-cut criterion for each pixel within the lesion that satisfies the alpha-cut criterion divided by the sum of eight-connected neighbors that have non-zero membership in

**B**for each pixel within the lesion that has non-zero membership in

**B**. This feature is similar to a crisp color clustering ratio investigated in previous research [26,27].

**B**. Note that the true positive and true negative results for α = 0.1 and 0.2 are contained in Figure 5b. From Figure 6 the highest true positive rate of 92.6% is obtained for α = 0.08 with a corresponding true negative rate of 86.5%. This combination of r = 1 and α = 0.08 also yielded the highest overall weighted true positive and true negative correct recognition rate of 88.51%, compared to the combination r = 0 and α = 1 giving the highest weighted correct recognition rate of 73.73%. These results highlight the significant lesion discrimination capability of the fuzzy clustering ratio, incorporating spatial information using neighbor clustering (r = 1) over individual pixel-based color descriptor determination (fuzzy ratio) for enhancing skin lesion discrimination.

**B**and its corresponding membership function μ

**and only requires information about the remaining class to find the threshold T for discrimination. In the feature calculation process, no decision is necessary to label colors as melanoma or benign. Rather, the data-driven process provides for the degree of association of different colors as melanoma or benign, depending on the class used to determine**

_{B}**B**, based on the frequency of occurrence in the training set of images. Because relative color is used for mapping RGB colors at each pixel location in the lesion to relative color bins, this framework can easily be updated as additional image data is acquired, adapting to the variations in image acquisition such as lighting and the types of lesions that may be observed in particular geographic locations.

**B**using the benign training set of images over the melanoma training set of images. This finding may be attributed to the presence of specified color clusters in benign lesions more consistently than in melanoma lesions. The features computed using the melanoma and benign training sets of images provide complementary information because only the specified class of training lesion images is used to populate the relative color histogram to determine

**B**. Experimental results presented here provide further confirmation of the effectiveness of relative color, since the image sets were acquired from different patient populations via significantly different imaging systems.

## 5. Conclusions

**B**. These results provide a substantial improvement over the baseline fuzzy ratio feature for r = 0.

## Author Contributions

## Conflicts of Interest

## References

- Marghoob, A.A.; Scope, A. The complexity of diagnosing melanoma. J. Investig. Dermatol.
**2009**, 129, 11–13. [Google Scholar] [CrossRef] [PubMed] - Stoecker, W.V.; Stolz, W. Dermoscopy and the diagnostic challenge of amelanotic and hypomelanotic melanoma. Arch. Dermatol.
**2008**, 144, 1207–1210. [Google Scholar] [CrossRef] [PubMed] - Menzies, S.W.; Moloney, F.J.; Byth, K.; Avramidis, M.; Argenziano, G.; Zalaudek, I.; Braun, R.P.; Malvehy, J.; Puig, S.; Rabinovitz, H.S.; et al. Dermoscopic evaluation of nodular melanoma. JAMA Dermatol.
**2013**, 149, 699–709. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Soon, S.L.; Solomon, A.R., Jr.; Papadopoulos, D.; Murray, D.R.; McAlpine, B.; Washington, C.V. Acral lentiginous melanoma mimicking benign disease: The Emory experience. J. Am. Acad. Dermatol.
**2003**, 48, 183–188. [Google Scholar] [CrossRef] [PubMed] - Kittler, H.; Pehamberger, H.; Wolff, K.; Binder, M. Diagnostic accuracy of dermoscopy. Lancet Oncol.
**2002**, 3, 159–165. [Google Scholar] [CrossRef] - Vestergaard, M.E.; Macaskill, P.; Holt, P.E.; Menzies, S.W. Dermoscopy compared with naked eye examination for the diagnosis of primary melanoma: A meta-analysis of studies performed in a clinical setting. Br. J. Dermatol.
**2008**, 159, 669–676. [Google Scholar] [CrossRef] [PubMed] - Ferris, L.K.; Harkes, J.A.; Gilbert, B.; Winger, D.G.; Golubets, K.; Akilov, O.; Satyanarayanan, M. Computer-aided classification of melanocytic lesions using dermoscopic images. J. Am. Acad. Dermatol.
**2015**, 73, 769–776. [Google Scholar] [CrossRef] [PubMed] - Esteva, A.; Kuprel, B.; Novoa, R.A.; Ko, J.; Swetter, S.M.; Blau, H.M.; Thrun, S. Dermatologist-level classification of skin cancer with deep neural networks. Nature
**2017**, 542, 115–118. [Google Scholar] [CrossRef] [PubMed] - Carrera, C.; Marchetti, M.A.; Dusza, S.W.; Argenziano, G.; Braun, R.P.; Halpern, A.C.; Jaimes, N.; Kittler, H.J.; Malvehy, J.; Menzies, S.W. Validity and Reliability of Dermoscopic Criteria Used to Differentiate Nevi From Melanoma: A Web-Based International Dermoscopy Society Study. JAMA Dermatol.
**2016**, 152, 798–806. [Google Scholar] [CrossRef] [PubMed] - Argenziano, G.; Puig, S.; Zalaudek, I.; Sera, F.; Corona, R.; Alsina, M.; Barbato, F.; Carrera, C.; Ferrara, G.; Guilabert, A.; et al. Dermoscopy improves accuracy of primary care physicians to triage lesions suggestive of skin cancer. J. Clin. Oncol.
**2006**, 24, 1877–1882. [Google Scholar] [CrossRef] [PubMed] - Siegel, R.L.; Miller, K.D.; Jemal, A. Cancer statistics, 2016. CA Cancer J. Clin.
**2016**, 66, 7–30. [Google Scholar] [CrossRef] [PubMed] - Siegel, R.L.; Miller, K.D.; Jemal, A. Cancer statistics, 2017. CA Cancer J. Clin.
**2017**, 67, 7–30. [Google Scholar] [CrossRef] [PubMed] - Bajaj, S.; Marchetti, M.A.; Navarrete-Dechent, C.; Dusza, S.W.; Kose, K.; Marghoob, A.A. The role of color and morphologic characteristics in dermoscopic diagnosis. JAMA Dermatol.
**2016**, 152, 676–682. [Google Scholar] [CrossRef] [PubMed] - Friedman, R.J.; Rigel, D.S.; Kopf, A.W. Early detection of malignant melanoma: The role of physician examination and self-examination of the skin. CA Cancer J. Clin.
**1985**, 35, 130–151. [Google Scholar] [CrossRef] [PubMed] - Rubegni, P.; Feci, L.; Nami, N.; Burroni, M.; Taddeucci, P.; Miracco, C.; Munezero Butorano, M.A.; Fimiani, M.; Cevenini, G. Computer-assisted melanoma diagnosis: A new integrated system. Melanoma Res.
**2015**, 25, 537–542. [Google Scholar] [CrossRef] [PubMed] - Andreassi, L.; Perotti, R.; Rubegni, P.; Burroni, M.; Cevenini, G.; Biagioli, M.; Taddeucci, P.; Dell’Eva, G.; Barbini, P. Digital dermoscopy analysis for the differentiation of atypical nevi and early melanoma: A new quantitative semiology. Arch. Dermatol.
**1999**, 135, 1459–1465. [Google Scholar] [CrossRef] [PubMed] - Landau, M.; Matz, H.; Ethel, T.; Dvir, M.; Brenner, S. Computerized system to enhance the clinical diagnosis of pigmented cutaneous malignancies. Int. J. Dermatol.
**1999**, 38, 443–446. [Google Scholar] [CrossRef] [PubMed] - Umbaugh, S.E.; Moss, R.H.; Stoecker, W.V. Automatic color segmentation of images with application to detection of variegated coloring in skin tumors. IEEE Eng. Med. Biol. Mag.
**1989**, 8, 43–50. [Google Scholar] [CrossRef] [PubMed] - Green, A.; Martin, N.; Pfitzner, J.; O’Rourke, M.; Knight, N. Computer image analysis in the diagnosis of melanoma. J. Am. Acad. Dermatol.
**1994**, 31, 958–964. [Google Scholar] [CrossRef] - Seidenari, S.; Burroni, M.; Dell’Eva, G.; Pepe, P.; Belletti, B. Computerized evaluation of pigmented skin lesion images recorded by a videomicroscope: Comparison between polarizing mode observation and oil/slide mode observation. Skin Res. Technol.
**1995**, 1, 187–191. [Google Scholar] [CrossRef] [PubMed] - Aitken, J.F.; Pfitzner, J.; Battistutta, D.; O’Rourke, P.K.; Green, A.C.; Martin, N.G. Reliability of computer image analysis of pigmented skin lesions of Australian adolescents. Cancer
**1996**, 78, 252–257. [Google Scholar] [CrossRef] - Ercal, F.; Chawla, A.; Stoecker, W.V.; Lee, H.C.; Moss, R.H. Neural network diagnosis of malignant melanoma from color images. IEEE Trans. Biomed. Eng.
**1994**, 41, 837–845. [Google Scholar] [CrossRef] [PubMed] - Ganster, H.; Pinz, A.; Röhrer, R.; Wildling, E.; Binder, M.; Kittler, H. Automated melanoma recognition. IEEE Trans. Med. Imaging
**2001**, 20, 233–239. [Google Scholar] [CrossRef] [PubMed] - Heckbert, P. Color image quantization for frame buffer display. In Proceedings of the 9th Annual Conference on Computer Graphics and Interactive Techniques—SIGGRAPH ’82, Boston, MA, USA, 26–30 July 1982; Volume 16, pp. 297–307. [Google Scholar]
- Faziloglu, Y.; Stanley, R.J.; Moss, R.H.; Stoecker, W.V.; McLean, R.P. Colour histogram analysis for melanoma discrimination in clinical images. Skin Res. Technol.
**2003**, 9, 147–156. [Google Scholar] [CrossRef] [PubMed] - Chen, J.; Stanley, R.J.; Moss, R.H.; Stoecker, W.V. Colour analysis of skin lesion regions for melanoma discrimination in clinical images. Skin Res. Technol.
**2003**, 9, 94–104. [Google Scholar] [CrossRef] [PubMed] - Stanley, R.J.; Stoecker, W.V.; Moss, R.H. A relative color approach to color discrimination for malignant melanoma detection in dermoscopy images. Skin Res. Technol.
**2007**, 13, 62–72. [Google Scholar] [CrossRef] [PubMed] - Stanley, R.J.; Moss, R.H.; Stoecker, W.V.; Aggarwal, C. A fuzzy-based histogram analysis technique for skin lesion discrimination in dermatology clinical images. Comput. Med. Imaging Graph.
**2003**, 27, 387–396. [Google Scholar] [CrossRef] - Barata, C.; Ruela, M.; Francisco, M.; Mendonça, T.; Marques, J.S. Two systems for the detection of melanomas in dermoscopy images using texture and color features. IEEE Syst. J.
**2014**, 8, 965–979. [Google Scholar] [CrossRef] - Stoecker, W.V. Computer Applications in Dermatology; Igaku-Shoin: New York, NY, USA, 1993; ISBN-13 978-0896402386. [Google Scholar]
- Nie, D. Classification of melanoma and clark nevus skin lesions based on medical image processing techniques. In Proceedings of the 3rd International Conference on Computer Research and Development (ICCRD), Shanghai, China, 11–13 March 2011; pp. 31–34. [Google Scholar] [CrossRef]
- Argenziano, G.; Soyer, H.P.; De Giorgi, V.; Piccolo, D.; Carli, P.; Delfino, M.; Ferrari, A.; Hofmann-Wellenhof, R.; Massi, D.; Mazzocchetti, G.; et al. Interactive Atlas of Dermoscopy (Book and CD-ROM); Edra Medical Publishing and New Media: Milan, Italy, 2000; ISBN 88-86457-30-8. [Google Scholar]
- McLean, R.P. Tumor Classification Based on Relative Color Analysis of Melanoma and Non-Melanoma Tumor Images. Master’s Thesis, University of Missouri, Rolla, MO, USA, 1994. [Google Scholar]
- Stoecker, W.V.; Li, W.W.; Moss, R.H. Automatic detection of asymmetry in skin tumors. Comput. Med. Imaging Graph.
**1992**, 16, 191–197. [Google Scholar] [CrossRef] - Hance, G.A.; Umbaugh, S.E.; Moss, R.H.; Stoecker, W.V. Unsupervised color image segmentation: With application to skin tumor borders. IEEE Eng. Med. Biol. Mag.
**1996**, 15, 104–111. [Google Scholar] [CrossRef] - Klir, G.J.; Folger, T.A. Fuzzy Sets, Uncertainty, and Information; Prentice Hall: Englewood Cliffs, NJ, USA, 1988; ISBN-13 978-0133459845. [Google Scholar]
- Stanley, R.J.; Stoecker, W.V.; Moss, R.H.; Rabinovitz, H.S.; Cognetta, A.B., Jr.; Argenziano, G.; Soyer, H.P. A basis function feature-based approach for skin lesion discrimination in dermatology dermoscopy images. Skin Res. Technol.
**2008**, 14, 425–435. [Google Scholar] [CrossRef] - Dalal, A.; Moss, R.H.; Stanley, R.J.; Stoecker, W.V.; Gupta, K.; Calcara, D.A.; Xu, J.; Shrestha, B.; Drugge, R.; Malters, J.M.; et al. Concentric decile segmentation of white and hypopigmented areas in dermoscopy images of skin lesions allows discrimination of malignant melanoma. Comput. Med. Imaging Graph.
**2011**, 35, 148–154. [Google Scholar] [CrossRef] [PubMed] - Rader, R.K.; Payne, K.S.; Guntupalli, U.; Rabinovitz, H.S.; Oliviero, M.C.; Drugge, R.J.; Malters, J.J.; Stoecker, W.V. The pink rim sign: Location of pink as an indicator of melanoma in dermoscopic images. J. Skin Cancer.
**2014**, 2014, 719740. [Google Scholar] [CrossRef] [PubMed] - Braun, R.P.; Gaide, O.; Oliviero, M.; Kopf, A.W.; French, L.E.; Saurat, J.H.; Rabinovitz, H.S. The significance of multiple blue-gray dots (granularity) for the dermoscopic diagnosis of melanoma. Br. J. Dermatol.
**2007**, 157, 907–913. [Google Scholar] [CrossRef] [PubMed] - Stoecker, W.V.; Wronkiewiecz, M.; Chowdhury, R.; Stanley, R.J.; Xu, J.; Bangert, A.; Shrestha, B.; Calcara, D.A.; Rabinovitz, H.S.; Oliviero, M.; et al. Detection of granularity in dermoscopy images of malignant melanoma using color and texture features. Comput. Med. Imaging Graph.
**2011**, 35, 144–147. [Google Scholar] [CrossRef] [PubMed]

**Figure 2.**A relative secondary histogram (

**a**) and its corresponding trapezoidal membership function for fuzzy set

**B**(

**b**). The frequency count F is labeled on the secondary histogram and membership function plot.

**Figure 3.**Boundary area percentage examples using 10% (

**a**), 25% (

**b**) and 75% (

**c**) of the lesion area for analysis (white region). (This is the same lesion as in Figure 1).

**Figure 4.**Average and standard deviation test results over 25 randomly generated training/test sets for different boundary area percentages for r = 0. FCN and FCM denote the fuzzy ratio features computed using the benign and melanoma training images to determine discrimination accuracy. (

**a**) Boundary area percentage = 10%; (

**b**) Boundary area percentage = 25%; (

**c**) Boundary area percentage = 75%; (

**d**) Boundary area percentage = 100%.

**Figure 5.**Average and standard deviation test results over 25 randomly generated training/test sets for different boundary area percentages for r = 1. FCN and FCM denote the fuzzy ratio features computed using the benign and melanoma training images to determine discrimination accuracy. (

**a**) Boundary area percentage = 10%; (

**b**) Boundary area percentage = 25%; (

**c**) Boundary area percentage = 75%; (

**d**) Boundary area percentage = 100%.

**Figure 6.**Average and standard deviation test results over 25 randomly generated training/test sets for 25% boundary area percentage for r = 1 and α = 0.02, 0.05, 0.08, 0.1, 0.15 and 0.2. FCN denotes the fuzzy ratio features computed using the benign training images to determine the fuzzy set

**B**.

Computer-Assisted Skin Lesion Diagnosis | ||
---|---|---|

Actual Skin Lesion Diagnosis | Benign | Melanoma |

Benign | True negative (tn) | False positive (fp) |

Melanoma | False negative (fn) | True positive (tp) |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Almubarak, H.A.; Stanley, R.J.; Stoecker, W.V.; Moss, R.H.
Fuzzy Color Clustering for Melanoma Diagnosis in Dermoscopy Images. *Information* **2017**, *8*, 89.
https://doi.org/10.3390/info8030089

**AMA Style**

Almubarak HA, Stanley RJ, Stoecker WV, Moss RH.
Fuzzy Color Clustering for Melanoma Diagnosis in Dermoscopy Images. *Information*. 2017; 8(3):89.
https://doi.org/10.3390/info8030089

**Chicago/Turabian Style**

Almubarak, Haidar A., R. Joe Stanley, William V. Stoecker, and Randy H. Moss.
2017. "Fuzzy Color Clustering for Melanoma Diagnosis in Dermoscopy Images" *Information* 8, no. 3: 89.
https://doi.org/10.3390/info8030089