Colored Texture Analysis Fuzzy Entropy Methods with a Dermoscopic Application

Abstract

Texture analysis is a subject of intensive focus in research due to its significant role in the field of image processing. However, few studies focus on colored texture analysis and even fewer use information theory concepts. Entropy measures have been proven competent for gray scale images. However, to the best of our knowledge, there are no well-established entropy methods that deal with colored images yet. Therefore, we propose the recent colored bidimensional fuzzy entropy measure, FuzEnC2D, and introduce its new multi-channel approaches, FuzEnV2D and FuzEnM2D, for the analysis of colored images. We investigate their sensitivity to parameters and ability to identify images with different irregularity degrees, and therefore different textures. Moreover, we study their behavior with colored Brodatz images in different color spaces. After verifying the results with test images, we employ the three methods for analyzing dermoscopic images of malignant melanoma and benign melanocytic nevi. FuzEnC2D, FuzEnV2D, and FuzEnM2D illustrate a good differentiation ability between the two-similar in appearance-pigmented skin lesions. The results outperform those of a well-known texture analysis measure. Our work provides the first entropy measure studying colored images using both single and multi-channel approaches.

Keywords: colored texture analysis; dermoscopy; entropy; fuzzy entropy; information theory; medical image analysis; melanoma; texture analysis.

Figure 1

Illustration for $FuzEn{C}_{2D}$ of an RGB color space image. (a) The image U is split into its corresponding channels U${}_R$, U${}_G$, and U${}_B$, respectively, from left to right; (b) the embedding dimension pattern of size $m\times m$ having m$=[2,2]$; (c) X${}_{i,j,K}^m$ and X${}_{a,b,K}^m$ for K = K1, K2, and K3 being the R, G, and B color channels, respectively.

Figure 2

Illustration for $FuzEn{V}_{2D}$ of an RGB color space image having m = [ 2,2,2]. (a) A portion of the colored image $\mathbf{U}$ with its R, G, and B channels; (b) the scanning pattern or embedding dimension with m$=[2,2,2]$ that is a $2\times 2\times 2$ cube; (c) X${}_{i,j,k}^m$ and X${}_{a,b,c}^m$, the fixed and moving templates defined above.

Figure 3

Illustration for $FuzEn{M}_{2D}$ of RGB color space image having m$=[2,2,3]$. (a) A portion of the colored image $\mathbf{U}$ with its R, G, and B channels; (b) the scanning pattern or embedding dimension with m$=[2,2,3]$ that is a $2\times 2\times 3$ cuboid; (c) the fixed and moving templates defined above.

Figure 4

Colored Brodatz texture (CBT) images of different colored irregularity degrees [41,42]. (a–i) CBT images that are used for the validation test (Section 4.3) to compare the entropy values of each colored texture to its corresponding sub-images in three color spaces (RGB, HSV, and YUV); (f) is used again for studying the sensitivity of the proposed measures to different initial parameters (Section 4.1).

Figure 5

Dermoscopic images segmentation for choosing the region of interest (ROI). (a) an example of the dermoscopic image for a pigmented skin lesion; (b,c) the contouring and segmentation of the lesion; (d) the ROI as the central $128\times 128\times 3$ pixels.

Figure 6

$FuzEn{C}_{2D}$ results for the red, green, and blue channels (left to right) of the colored Brodatz image, Figure 4f, with varying r and m.

Figure 7

$FuzEn{V}_{2D}$ results with varying r and m of the colored Brodatz image, Figure 4f.

Figure 8

$FuzEn{M}_{2D}$ results with varying r and m of the colored Brodatz image, Figure 4f.

Figure 9

$FuzEn{C}_{2D}$ mean and standard deviation for MIX${}_{2D}$(p) images with 10 repetitions.

Figure 10

$FuzEn{V}_{2D}$ mean and standard deviation for MIX${}_{3D}$(p) images with 10 repetitions.

Figure 11

$FuzEn{M}_{2D}$ mean and standard deviation for MIX${}_{3D}$(p) images.

Figure 12

$FuzEn{C}_{2D}$ results for the 144 sub-images and 300 × 300 pixels of the CBT in the three color spaces: RGB, HSV, and YUV, with $K1$, $K2$, and $K3$ being the first, second, and third channel, respectively. The mean of the 144 sub-images is displayed as a “∘” sign and the value for the 300 × 300 pixels is displayed as “*”.

Figure 13

$FuzEn{V}_{2D}$ results for the 144 sub-images and 300 × 300 pixels of the CBT in the three color spaces: RGB, HSV, and YUV. The mean of the 144 sub-images is displayed as a “∘” sign and the value for the 300 × 300 pixels is displayed as “*”.

Figure 14

$FuzEn{V}_{2D}$ and Haralick feature p-values of 40 melanoma and 40 melanocytic nevi dermoscopic images in the 3 color spaces: RGB, HSV, and YUV. d represents the inter-pixel distances for the co-occurrence matrices.

Figure 15

$FuzEn{M}_{2D}$ and Haralick feature p-values of 40 melanoma and 40 melanocytic nevi dermoscopic images in the 3 color spaces: RGB, HSV, and YUV. d represents the inter-pixel distances for the co-occurrence matrices.

Figure 16

ROC curves for $FuzEn{C}_{2D}$ results of the 40 melanoma and 40 melanocytic nevi images in the RGB color space. The curves are for $FuzEn{C}_{R2D}$, $FuzEn{C}_{G2D}$, and $FuzEn{C}_{B2D}$ from left to right.

Figure 17

ROC curves for $FuzEn{V}_{2D}$ results of the 40 melanoma and 40 melanocytic nevi images in the RGB color space.

Figure 18

ROC curves for $FuzEn{M}_{2D}$ results of the 40 melanoma and 40 melanocytic nevi images in the RGB color space.