Classification of Skin Lesion Images Using Artificial Intelligence Methodologies through Radial Fourier–Mellin and Hilbert Transform Signatures

Featured Application

A method to develop a potential automated skin lesion classification.

Abstract

This manuscript proposes the possibility of concatenated signatures (instead of images) obtained from different integral transforms, such as Fourier, Mellin, and Hilbert, to classify skin lesions. Eight lesions were analyzed using some algorithms of artificial intelligence: basal cell carcinoma (BCC), squamous cell carcinoma (SCC), melanoma (MEL), actinic keratosis (AK), benign keratosis (BKL), dermatofibromas (DF), melanocytic nevi (NV), and vascular lesions (VASCs). Eleven artificial intelligence models were applied so that eight skin lesions could be classified by analyzing the signatures of each lesion. The database was randomly divided into 80% and 20% for the training and test dataset images, respectively. The metrics that are reported are accuracy, sensitivity, specificity, and precision. Each process was repeated 30 times to avoid bias, according to the central limit theorem in this work, and the averages and ± standard deviations were reported for each metric. Although all the results were very satisfactory, the highest average score for the eight lesions analyzed was obtained using the subspace k-NN model, where the test metrics were 99.98% accuracy, 99.96% sensitivity, 99.99% specificity, and 99.95% precision.

1. Introduction

The skin is the largest organ in the body; it covers and protects externally. Its condition and appearance show the state of health and wellbeing of a person; however, due to exposure to the environment and other factors, specific skin injuries may occur; these can vary in size and shape. Different types of skin diseases vary according to the symptoms. The presence of any mild skin condition can lead to severe complications and even death. Skin cancer is a serious disease and one of the most common carcinomas. It is mainly classified into basal cell carcinoma (BCC), squamous cell carcinoma or epidermoid carcinoma (SCC), and melanoma (MEL) [1,2,3,4]. BCC is the most frequent skin cancer in the worldwide population, and its growth is slow. It can grow and destroy the skin. It is generally observed as a flat or raised lesion and its color is reddish [1,5,6,7]. SCC is a malignant tumor that appears as red spots with raised growths like warts; it is the second most common skin cancer [1,2]. Melanoma is the most aggressive skin cancer, appearing as a pigmented lesion, usually beginning on normal skin as a new, small, pigmented growth [2]. Other common skin diseases are actinic keratosis (AK), benign keratosis (BKL), dermatofibromas (DF), melanocytic nevi (NV), and vascular lesions (VASCs), among others.

Actinic keratosis occurs due to frequent exposure to ultraviolet rays from the sun or tanning beds; it usually appears as small rough spots and presents color variations. Some areas are generally malignant, causing squamous cell carcinoma [7,8,9]. Seborrheic keratoses or benign keratoses are benign tumors that frequently occur in the geriatric population. This type of tumor consists of a brown, black, or light brown spot or lesion. In some cases, it is often confused with basal cell carcinoma or melanoma [10,11]. Dermatofibroma is a benign skin lesion; it appears as a slow-growing papule, and its color varies from light to dark brown, purple to red, or yellowish. Its clinical diagnosis is simple; however, sometimes it is difficult to differentiate it from other tumors, such as malignant melanoma [12,13]. Melanocytic nevi or moles are the most common benign lesions and have smooth, flat, or palpable surfaces. They form as a brown spot or freckle that varies in size and thickness [14,15]. Vascular lesions are disorders of the blood vessels. They become evident on the skin’s surface, forming red structures, dark spots, or scars, presenting an aesthetic problem. Some VASCs develop over time due to environmental changes, temperature, poor blood circulation, or sensitive skin [16,17]. The skin can warn of a health problem; its care is critical for physical and emotional aspects. Different conditions can affect the skin; some are present at birth, whereas others are acquired throughout life. Some lesions may have similar characteristics, making it difficult to differentiate them from the most common malignant neoplasms. Skin diseases are a significant health problem. The development of new digital tools and technologies based on artificial intelligence (AI) to detect and treat diseases is due to the ability to analyze large amounts of data. The latest developments based on artificial intelligence tools help identify health problems in the early stages. These developments are also based on image processing, where the recognition of visual patterns through images represents a potential solution for the failure of the human eye to detect disease. Applying algorithms based on artificial intelligence allows the development of non-invasive tools in the health area.

In recent decades, machine learning (ML) techniques have been used in impressive applications in many research areas and are still growing. Since many studies about medical imaging are focused on automating skin lesion identification from dermatological images to provide an adequate diagnosis and treatment to patients, ML techniques can be a powerful tool to detect malignant lesions automatically, quickly, and reliably.

Some ML techniques, such as convolutional neural networks (CNNs), are the most popular as they represent the closest technique to the learning process of human vision. CNNs are based on the mathematical operator of the convolution between the image and filters to extract information. Even though CNNs have provided successful results for image classification, their high computational cost, as well the non-invariance properties under rotation, scale, and translation of the convolution operation, make CNNs, in practice, an ineffective tool to implement in the identification or classification of some images, especially for those corresponding to skin lesions where vital information could be lost due to the low contrast that often exists between the lesion and healthy skin. This low contrast can mean that during the segmentation carried out by some filters, information on the lesion is not extracted correctly [18,19]. In this context, other ML techniques, such as the support vector machine (SVM), k-nearest neighbor (k-NN), or ensemble classifiers, have shown acceptable performance [20,21].

Although the SVM, k-NN, and ensemble classifiers have been successfully implemented to classify skin lesions, digital images under rotation, scaling, or translation were not considered. The application of the fractional radial Fourier transform in pattern recognition for digital images is invariant to translation, scale, and rotation, and the results obtained to classify phytoplankton species showed a high level of confidence (greater than 90%) [22]. In this paper, we implemented the Hilbert mask on the module of the Fourier–Mellin Transform to obtain a unique signature of the skin lesion called the radial Fourier–Mellin signature, which is invariant to rotation, scale, and translation. Additionally, we included as a signature the extraction of the uniform local binary pattern (LBP-U) image features. The classification task was obtained using the k-NN, SVM, and ensemble classifiers. Section 2 contains the description and image dataset pre-processing procedure and methods used to achieve its skin lesion classification. Section 3 presents the results using these supervised machine learning methods. In Section 4, we discuss the obtained results.

2. Materials and Methods

2.1. Image Dataset

The images used in our study were obtained from the 2019 challenge training data of the “International Skin Imaging Collaboration” (ISIC) [23]. Some examples are shown in Figure 1. This dataset consists of 25,331 digital images of 8 types of skin lesions. A total of 3323 basal cell carcinoma (BCC) digital images, 628 digital images of squamous cell carcinoma (SCC), 4522 melanoma (MEL) digital images, 867 actinic keratosis (AK) skin lesion digital images, 2624 benign keratosis (BKL) skin lesion images as solar lentigo, seborrheic keratosis, and lichen planus-like keratosis, 239 dermatofibroma (DF) digital skin lesion images, 12,875 melanocytic nevus (NV) digital images, and 253 images of vascular skin lesions (VASCs). However, we proceeded to eliminate the skin lesion images that contained noise, such as hair, measurement artifacts, and other noise types that made it difficult to segment the lesions. The image dataset debugging reduced the data to 9067 dermatologic skin lesions, where 6747 images were for NV, 1032 for MEL, 512 for BCC, 471 for BKL, 130 for VASC, 67 for DF, 62 for SCC, and 46 for AK. This dramatic reduction motivated us to include a data augmentation procedure resulting in 362,680 dermatologic skin lesion images, and we randomly selected images to classify using the SVM, k-NN, and ensemble classifier machine learning methodologies. To avoid classification bias, we homogenized the classes in the database using 1840 images for each type of skin lesion. Each of these 14,720 randomly selected dataset images were transformed into their radial Fourier signatures and texture descriptors using the Hilbert transform.

2.2. The Signatures

We generated several signature vectors for each RGB channel and gray-scale images using our dataset (362,680) obtained through data augmentation. The data augmentation procedure considered five image scale percentages (100%, 95%, 90%, 85%, and 80%) and eight rotation angle values (45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360°). These signatures or descriptors used invariance properties to the translation and scale of the modules of the Fourier transform and the Mellin transform, respectively. To include the invariant object rotation property, we used the Hilbert transform. To calculate the unique signatures of the image, we summed the pixel value for each ring obtained after using the Hilbert masks as a filter. We incorporated the texture signatures or descriptors on the previously generated radial Fourier signatures. The process to obtain this one-dimensional skin lesion digital image representation or signature is shown in Figure 2 and Figure 3. The original image ($Im(x,y)$) contains three matrix channels in RGB (red, green, and blue channels). Thus, the picture was segmented into these three primary color channels to apply the radial Fourier–Mellin method and the uniform LBP image features extraction. In addition, we considered the gray-scale skin lesion digital image obtained by a weighted sum of RGB values defined by: 0.299R + 0.587G + 0.114B.

2.3. Radial Fourier–Mellin Signatures through Hilbert Transform

To generate the radial Fourier–Mellin signatures, first the image was split into its RGB channels and gray scale (Figure 3a). Then, the module of the Fourier–Mellin (FM) transforms of each skin digital image, named $Im(x,y)$, was obtained using the next equation [24,25,26] (Figure 3b).

$${|F}_M\left(s,t\right)|={\iint }_0^{\infty }\left|FT\right[Im(x,y)\left]\right|x^{s-1}{y}^{t-1}dxdy=M\left\{\left|FT\right[Im(x,y)\left]\right|\right\}$$

(1)

where ${|F}_M\left(s,t\right)|$ is the module of the Mellin transform, which give us a scale invariance of an object in the image that is necessary as the skin lesion digital images were obtained from different lesion to camera distances. Thus, the lesion region is smaller for longer lesion to camera distances and the images contain a larger lesion region when the opposite is true. Moreover, $(s,t)$ represents the 2D coordinates of the transformed $\left(x,y\right)$ pixel coordinates on Mellin’s plane. Notice that these pixel coordinates $\left(x,y\right)$ correspond to the module Fourier transform of the image ($\left|FT\right[Im(x,y)\left]\right|$), taking advantage of its translation invariance. Therefore, at this moment, the object (skin lesion) in the image is invariant to translation and scale.

Now, using the Hilbert transform, we also achieve the skin lesion in the image being invariant to rotation. The Hilbert transform of the image is given by [22,26,27,28,29]:

$$\mathcal{F}\left\{H_r\left[Im\right(x,y\left)\right]\right\}=e^{ip\theta }FT\left[Im\left(x,y\right)\right]=e^{ip\theta }F\left(u,v\right)$$

(2)

where $p$ is the order of the radial Hilbert transform, $\theta$ is the angle on frequency domain/space of the pixel coordinates in the image $(x,y)$ after being transformed to the Fourier plane coordinates as $(u,v)$. Therefore, this angle is determined by $\theta =\mathrm{a}\mathrm{c}\mathrm{o}\mathrm{s}\left(u/\sqrt{u^2+v^2}\right)$. Then, using the Euler’s formula, we calculated the binary ring masks of the RGB channels and gray-scale skin lesion digital image, using both the real ($H_R$) and imaginary ($H_I$) parts of the radial Hilbert transform of the image as follows (Figure 2), [22,26,27,28,29].

$$H_R=Re\left[H_r\left(u,v\right)\right]=\left\{\begin{array}{c}1, if \mathrm{s}\mathrm{i}\mathrm{n}=\left(p\theta \right)>0 \\ 0, otherwise\end{array}\right.$$

(3)

$$H_I=Im\left[H_r\left(u,v\right)\right]=\left\{\begin{array}{c}1, if cos\left(p\theta \right)>0 \\ 0, otherwise\end{array}\right.$$

(4)

The binary ring masks obtained above were applied to filter the skin lesion digital images that were previously processed using the module of the Fourier–Mellin transform (Figure 3c). The results require the sum of the values in the pixels of each ring obtaining two unique signatures of each skin gray-scale lesion image ${(Sgray}_{H_R} \mathrm{a}\mathrm{n}\mathrm{d} {Sgray}_{H_I})$ and its RGB channels given by: ${SR}_{H_R}$, ${SR}_{H_I}$, ${SG}_{H_R}$, ${SG}_{H_I}$, ${SB}_{H_R}$, and ${SB}_{H_I}$ (Figure 3d). Finally, each signature is normalized by its maximum value (Figure 3e,g).

To include texture descriptors, we used the uniform local binary pattern (LBP) technique (Figure 3f). This is a texture analysis tool in computer vision and image processing [30].

It is a simple and efficient descriptor that describes textures, edges, corners, spots, and flat regions. Taking blocks of 3 × 3 pixels, the intensity of each of the eight neighboring pixels is compared with the intensity of the central pixel (defined as the threshold). Suppose the intensity of the adjacent pixel is greater than or equal to the intensity of the central pixel; in this case, the position of the neighboring pixel is assigned a value of 1 (or otherwise a value of 0). Once all the pixels are compared, we obtain a set of zeros and ones that represent a binary number. Each position of the binary number is multiplied by its corresponding decimal value and then all the values are added. This sum is the LBP value that labels the central pixel. Figure 4 shows an example of the LBP calculation on any pixel for P = 8 neighborhood pixels.

To calculate the LBP on a gray-scale image, the following equation is used:

$$LBP\left(x_c,y_c\right)={\sum }_{p=0}^{P-1}{s(I}_p-I_c)2^p,$$

(5)

where $\left(x_c,y_c\right)$ represents the position of the central pixel, P is the number of pixels in the neighborhood, $I_p$ is the intensity of the neighboring pixels, $I_c$ is the intensity of the central pixel, and $s$ is the function:

$$s\left(x\right)=\left\{\begin{array}{c}1, x\ge 0\hfill \\ 0, another value\hfill \end{array}\right..$$

(6)

The so-called uniform LBP (LBP-U) is a variant of the LBP that reduces the original LBP characteristic vector; this technique allows invariance against rotations. An LBP is uniform when there are at most two transitions from 1 to 0 and from 0 to 1; for example, the binary patterns 11111111 (0 transitions), 11111000 (1 transition), and 11001111 (2 transitions) are uniform, whereas the patterns 11010110 (6 transitions) and 110010001 (4 transitions) are not. In a neighborhood of eight pixels, 256 patterns can be identified; of which, 58 will be uniform. In this way, 58 labels are obtained for the uniform patterns, and for the non-uniform patterns, the same label is assigned, which will be 59. In this work, we use the LBP-U.

After calculating the uniform LBP value for each pixel in the image, we create a histogram of the uniform LBP values to represent the distribution of different image features of both the RGB and gray-scale images ${LBP}_R$, ${LBP}_G$, ${LBP}_B$, and ${LBP}_{gray}$. We concatenate these signatures to obtain 444 components of one-dimensional objects/signatures (Figure 3g).

2.4. Signature Classification

We generated radial Fourier and texture signature vectors for each RGB channel and gray-scale dermatological digital image in our dataset. These descriptors are invariant to scale, rotation, illumination, and noise on the image being analyzed. A data augmentation procedure considering scale and rotation was included. To homogenize the classes in the database, we used 1840 images for each type of skin lesion. The signature classification was performed with the support vector machine (SVM), k-nearest neighbor (k-NN), and ensemble classifiers.

Variations of these methods were implemented. In the case of the SVM, four different kernels were used [31]: Quadratic SVM works by implementing a polynomial of degree = 2 as a kernel, whereas the cubic SVM method uses a polynomial of degree = 3. The fine Gaussian SVM method uses a Gaussian kernel with a kernel scale = 5.3. The medium Gaussian SVM works with a wider Gaussian kernel, using a kernel scale = 21.

Additionally, five k-NN variations were explored [32,33]: Fine k-NN works using the Euclidean distance and a k = 1 neighbor. The medium k-NN algorithm also uses Euclidean distance, but the number of neighbors is k = 10. The cosine k-NN algorithm implements the cosine distance with k = 10 neighbors. The Minkowski distance, with exponent p = 3, is used for the cubic k-NN method. For the weighted k-NN, the same length and number of neighbors were used as in the medium k-NN, but for this case, the neighbors are weighted based on the square inverse of the distance.

Finally, two ensemble classifiers were used. These classifiers aggregate the predictions of a group of predictors to obtain better forecasts than the best individual predictor [34]. The bagged trees method implements decision trees using bootstrap aggregation (bagging) [35]. The subspace k-NN method uses the random subspace method for k-NN classification [36,37].

In total, 11 algorithms were explored; these are shown in

Table 1. This table shows a description of the 11 algorithms implemented.

Algorithm	Description
Quadratic SVM	Type: Support vector machine Kernel type: Quadratic polynomial
Cubic SVM	Type: Support vector machine Kernel type: Cubic polynomial
Fine Gaussian SVM	Type: Support vector machine Kernel type: Gaussian Kernel scale: 5.3
Medium Gaussian SVM	Type: Support vector machine Kernel type: Gaussian Kernel scale: 21
Fine k-NN	Type: K-nearest neighbor Number of neighbors: 1 Distance: Euclidean
Medium Gaussian k-NN	Type: K-nearest neighbor Number of neighbors: 10 Distance: Euclidean
Cosine k-NN	Number of neighbors: 10 Distance: Cosine
Cubic k-NN	Type: K-nearest neighbor Number of neighbors: 10 Distance: Minkowski distance with exponent p = 3
Weighted k-NN	Type: K-nearest neighbor Number of neighbors: 10 Distance: Euclidean Distance weight: Squared inverse
Bagged Trees	Type: Ensemble classifier Method: Bootstrap aggregating
Subspace k-NN	Type: Ensemble classifier Method: Subspace-based KNN

.

MATLAB 2022b was used to carry out the classification process, using the same dataset for all 11 algorithms. The dataset was balanced by selecting 1840 signatures from each skin lesion. Therefore, the dataset consists of 14,720 signatures.

3. Results

The data were divided by randomly selecting 80% of the data to train and 20% of the data to test each methodology used. In the training process, k-fold cross-validation with k = 5 was used. For the training dataset and the testing dataset, the accuracy, sensitivity, specificity, and precision [33] were calculated for each class. These parameters are given by

$$accuracy\left(C_i\right)=\frac{{TP}_i+{TN}_i}{{TP}_i+{TN}_i+{FP}_i+{FN}_i}$$

(7)

$$sensitivity\left(C_i\right)=\frac{{TP}_i}{{TP}_i+{FN}_i }$$

(8)

$$specificity\left(C_i\right)=\frac{{TN}_i}{{TN}_i+{FP}_i}$$

(9)

$$precision\left(C_i\right)=\frac{{TP}_i}{{TP}_i+{FP}_i}$$

(10)

where:

• ${TP}_i$: true positives for class $i$.
• ${TN}_i$: true negatives for class $i$.
• ${FP}_i$: false positives for class $i$.
• ${FN}_i$: false negatives for class $i$.

Table 2. Results for quadratic SVM.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.997713	0.000435	0.992518	0.001918	0.998454	0.000441	0.989201	0.003089
SCC	0.994121	0.000502	0.989432	0.002688	0.994789	0.000394	0.96442	0.002662
MEL	0.995564	0.000634	0.978523	0.00349	0.997998	0.000466	0.985882	0.003276
AK	0.994141	0.00064	0.969387	0.004028	0.997692	0.000405	0.983691	0.002828
BKL	0.994707	0.000585	0.982108	0.003661	0.9965	0.000433	0.975644	0.002831
DF	0.996077	0.00053	0.975942	0.003758	0.998964	0.0003	0.992662	0.00211
NV	0.995768	0.000637	0.987118	0.003555	0.996996	0.00054	0.979067	0.003622
VASC	0.998452	0.000227	0.991186	0.001829	0.999489	0.000202	0.996405	0.001409
MEAN ± 1SD	0.995818	0.001585	0.983277	0.008205	0.99761	0.001502	0.983371	0.01024
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.998902	0.000771	0.995155	0.003451	0.999443	0.000747	0.996129	0.005223
SCC	0.996671	0.001348	0.994984	0.006641	0.99692	0.001477	0.978896	0.009978
MEL	0.997328	0.001484	0.984985	0.011026	0.999095	0.000836	0.993616	0.005861
AK	0.996467	0.001355	0.981774	0.008303	0.998527	0.001044	0.989513	0.007158
BKL	0.99692	0.001044	0.99105	0.006158	0.997775	0.001073	0.984501	0.00745
DF	0.997656	0.00109	0.984903	0.008138	0.999431	0.000583	0.995944	0.004108
NV	0.997464	0.001555	0.99428	0.006072	0.99791	0.00166	0.98595	0.010578
VASC	0.998913	0.000538	0.993741	0.004151	0.999651	0.000327	0.997529	0.002344
MEAN ± 1SD	0.99754	0.000933	0.990109	0.005392	0.998594	0.000981	0.99026	0.006679

,

Table 3. Results for cubic SVM.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.997931	0.000475	0.991772	0.002502	0.998815	0.0004	0.99175	0.002773
SCC	0.998225	0.000515	0.9958	0.00246	0.998571	0.000366	0.990031	0.002564
MEL	0.998585	0.000376	0.995069	0.002159	0.999085	0.000309	0.993581	0.002148
AK	0.997857	0.000469	0.98977	0.002736	0.99901	0.000418	0.993046	0.002911
BKL	0.997951	0.000604	0.99258	0.003565	0.998719	0.000419	0.991067	0.002932
DF	0.998488	0.00042	0.993297	0.003042	0.99923	0.000292	0.994617	0.002015
NV	0.998321	0.000412	0.99141	0.002184	0.999311	0.000323	0.995173	0.002237
VASC	0.999768	0.000158	0.998817	0.001053	0.999903	0.000108	0.99932	0.000756
MEAN ± 1SD	0.998391	0.000617	0.993565	0.002882	0.99908	0.000417	0.993573	0.002906
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.999241	0.000701	0.997109	0.004113	0.999535	0.000714	0.996713	0.005081
SCC	0.999411	0.000667	0.998569	0.003459	0.999534	0.000685	0.996772	0.00483
MEL	0.999468	0.000548	0.998491	0.003087	0.999611	0.000568	0.997317	0.003941
AK	0.999207	0.000769	0.996019	0.004335	0.999665	0.000615	0.997598	0.004424
BKL	0.999343	0.000807	0.997474	0.005446	0.999612	0.000638	0.997301	0.004364
DF	0.999683	0.000527	0.999094	0.002063	0.999767	0.000507	0.998393	0.003469
NV	0.999162	0.000816	0.995287	0.00487	0.999716	0.000584	0.997986	0.004132
VASC	1	0	1	0	1	0	1	0
MEAN ± 1SD	0.99944	0.000281	0.997755	0.001587	0.99968	0.000153	0.99776	0.001067

,

Table 4. Results for fine Gaussian SVM.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.990617	0.001202	0.938094	0.009789	0.998108	0.000634	0.986097	0.004562
SCC	0.991729	0.000776	0.9374	0.006256	0.999511	0.000248	0.996384	0.001816
MEL	0.990704	0.000929	0.948301	0.004959	0.99677	0.000679	0.976802	0.004607
AK	0.964331	0.002284	0.992258	0.002383	0.960355	0.002588	0.781032	0.01118
BKL	0.988485	0.000888	0.915523	0.006838	0.998884	0.000384	0.991531	0.002881
DF	0.993657	0.000814	0.963894	0.006035	0.997907	0.000437	0.985045	0.003063
NV	0.987007	0.000943	0.955562	0.006548	0.991504	0.000797	0.941491	0.00538
VASC	0.993679	0.000848	0.949736	0.006868	0.999951	7.96E−05	0.999643	0.000587
MEAN ± 1SD	0.987526	0.009651	0.950096	0.022366	0.992874	0.013403	0.957253	0.073477
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.994792	0.001981	0.963688	0.014052	0.999249	0.000668	0.994572	0.004833
SCC	0.996071	0.000904	0.968772	0.007678	0.999922	0.000214	0.999446	0.001521
MEL	0.996535	0.001641	0.980529	0.012471	0.998837	0.00096	0.991698	0.006806
AK	0.982756	0.002737	0.994899	0.00495	0.980997	0.002822	0.883549	0.015957
BKL	0.99435	0.001641	0.960839	0.010733	0.999222	0.000671	0.994451	0.004731
DF	0.997226	0.001441	0.983665	0.008772	0.999148	0.00091	0.993885	0.006639
NV	0.994124	0.001773	0.982219	0.008845	0.995812	0.001428	0.970819	0.010054
VASC	0.997271	0.001331	0.978214	0.010582	1	0	1	0
MEAN ± 1SD	0.994141	0.004764	0.976603	0.011407	0.996649	0.006459	0.978552	0.039459

,

Table 5. Results for medium Gaussian SVM.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.970352	0.001239	0.904254	0.007983	0.979737	0.001104	0.863793	0.006639
SCC	0.973061	0.001097	0.893946	0.007351	0.984325	0.00116	0.890457	0.006616
MEL	0.970867	0.000961	0.829685	0.006684	0.991048	0.000499	0.929828	0.003744
AK	0.977499	0.000898	0.897616	0.006106	0.988921	0.00103	0.920629	0.006421
BKL	0.972529	0.000865	0.865436	0.00704	0.987814	0.000886	0.910286	0.005526
DF	0.985904	0.000616	0.921273	0.004687	0.995152	0.000607	0.96458	0.004144
NV	0.959978	0.000896	0.944947	0.003669	0.96213	0.001128	0.781547	0.004489
VASC	0.991525	0.000697	0.949302	0.005961	0.997563	0.000433	0.982402	0.002982
MEAN ± 1SD	0.975214	0.009798	0.900808	0.039817	0.985836	0.011125	0.90544	0.062767
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.977502	0.003381	0.93541	0.015774	0.98365	0.003091	0.89323	0.018677
SCC	0.979337	0.002892	0.921498	0.020366	0.987716	0.0027	0.915755	0.017457
MEL	0.976551	0.003395	0.858984	0.024565	0.993301	0.00136	0.947996	0.010845
AK	0.983243	0.002995	0.913926	0.013777	0.993147	0.002206	0.949931	0.015829
BKL	0.978023	0.003674	0.893106	0.022957	0.990187	0.001856	0.928795	0.012963
DF	0.991078	0.001802	0.947692	0.011963	0.997261	0.001098	0.979965	0.008013
NV	0.966044	0.004155	0.952837	0.010116	0.967897	0.005143	0.807599	0.024077
VASC	0.993671	0.001883	0.959445	0.013131	0.998526	0.000779	0.989305	0.005602
MEAN ± 1SD	0.980681	0.008731	0.922862	0.033929	0.988961	0.009796	0.926572	0.057544

,

Table 6. Results for fine k-NN.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.996612	0.000647	0.988253	0.003377	0.997809	0.000452	0.984767	0.003143
SCC	0.996459	0.000687	0.992086	0.00247	0.997082	0.000661	0.979832	0.004407
MEL	0.991981	0.000865	0.967874	0.005457	0.995412	0.00063	0.967787	0.004308
AK	0.997019	0.000537	0.98884	0.00308	0.998188	0.000476	0.98736	0.003258
BKL	0.993662	0.000735	0.968304	0.005179	0.997277	0.000491	0.980674	0.003422
DF	0.995847	0.00054	0.984048	0.003433	0.997534	0.000475	0.9828	0.003276
NV	0.9906	0.000995	0.962863	0.005059	0.994565	0.000698	0.962032	0.004756
VASC	0.997852	0.000516	0.987744	0.003771	0.999295	0.000296	0.995033	0.002071
MEAN ± 1SD	0.995004	0.002616	0.980001	0.011626	0.997145	0.001511	0.980036	0.010578
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.998562	0.000776	0.995856	0.00456	0.998941	0.00065	0.992512	0.004646
SCC	0.998709	0.000954	0.997816	0.002984	0.998835	0.000948	0.991932	0.006699
MEL	0.996581	0.001444	0.98485	0.010675	0.998316	0.001431	0.988392	0.009868
AK	0.998913	0.001019	0.996475	0.005015	0.999275	0.000801	0.994956	0.005579
BKL	0.997101	0.001219	0.984999	0.007762	0.998836	0.001008	0.991779	0.007134
DF	0.998358	0.000953	0.995091	0.004975	0.998823	0.000948	0.991805	0.006562
NV	0.995811	0.001733	0.983651	0.008814	0.997541	0.001488	0.982872	0.010041
VASC	0.999026	0.000761	0.993904	0.006181	0.999754	0.00033	0.998266	0.002323
MEAN ± 1SD	0.997883	0.001215	0.99158	0.00598	0.99879	0.000652	0.991564	0.004523

,

Table 7. Results for medium Gaussian k-NN.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.968962	0.001612	0.902908	0.008807	0.978419	0.001602	0.857063	0.008559
SCC	0.964886	0.001417	0.886476	0.009336	0.976084	0.001643	0.841252	0.008924
MEL	0.956256	0.001899	0.817315	0.011059	0.976133	0.001703	0.830625	0.009523
AK	0.966205	0.001226	0.862392	0.009765	0.98104	0.001444	0.866847	0.008002
BKL	0.963505	0.00187	0.84941	0.00938	0.979755	0.002278	0.856939	0.013198
DF	0.969574	0.001417	0.849535	0.010333	0.986664	0.001288	0.900786	0.008433
NV	0.951404	0.001651	0.834493	0.010815	0.968077	0.001882	0.788632	0.009132
VASC	0.985493	0.001017	0.902211	0.007839	0.997421	0.000526	0.980456	0.003871
MEAN ± 1SD	0.965786	0.010118	0.863092	0.031504	0.980449	0.008639	0.865325	0.056466
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.977899	0.002878	0.946323	0.014022	0.982366	0.003188	0.884054	0.017584
SCC	0.975928	0.003423	0.906904	0.021586	0.985793	0.00251	0.901248	0.016761
MEL	0.965308	0.004586	0.879849	0.023875	0.977466	0.003912	0.847469	0.023878
AK	0.97474	0.003065	0.891863	0.016402	0.986582	0.002767	0.904245	0.020062
BKL	0.971558	0.00339	0.897429	0.017104	0.982317	0.002985	0.879933	0.018989
DF	0.977219	0.002996	0.877022	0.024321	0.991761	0.002146	0.939128	0.015253
NV	0.960462	0.004176	0.85456	0.025912	0.975699	0.004218	0.83514	0.02571
VASC	0.988055	0.00234	0.912879	0.018859	0.998694	0.000701	0.990039	0.005171
MEAN ± 1SD	0.973896	0.008384	0.895854	0.027499	0.985085	0.0075	0.897657	0.049623

,

Table 8. Results for cosine k-NN.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.96834	0.00108	0.851159	0.010441	0.985047	0.001385	0.890453	0.008299
SCC	0.963689	0.001617	0.849973	0.013445	0.979887	0.001611	0.857745	0.009328
MEL	0.954031	0.001684	0.798347	0.012674	0.976334	0.002385	0.828959	0.012168
AK	0.965667	0.001554	0.867501	0.009935	0.9797	0.002158	0.859622	0.011847
BKL	0.959197	0.001785	0.813381	0.012224	0.979997	0.001902	0.853189	0.010953
DF	0.969908	0.001379	0.833521	0.010051	0.989456	0.001226	0.918975	0.008551
NV	0.941463	0.002009	0.890112	0.013375	0.94879	0.00315	0.71319	0.010549
VASC	0.981986	0.001287	0.91312	0.008143	0.991796	0.001024	0.940725	0.006908
MEAN ± 1SD	0.963035	0.01197	0.852139	0.038069	0.978876	0.013264	0.857857	0.069131
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.977434	0.002263	0.911182	0.014176	0.986988	0.002337	0.909599	0.016076
SCC	0.972271	0.003538	0.871525	0.020069	0.986818	0.002835	0.904842	0.020734
MEL	0.9643	0.00416	0.853384	0.026301	0.979937	0.0029	0.857077	0.018503
AK	0.973607	0.003901	0.895428	0.016813	0.98474	0.003515	0.893324	0.023071
BKL	0.967969	0.004153	0.871239	0.02185	0.981898	0.003421	0.873844	0.020752
DF	0.974411	0.00296	0.85076	0.016279	0.99186	0.002333	0.936737	0.016802
NV	0.95608	0.003435	0.912351	0.018579	0.962345	0.004294	0.7758	0.022732
VASC	0.985847	0.00222	0.921673	0.014345	0.995114	0.001557	0.964687	0.010787
MEAN ± 1SD	0.97149	0.008917	0.885943	0.027834	0.983713	0.009942	0.889489	0.057024

,

Table 9. Results for cubic k-NN.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.967544	0.001553	0.892731	0.011109	0.978245	0.00162	0.85463	0.008652
SCC	0.958837	0.002056	0.87173	0.011594	0.971249	0.002404	0.812395	0.011305
MEL	0.951254	0.001966	0.792743	0.016617	0.973954	0.002412	0.813743	0.012396
AK	0.961603	0.001413	0.843246	0.008752	0.978504	0.001808	0.84871	0.010153
BKL	0.958948	0.001545	0.83026	0.009622	0.977347	0.001845	0.839881	0.010704
DF	0.965498	0.001278	0.833468	0.010531	0.984356	0.001613	0.884018	0.009842
NV	0.950286	0.001692	0.834216	0.013508	0.966907	0.002334	0.783326	0.010768
VASC	0.984078	0.000932	0.893935	0.007509	0.996871	0.000587	0.975965	0.004312
MEAN ± 1SD	0.962256	0.010704	0.849041	0.034759	0.978429	0.009109	0.851583	0.058924
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.977231	0.002806	0.950159	0.012809	0.98111	0.003381	0.876928	0.021674
SCC	0.970211	0.003376	0.883554	0.021992	0.982757	0.003779	0.880785	0.024607
MEL	0.962183	0.00427	0.867746	0.025005	0.975543	0.003754	0.83374	0.023414
AK	0.970652	0.003369	0.869158	0.015176	0.985198	0.003215	0.893751	0.021674
BKL	0.966769	0.003754	0.882164	0.019933	0.978868	0.003254	0.856108	0.020597
DF	0.972883	0.003797	0.859058	0.019839	0.989167	0.002575	0.919144	0.017968
NV	0.960417	0.003748	0.849669	0.027438	0.976155	0.004667	0.834863	0.027576
VASC	0.986458	0.002753	0.907463	0.018557	0.998054	0.000889	0.985479	0.006777
MEAN ± 1SD	0.97085	0.008363	0.883622	0.032105	0.983357	0.00748	0.8851	0.049853

,

Table 10. Results for weighted k-NN.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.99101	0.000853	0.966399	0.004479	0.99452	0.000799	0.961846	0.005073
SCC	0.990489	0.000854	0.973897	0.005359	0.992855	0.000691	0.951129	0.004412
MEL	0.98292	0.001179	0.929858	0.006006	0.990501	0.000993	0.933329	0.006406
AK	0.990648	0.000956	0.961649	0.00594	0.994779	0.000829	0.963376	0.005514
BKL	0.987704	0.001124	0.94218	0.007959	0.994208	0.000832	0.958831	0.005584
DF	0.991358	0.000866	0.961126	0.005819	0.995669	0.000647	0.969407	0.004409
NV	0.978637	0.001198	0.930944	0.008927	0.985455	0.001282	0.901657	0.006904
VASC	0.994882	0.000687	0.964408	0.004778	0.999236	0.000312	0.994494	0.002249
MEAN ± 1SD	0.988456	0.005248	0.953808	0.016992	0.993403	0.00405	0.954259	0.02732
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.995143	0.001416	0.980286	0.006849	0.997283	0.001247	0.980993	0.008724
SCC	0.995709	0.001617	0.989698	0.008021	0.996571	0.001178	0.976347	0.008376
MEL	0.989232	0.002362	0.953552	0.012095	0.994358	0.001925	0.960311	0.013101
AK	0.995822	0.001604	0.982016	0.008189	0.997812	0.001377	0.984743	0.009674
BKL	0.993795	0.002086	0.967452	0.010927	0.997569	0.001363	0.982643	0.009614
DF	0.995958	0.001499	0.984228	0.007814	0.997658	0.001094	0.983658	0.007641
NV	0.985892	0.002686	0.957146	0.013847	0.989976	0.00227	0.931492	0.013995
VASC	0.997543	0.001159	0.982462	0.007462	0.99969	0.000459	0.997759	0.003378
MEAN ± 1SD	0.993637	0.003989	0.974605	0.013462	0.996365	0.002976	0.974743	0.020327

,

Table 11. Results for bagged trees.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.998053	0.000557	0.991325	0.003305	0.999013	0.000478	0.993097	0.003319
SCC	0.996912	0.000734	0.985676	0.004545	0.998515	0.000531	0.989579	0.003716
MEL	0.997727	0.000607	0.990838	0.002973	0.998709	0.000528	0.990981	0.003639
AK	0.996932	0.000557	0.991146	0.00306	0.997758	0.00052	0.984448	0.003544
BKL	0.995689	0.00073	0.98531	0.004189	0.997167	0.00062	0.980236	0.004258
DF	0.997554	0.000714	0.987148	0.003966	0.999039	0.000378	0.993235	0.002618
NV	0.997815	0.000605	0.991293	0.003389	0.998745	0.000487	0.991221	0.003352
VASC	0.99912	0.000359	0.996388	0.001829	0.999511	0.000323	0.996589	0.00225
MEAN ± 1SD	0.997475	0.001002	0.98989	0.003684	0.998557	0.000754	0.989923	0.00524
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.999241	0.000712	0.996774	0.003976	0.999586	0.000548	0.997078	0.00388
SCC	0.998992	0.001031	0.994303	0.007762	0.999665	0.000483	0.997583	0.003562
MEL	0.999479	0.000826	0.998582	0.002601	0.999611	0.000737	0.997366	0.004978
AK	0.999253	0.000693	0.997617	0.003347	0.999483	0.00057	0.996359	0.003996
BKL	0.998471	0.001062	0.996698	0.003667	0.998732	0.001071	0.991193	0.00753
DF	0.999377	0.000606	0.99615	0.003906	0.999844	0.000283	0.998946	0.001909
NV	0.999298	0.000719	0.997054	0.004332	0.999625	0.000591	0.997368	0.004074
VASC	0.999841	0.000365	0.998721	0.002971	1	0	1	0
MEAN ± 1SD	0.999244	0.000395	0.996987	0.001413	0.999568	0.000375	0.996987	0.002606

and

Table 12. Results for subspace k-NN.

	TRAINING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.999462	0.000296	0.997958	0.001851	0.999677	0.000245	0.997737	0.0017
SCC	0.999038	0.000615	0.995829	0.002757	0.999496	0.000445	0.99646	0.003122
MEL	0.998709	0.000469	0.995324	0.003062	0.999194	0.000339	0.994398	0.002311
AK	0.998958	0.000546	0.995273	0.003405	0.999485	0.000285	0.996408	0.00199
BKL	0.999128	0.000355	0.997912	0.001905	0.999301	0.00039	0.995139	0.0027
DF	0.999176	0.000554	0.99656	0.002521	0.99955	0.000403	0.996853	0.002832
NV	0.998814	0.000494	0.99408	0.003025	0.999486	0.000315	0.996381	0.002206
VASC	0.999853	0.00013	0.999591	0.000708	0.99989	0.000134	0.999234	0.000934
MEAN ± 1SD	0.999142	0.000368	0.996566	0.001806	0.99951	0.000213	0.996576	0.001482
	TESTING SET
	ACCURACY		SENSITIVITY		SPECIFICITY		PRECISION
LESION	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD	MEAN	±1SD
BCC	0.999955	0.000248	1	0	0.999948	0.000284	0.999642	0.001963
SCC	0.999774	0.000515	0.998957	0.003181	0.999896	0.000394	0.999284	0.002726
MEL	0.999909	0.000345	1	0	0.999897	0.000393	0.999268	0.002791
AK	0.999909	0.000345	0.999643	0.001958	0.999948	0.000283	0.999637	0.00199
BKL	0.999864	0.000415	1	0	0.999845	0.000473	0.998915	0.003311
DF	0.999864	0.000415	0.998952	0.0032	1	0	1	0
NV	0.999909	0.000345	0.999282	0.002732	1	0	1	0
VASC	1	0	1	0	1	0	1	0
MEAN ± 1SD	0.999898	6.74 × 10−5	0.999604	0.000475	0.999942	5.82 × 10−5	0.999593	0.000407

show the results for each algorithm.

Because the splitting, training, and testing process described above was performed randomly, it was repeated 30 times to avoid bias according to the central limit theorem, and the mean ±1 standard deviation was calculated for each metric to determine the repeatability of each implemented method.

An example of the subspace k-NN method’s performance in each cycle is presented. In Figure 5, the ROC curve for the training and test sets from an example cycle of the subspace k-NN method is shown. Both curves have excellent performance for each of the eight classes.

The confusion matrix for the training and testing of the example process of the subspace k-NN method are shown in Figure 6.

4. Discussion

The results obtained from this new methodology for classifying skin lesions by employing eleven artificial intelligence algorithms using concatenated signatures were promising. This methodology proposes using several integral transforms (Fourier, Mellin, and Hilbert) along with the uniform LBP method of texture features to obtain a series of concatenated signatures for each lesion. This methodology works quite well for those images of skin lesions that lack noise. It is important to note that the concatenation of the signatures was achieved using the three color spaces (RGB) and the gray image to extract as much information as possible. This allows the artificial intelligence algorithms to detect the most subtle differences between the lesions. The eleven tables show excellent results for the accuracy, sensitivity, specificity, and precision metrics of the method, both for the training set and the test set. The group of lesions used to test this methodology was absent in the set of images used to train the various artificial intelligence algorithms. For both the training and test sets, the algorithms were run 30 times, thus obtaining an average and a ±standard deviation for each case. When defining the best classifier from the eleven presented in this work for this class of images, we observed that the classifier with the best performance was the subspace k-NN classifier, which had the best results for the test set. The same happens when we compare the metrics regarding the training of the various classifiers. The remaining ten classifiers also performed well. Using these classifiers when the input consists of concatenated signatures that are invariant to rotation, scale, and translation is an excellent contribution to this work. This work aligns with previous studies on the classification of skin lesions using artificial intelligence algorithms. For example, ref. [38] presented a dataset of 2241 histopathological images from 2008 to 2018. They employed two deep learning architectures, namely VGG19 and ResNet50. The results showed a high accuracy for distinguishing melanoma from nevi, with an average F1 score of 0.89, a sensitivity of 0.92, a specificity of 0.94, and an AUC of 0.98. In reference [39], the authors present an automated skin lesion detection and classification technique utilizing an optimized stacked sparse autoencoder (OSSAE)-based feature extractor with a backpropagation neural network (BPNN), named the OSSAE-BPNN technique, that reached a testing accuracy of 0.947, a sensitivity of 0.824, a specificity of 0.974, and a precision of 0.830. More studies in these areas are described in

Table 13. Literature review. Works that implement machine learning techniques for skin lesion classification.

Reference	Classification Method	Dataset	Number of Images	Classes	Balance Strategy	Classified Type	Train–Test (%)	Training Results Reported	Test Results
									Accuracy (%)	Sensitivity (%)	Specificity (%)	Precision (%)
Ballerini (2012) [40]	k-Nearest Neighbor.	Not reported	960	5	No	Multiclass	Not reported	Yes	74.30	Not reported	Not reported	Not reported
Ozkan and Koklu (2017) [41]	Support Vector Machine. k-Nearest Neighbor. Artificial Neural Network. Decision Tree.	PH2	200	3	No	Multiclass	Not reported	No	92.50	90.86	96.11	90.45
Nasir et al. (2018) [42]	Support Vector Machine.	PH2	200	2	No	Binary	50–50	No	97.5	97.7	96.7	Not reported
Chatterjee et al. (2019) [43]	Support Vector Machine.	Different sources	6579	3	Yes	Binary	80–20	No	By Class: MEL = 98.99 NV = 97.54 BCC = 99.65	By Class: MEL = 98.28 NV = 91.07 BCC = 100	By Class: MEL = 98.48 NV = 99.39 BCC = 99.63	Not reported
Fisher et al. (2019) [44]	k-Nearest Neighbor. Artificial Neural Network. Decision Tree.	Edinburgh DERMOFIT	1300	10	No	Binary and Multiclass	Not reported	No	Binary = 91.30 8 class = 87.10 10 class = 80.10	Not reported	Not reported	Not reported
Molina-Molina et al. (2020) [45]	Ensemble Classifiers.	ISIC2019	25,331	8	No	Multiclass	70–30	Yes	By class: AK = 98.64 BCC = 96.55 SCC = 98.54 BKL = 97.24 MEL = 95.76 NEV = 93.44 DF = 99.24 VASC = 99.37 Mean ± SD = 97.35 ± 2.04	By class: AK = 82.54 BCC = 80.97 SCC = 93.56 BKL = 92.12 MEL = 96.02 NEV = 89.75 DF = 97.92 VASC = 100 Mean ± SD = 91.61 ± 6.89	By class: AK = 76.36 BCC = 96.39 SCC = 43.95 BKL = 80.22 MEL = 79.54 NEV = 98.32 DF = 19.67 VASC = 37.15 Mean ± SD = 66.45 ± 29.09	By class: AK = 99.43 BCC = 96.58 SCC = 99.92 BKL = 99.21 MEL = 99.28 NEV = 88.39 DF = 100 VASC = 100 Mean ± SD = 97.85 ± 3.98
Afza, F (2020) [46]	Support Vector Machine. k-Nearest Neighbor. Ensemble Classifiers. Linear Discriminant.	ISBI 2017	2750	2	No	Binary	70–30	No	96.20	96.00	100	96.00
Ghalejoogh, G.S (2020) [47]	Hybrid Approach.	PH2 Ganster	470	3	Yes	Binary and Multiclass	Not reported	No	Binary PH2 = 98.50 Ganster = 97.78 Multiclass: PH2 = 96.00 Ganster = 93.33	Binary: PH2 = 97.5 Ganster = 94.29 Multiclass: PH2 = 94.00 Ganster = 90.00	Binary c: PH2 = 98.75 Ganster = 97.00 Multiclass: PH2 = 97.00 Ganster = 95.00	Not reported
Moldovanu et al. (2021) [48]	k-Nearest Neighbor. Radial Basis Function Neural Network.	7-Point. Med-Node Pedro Hispano Hospital (PH2).	655	2	No	Binary	Not reported	No	7-Point 80.77 Med-Node 94.71 PH2 94.88	7-Point 98.01 Med-Node 96.42 PH2 1.00	Not reported	7-Point 94.44 Med-Node 88.61 PH2 85.62
Afza et al. (2022) [20]	Support Vector Machine. k-Nearest Neighbor. Ensemble Classifiers. Decision Tree. Naïve Bayes. Single Hidden Layer Extreme Learning Machine.	HAM10000 ISIC2018	10,015 12,500	7	Yes	Multiclass	50–50	No	HAM10000: 93.40 ISIC2018: 94.36	Not reported	Not reported	HAM10000: 93.10 ISIC2018: 94.80
Shetty et al. (2022) [49]	Support Vector Machine. k-Nearest Neighbor. Decision Tree. Logistic Regression. Naïve Bayes. Linear Discriminant. Convolutional Neural Network.	HAM10000	10,015	7	Yes	Multiclass	80–20	No	94.00	85.00	Not reported	88.00
Mohanty et al. (2022) [50]	Support Vector Machine. Decision Tree. Multi-Layer Perceptron. Naïve Baye.	HAM10000 BCN20000	10,000. 19,424.	7	No	Multiclass	Not reported	No	HAM10000: 97.79 BCN20000: 97.79	HAM10000: 94.99 BCN20000: 95.39	Not reported	HAM10000: 95.24 BCN20000: 96.24
Camacho-Gutiérrez et al. (2022) [51]	Support Vector Machine. k-Nearest Neighbor. Linear Discriminant. Ensemble Classifiers.	ISIC2019	25,331	8	No	Multiclass	80–20	Yes	87.00	64.00	90.00	1.00

. Table 13 compares our work with other approaches, and our results are generally better. However, the results show that training and validation data metrics are around 99%. The signatures are invariant to each image’s rotation, scale, and displacement.

These studies demonstrate the potential of artificial intelligence algorithms in the classification of skin lesions, and this work furthers our understanding of how to achieve the best results. Our methodology is a breakthrough in classifying skin lesions using artificial intelligence algorithms and concatenated signatures. Indeed, the main contribution of this manuscript is how the images have been converted into linked signatures using the different integral transforms mentioned above, as well as the uniform LBP vectors.

This is a promising development in medical diagnosis and has the potential to revolutionize how medical professionals diagnose and treat skin lesions. It is worth mentioning that concatenated signatures cannot only be used for classifying skin lesions; they can be used for other medical imaging tasks, such as identifying tumors or categorizing brain scans. Furthermore, this technique can be applied to other areas, such as facial recognition or the categorization of satellite images.