## 4 Results
### Tests with the Statistical Classifier  
The LBP, OC-LBP, CS-LTP, ICS-TS, and CCR texture spectra were calculated through a \(3\times 3\) window, and, subsequently, they were employed as characteristic vectors with the classifier described in Section 4.1. The classifier consists of two phases: training and recognition. During the training phase, each carcinogenic image \(S_{m}\) is considered a class; thus, the number of classes is \(M=20\) (in experiment 4, \(M=60\)). For each \(S_{m}\) class, 1000 sub-images \(S_{m}^{a}\) (\(\alpha=1,2,\ldots,P=1000\)) are randomly extracted, and every sub-image \(S_{m}^{a}\) has its texture spectrum extracted \(F_{m}^{a}[k]\). Subsequently, the \(S_{m}\) class is characterized according to Equation (8), where the \(F_{m}[k]\) vector is the prototype of class \(m\). In the recognition phase, the test images are the same as those in the training phase. A set of 1000 sub-images \(S_{t}^{\beta}(\beta=1,2,\ldots,K=1000)\) is randomly extracted from the \(S_{t}\) test carcinogenic image, and each \(S_{t}^{\beta}\) sub-image has its texture spectrum \(F_{T}^{\beta}[k]\) calculated. For the characterization of carcinogenic location test image \(S_{t}\), Equation (9) is employed. As a final step, \(S_{t}\) images are identified through Equation (10). Four series of experiments are developed for each texture descriptor. In the first series, type 1 carcinogenic images are identified. In the second and third series, types 2 and 3 are identified. To conclude, in the fourth series of experiments, all carcinogenic images are combined and subsequently identified. The results are expressed through a confusion matrix \(C_{mm}\), where the main diagonal elements denote the correct classification predictions; the elements surrounding the diagonal describe the identification error; the columns correspond to the carcinogenic images; and the rows correspond to the prototypes [49]. Figure 7a-d illustrates the projections of four confusion matrixes when the LBP histogram is employed as characteristic vector, and the carcinogenic images are classified with it. The identification efficiency of the carcinogenic images in terms of percentage was estimated through the following expression (11):  
\[E(\%)=\frac{\sum diag\{C_{mm}\}}{\sum_{m}\sum_{m}\{C_{mm}\}}\times 100. \tag{11}\]  
where \(C_{mm}\) is the confusion matrix, \(\sum diag\{C_{mm}\}\) is the sum of the main diagonal of the \(C_{mm}\) matrix (sum of correct classification predictions), \(\sum_{m}\sum_{m}\{C_{mm}\}\) is the sum of all elements of the \(C_{mm}\) matrix, and \(E(\%)\) is the classification efficiency of carcinogenic images based on percentage terms. Based on Figure 8, the efficiency results with LBP were as follows: \(E(\%)=100\%\) (Type 1); \(E(\%)=100\%\) (Type 2); \(E(\%)=100\%\) (Type 3), and \(E(\%)100\%\) (all types combined). Figure 8 illustrates the experimental results obtained in the classification of the carcinogenic images, employing five texture spectra. Figure 8: Efficiency results obtained in the numerical experiments performed for the classification of carcinogenic images, deploying the multi-class statistical classifier and the LBP, OC_LBP, CS_LTP, ICS_TS, and CCR histograms as characteristic vectors. Figure 7: Confusion matrix obtained during the recognition of carcinogenic images when the LBP histogram is applied for characterization with the multi-class statistical classifier: (**a**) Type 1 (\(E(\%)=100\%\)); (**b**) Type 2 (\(E(\%)=100\%\)); (**c**) Type 3 (\(E(\%)=100\%\)); and (**d**) Types 1, 2, and 3 carcinogenic images combined (\(E(\%)=100\%\)). Analyzing Figure 8, the carcinogenic images are recognized efficiently (80% and 100%) when the statistical classifier is employed and its characteristic vector is any of the texture spectra: LBP; OC-LBP; CS-LTP; ICS-TS, or CCR. The five techniques entertain high efficiency in the first three experiments (\(E(\%)=80\%\) and 100%).