## 4 Discussion  
The results of this study confirm the effectiveness of the proposed hybrid approach for skin lesion classification. By integrating the Hermite transform with the Radial Fourier-Mellin and Hilbert transform, we achieved a balanced extraction of local and global features essential for robust classification. The Hermite transform's capability to decompose images into localized polynomial coefficients allowed us to analyze fine-grained spatial details within skin lesions, particularly in the RGB channels. This analysis is critical for identifying pigmentation, texture variations, and boundary definitions, which are vital in distinguishing benign lesions from malignant ones. On the other hand, the Radial Fourier-Mellin transform ensured scale and translation invariance, addressing challenges posed by varying lesion sizes and positions across images. The Hilbert transform further complemented these by introducing rotational invariance, thus generating repeatable and stable signatures. Combining these three transforms provided a rich and comprehensive feature set, enhancing the discriminative power of the machine learning models applied. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Class** & **Recall** & **FP Rate** & **Specificity** & **Precision** & **Accuracy** & **F1 Score** \\ \hline NV & 55.85 \(\pm\) 2.33 & 4.50 \(\pm\) 0.33 & 95.50 \(\pm\) 0.33 & 63.92 \(\pm\) 1.43 & 90.60 \(\pm\) 0.22 & 59.34 \(\pm\) 1.44 \\ MEL & 59.31 \(\pm\) 2.11 & 5.25 \(\pm\) 0.44 & 94.75 \(\pm\) 0.44 & 62.07 \(\pm\) 1.57 & 90.34 \(\pm\) 0.32 & 60.39 \(\pm\) 1.26 \\ BCC & 75.16 \(\pm\) 1.18 & 2.93 \(\pm\) 0.29 & 97.07 \(\pm\) 0.29 & 78.54 \(\pm\) 1.76 & 94.35 \(\pm\) 0.29 & 76.73 \(\pm\) 1.16 \\ BKL & 71.68 \(\pm\) 7.11 & 3.94 \(\pm\) 0.31 & 96.06 \(\pm\) 0.31 & 72.61 \(\pm\) 1.32 & 92.99 \(\pm\) 0.28 & 72.01 \(\pm\) 1.06 \\ VASC & 94.77 \(\pm\) 0.99 & 0.97 \(\pm\) 0.10 & 99.03 \(\pm\) 0.10 & 93.37 \(\pm\) 0.60 & 98.50 \(\pm\) 0.12 & 94.03 \(\pm\) 0.50 \\ DF & 97.54 \(\pm\) 0.72 & 1.17 \(\pm\) 0.13 & 98.83 \(\pm\) 0.13 & 92.29 \(\pm\) 0.79 & 98.66 \(\pm\) 0.17 & 94.83 \(\pm\) 0.65 \\ SCC & 97.01 \(\pm\) 0.83 & 1.59 \(\pm\) 0.17 & 98.41 \(\pm\) 0.17 & 89.71 \(\pm\) 1.00 & 98.23 \(\pm\) 0.22 & 93.20 \(\pm\) 0.82 \\ AK & 98.62 \(\pm\) 0.58 & 0.98 \(\pm\) 0.16 & 99.02 \(\pm\) 0.16 & 93.64 \(\pm\) 0.95 & 98.97 \(\pm\) 0.18 & 96.05 \(\pm\) 0.65 \\ \hline Overall Average & 81.24 \(\pm\) 2.19 & 2.67 \(\pm\) 0.22 & 97.33 \(\pm\) 0.22 & 80.77 \(\pm\) 1.64 & 95.33 \(\pm\) 0.45 & 80.82 \(\pm\) 1.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance evaluation metrics (multiplied by 100) for the proposed classification model across eight skin lesion classes. The multi-channel analysis (RGB and grayscale) was found to be particularly beneficial. Each channel emphasized unique lesion characteristics, with the red channel highlighting pigmentation, the green channel focusing on intermediate structures, and the blue channel enhancing fine textures. This approach is consistent with recent studies showing that multi-channel feature extraction outperforms single-channel medical image analysis methods. Table 3 presents a comparative analysis of various state-of-the-art models for skin lesion classification using different datasets. Among the listed models, Inception-v2 achieved the highest recall (0.9015) and F1 score (0.8876), indicating strong sensitivity and overall performance. VGG19 and ResNeXt101 also demonstrated competitive results across precision, accuracy, and F1 score. However, it is important to highlight that our proposed method shows strength in terms of false positive (FP) rate and specificity, with values of 0.0267 and 0.9733, respectively--metrics not reported for the other methods. This low FP rate suggests a significantly reduced rate of incorrect positive classifications, which is crucial in medical applications to avoid unnecessary patient anxiety or treatment.