## 1 Introduction  
Early detection of skin cancer is crucial for improving patient outcomes, as it remains a common and potentially deadly disease worldwide. To support dermatologists in diagnosis, automated classification of skin lesions has gained significant attention through the integration of machine learning (ML) and advanced digital image processing. By leveraging mathematical transformations and feature extraction techniques, Machine learning models have demonstrated promising capabilities in identifying diagnostic patterns from digital image data, making them practical tools for classifying skin lesions [1, 2, 3, 4, 5, 6, 7, 8]. Integral transforms, such as Fourier, Mellin, and Hilbert, have proven particularly useful in generating feature sets that are invariant to changes in rotation, scale, and translation--properties that are essential for analyzing skin lesions, which exhibit considerable variability in shape, size, and orientation [9, 10, 11]. Frequency-based patterns, essential for differentiating various lesion textures and structures, have been analyzed using the Fourier transform, which is widely used in image processing [12, 13]. The Mellin transform has also been applied to address the issue of varying lesion sizes in images, introducing scale invariance to the extracted features and enhancing their robustness [14, 15, 16]. Hilbert transform complements this by ensuring rotational invariance, thus producing unique and repeatable signatures, as demonstrated in skin lesion classification studies [17]. In our previous work, we successfully implemented the Radial Fourier-Mellin and Hilbert transform to classify skin lesions accurately. This approach created stable image signatures across eight lesion types, producing vital classification metrics [17]. These results underscore the potential of combining transform-based feature extraction with ML for robust lesion classification, especially when global invariance properties are required. This study builds on previous work by incorporating the Hermite transform, which is applied independently to the image's red, green, and blue channels and grayscale. The Hermite transform is well suited for capturing localized spatial features and intricate textures, essential for skin lesion analysis, as different color channels often contain unique structural information relevant to pigmentation, boundary definition, and textural detail [18; 19; 20]. Although the Hermite transform has primarily been used in areas such as biometric recognition, where fine-grained spatial analysis is essential, recent research suggests that the Hermite transform can be effectively applied to medical imaging for detailed feature extraction [21]. This study aims to enhance the classification of skin lesions by integrating the Hermite transform with the Radial Fourier-Mellin and Hilbert transform across separated RGB channels. It is hypothesized that this hybrid approach will enhance the robustness and accuracy of lesion classification, thereby advancing AI-driven, non-invasive diagnostic tools in dermatology. The following sections outline our methodology, experimental setup, results, and the impact of the Hermite transform on the overall classification performance. The development of automated skin lesion classification systems has been an area of extensive research in medical image analysis, driven by the critical need for early skin cancer detection. Artificial intelligence (AI) and machine learning (ML) have significantly contributed to dermatology by improving the classification of lesion types using digital images. These approaches enhance diagnostic precision by employing feature extraction methods, multi-channel image analysis, and a range of mathematical transformations. Several studies have highlighted the effectiveness of Fourier, Mellin, and Hilbert transforms for extracting stable invariant features under changes in rotation, scale, and translation--crucial properties for skin lesion analysis where lesions vary in appearance.