Face analysis systems commonly rely on integer-order image operators that emphasize either local texture or global structure, limiting their ability to represent the continuous, multi-scale nature of facial appearance. This paper presents a fractional-order (FO) image processing and statistical learning framework for face analysis and evaluates its effectiveness on two large-scale tasks: age estimation and gender classification. Experiments are conducted on the UTKFace dataset and a second large gender-classification benchmark, demonstrating that fractional calculus provides a principled and flexible representation for modeling gradual facial variations across scales.
The proposed framework integrates three complementary FO components. First, variable-order fractional gradients are computed on perceptually meaningful colour channels, where the fractional order adapts spatially to local structural complexity, enabling a smooth transition between fine texture sensitivity and coarse shape information. Second, fractional spectral representations, including fractional Fourier and multi-resolution wavelet statistics, are employed to capture long-range spatial correlations and anisotropic facial patterns that are poorly represented by conventional integer-order operators. Third, fractional diffusion–based embeddings are constructed on feature similarity graphs to support exploratory data analysis, preserving non-Gaussian and anomalous diffusion characteristics in the resulting low-dimensional manifolds. The extracted FO statistics are combined with standard machine-learning regression and classification models for age prediction and gender recognition.
Experimental results on UTKFace show that fractional-order features improve age estimation accuracy across the full lifespan (0–116 years), with particularly notable error reductions in early childhood and older age groups where texture–shape transitions are subtle. For gender classification, the proposed representation demonstrates increased robustness to illumination, pose, and image quality variations compared with integer-order baselines. Exploratory analyses further reveal smooth manifolds aligned with age progression while avoiding over-segmentation caused by dataset artifacts. Although race annotations are available in UTKFace, they are not used for prediction.
