Nonlinear image processing with α-tension field: A geometric approach

In this paper, we apply an α-tension field from differential geometry to classical image processing tasks of denoising with edge preservation and multiphase feature enhancement. The main contribution of this work is that it is the first systematic investigation of the α-tension field for image processing. Contrary to traditional operators, such as the Laplacian, which are susceptible to noise amplification or are ineffective for complex structures, the α-tension field relies on a nonlinear adaptive mechanism depending on the magnitudes of local gradients. It allows effective denoising and retains edges and fine details by utilizing higher-order gradient information. The field of α-tension provides more sensitive and adaptive models than linear models, such as total variation regularization, anisotropic diffusion, etc. The study exemplifies its advantages over previous methods in preserving structural integrity and minimizing artifacts. It also considers numerical implementation issues and provides guidelines for real-time and large-scale processing. This framework adds up to the known need for faster image-processing tools while links connections to differential geometry.