A PDE-Free Variational Method for Multi-Phase Image Segmentation Based on Multiscale Sparse Representations

We introduce a variational model for multi-phase image segmentation that uses a multiscale sparse representation frame (wavelets or other) in a modified diffuse interface context. The segmentation model we present differs from other state-of-the-art models in several ways. The diffusive nature of the method originates from the sparse representations and thus propagates information in a different manner comparing to any existing PDE models, allowing one to combine the advantages of non-local information processing with sharp edges in the output. The regularizing part of the model is based on the wavelet Ginzburg–Landau (WGL) functional, and the fidelity part consists of two terms: one ensures the mean square proximity of the output to the original image; the other takes care of preserving the main edge set. Multiple numerical experiments show that the model is robust to noise yet can preserve the edge information. This method outperforms the algorithms from other classes in cases of images with significant presence of noise or highly uneven illuminatio