Higher order PDE based model for segmenting noisy image

In this study, a fourth-order non-linear partial differential equation (PDE) model together with multi-well potential has been proposed for greyscale image segmentation. The multi-well potential is constructed from the histogram of the given image to make the segmentation process fully automatic and unsupervised. Further, the model is refined for effective segmentation of noisy greyscale image. The fourth-order anisotropic term with the multi-well potential is shown to properly segment noisy images. Fourier spectral method in space with semi-implicit convexity splitting in time is used to derive an unconditionally stable scheme. Numerical studies on some standard test images and comparison of results with those in literature clearly depict the superiority of the anisotropic variant of the non-linear PDE model.