Additive & multiplicative piecewise-smooth segmentation models in a functional minimization approach

Abstract. We propose several models to segment images corrupted by additive or multiplicative noise, and by a smooth field (as global intensity inhomogeneity) in a variational curve evolution approach. The proposed energies can be seen as particular K −functionals or J −functionals that arise in the theory of interpolation between spaces. In the additive case, we decompose a data function u0 into the sum v + w + noise. Here, v is a piecewise-constant component, capturing edges and discontinuities, while w is a smooth component, capturing global intensity inhomogeneities. We also propose a piecewiseconstant segmentation model of data corrupted by multiplicative noise. The fidelity term is chosen appropriately for such degradation model. Then, we extend this model to piecewise-smooth segmentation, decomposing the data u0 into the product v · w · noise, where again v is piecewise-constant, while w is smooth. Theoretical and experimental results are presented.