Additive and Multiplicative Piecewise-Smooth Segmentation Models in a Variational Level Set Approach

We propose new models to segment images corrupted by additive or multiplicative noise, in a variational level set approach. In the additive case, we decompose the data u0 into the sum v+w+noise. Here, v is a piecewise-constant component, capturing edges and discontinuities, and it is modeled in a level set approach, while w is a smooth component, capturing the intensity inhomogeneities. The additive noise is removed from the initial data. In the multiplicative case, we introduce two new models: first, we propose a new piecewise-constant segmentation model of the data corrupted by multiplicative noise, in a multiphase level set approach. 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. Experimental results on synthetic and real images are presented