Elastic bending total variation model for image inpainting with operator splitting method

The elastic bending energy model is commonly used to describe the shape transformation of biological lipid vesicles, making it a classical phase field model. In this paper, by coupling the elastic bending energy with the total variation (TV) regularization, we develop an elastic bending-TV model for image inpainting. By solving the energy minimization problem of this model, we obtain the results for image processing. We adopt an operator splitting method for the model and the numerical scheme involves the introduction of two vector- and scalar-valued functions to reconstruct this functional. The energy minimization problem is transformed into finding the steady state solution of artificial time-dependent PDE systems. At each fractional step, we can find either a closed-form solution or being solved by an efficient algorithm, which is a very robust and stable algorithm. Experimental results validate the superiority of our model and the effectiveness of the scheme for image inpainting.