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Euler's elastica constitute an appealing variational image inpainting model.It minimises an energy that involves the total variation as well as the levelline curvature. These components are transparent and make it attractive forshape completion tasks. However, its gradient flow is a singular, anisotropic,and nonlinear PDE of fourth order, which is numerically challenging: It isdifficult to find efficient algorithms that offer sharp edges and good rotationinvariance. As a remedy, we design the first neural algorithm that simulatesinpainting with Euler's Elastica. We use the deep energy concept which employsthe variational energy as neural network loss. Furthermore, we pair it with adeep image prior where the network architecture itself acts as a prior. Thisyields better inpaintings by steering the optimisation trajectory closer to thedesired solution. Our results are qualitatively on par with state-of-the-artalgorithms on elastica-based shape completion. They combine good rotationinvariance with sharp edges. Moreover, we benefit from the high efficiency andeffortless parallelisation within a neural framework. Our neural elasticaapproach only requires 3x3 central difference stencils. It is thus much simplerthan other well-performing algorithms for elastica inpainting. Last but notleast, it is unsupervised as it requires no ground truth training data.

CNN-based Euler's Elastica Inpainting with Deep Energy and Deep Image Prior