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

by   Karl Schrader, et al.

Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape completion tasks. However, its gradient flow is a singular, anisotropic, and nonlinear PDE of fourth order, which is numerically challenging: It is difficult to find efficient algorithms that offer sharp edges and good rotation invariance. As a remedy, we design the first neural algorithm that simulates inpainting with Euler's Elastica. We use the deep energy concept which employs the variational energy as neural network loss. Furthermore, we pair it with a deep image prior where the network architecture itself acts as a prior. This yields better inpaintings by steering the optimisation trajectory closer to the desired solution. Our results are qualitatively on par with state-of-the-art algorithms on elastica-based shape completion. They combine good rotation invariance with sharp edges. Moreover, we benefit from the high efficiency and effortless parallelisation within a neural framework. Our neural elastica approach only requires 3x3 central difference stencils. It is thus much simpler than other well-performing algorithms for elastica inpainting. Last but not least, it is unsupervised as it requires no ground truth training data.


page 1

page 4

page 5

page 6


Total Variation and Euler's Elastica for Supervised Learning

In recent years, total variation (TV) and Euler's elastica (EE) have bee...

On Variational Methods for Motion Compensated Inpainting

We develop in this paper a generic Bayesian framework for the joint esti...

Unsupervised Learning of the Total Variation Flow

The total variation (TV) flow generates a scale-space representation of ...

Diversity-Generated Image Inpainting with Style Extraction

The latest methods based on deep learning have achieved amazing results ...

A nonlocal feature-driven exemplar-based approach for image inpainting

We present a nonlocal variational image completion technique which admit...

Deep image prior inpainting of ancient frescoes in the Mediterranean Alpine arc

The unprecedented success of image reconstruction approaches based on de...

Please sign up or login with your details

Forgot password? Click here to reset