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.
翻译:Euler 的 Euler 等离子体构成一个充满吸引力的变异图像涂色模型。 它将包含全部变异和水平线曲线曲线的能量最小化。 这些组件是透明的, 并且对形状完成任务具有吸引力 。 然而, 它的梯度流是一个单一的、 厌异的和非线性的第四顺序的 PDE, 它在数字上具有挑战性 : 很难找到提供尖锐边缘和良好旋转的高效算法 。 作为补救措施, 我们设计了第一个模拟与 Euler 的 Eliastica 相容的神经算法 。 我们用深能量概念来使用变异能量作为神经网络的损耗。 此外, 我们把它与网络结构本身作为前一个动作的深层图像匹配 。 通过将优化轨迹轨迹的轨迹引向更接近理想的解决方案, 很难找到有效的算法 。 我们的结果与基于弹性形状完成的状态的算法质量相当。 它们把良好的变异和锐边缘结合起来。 此外, 我们从高效率和不努力的同步平行的轨法 3 中要求它成为最不固定的常规的中央分析框架 。 我们要求它只有最慢的内最慢的轨迹。 。 。</s>