论文标题
基于CNN的Euler的Elastica与深度能量和深图像之前
CNN-based Euler's Elastica Inpainting with Deep Energy and Deep Image Prior
论文作者
论文摘要
Euler的Elastica构成了一个吸引人的变异图像镶嵌模型。它最小化涉及总变化以及水平线曲率的能量。这些组件是透明的，使其对于形状完成任务有吸引力。但是，其梯度流是第四阶的单数，各向异性和非线性PDE，这在数值上具有挑战性：很难找到具有尖锐边缘和良好旋转不变性的有效算法。作为一种补救措施，我们设计了模拟与Euler的Elastica插入的第一种神经算法。我们使用采用变异能量作为神经网络损失的深度能量概念。此外，我们将其与深层图像搭配，其中网络体系结构本身就是先验。通过将优化轨迹转移到所需的解决方案上，这可以使其产生更好的覆盖。我们的结果与基于Elastica的形状完成的最新算法相同。它们将良好的旋转不变性与锋利的边缘结合在一起。此外，我们受益于神经框架内的高效率和轻松的并行化。我们的神经弹性方法仅需要3x3中心差模板。因此，它比其他表现出色的算法要简单得多。最后但并非最不重要的一点是，它不受监督，因为它不需要地面真相培训数据。
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.
