论文标题
时空变形
Space-time metamorphosis
论文作者
论文摘要
我们研究记录图像的问题。我们使用的框架是变态，我们构建了各种欧拉时空设置，并将注册问题作为无限维度优化问题。测量方程对应于对流和连续性方程的系统，并通过分析求解。建立了原始构象有限元法的适应性，并通过数值研究其收敛性。这为通过时空速度字段参数匹配的匹配提供了一个离散的正向操作员。我们在此控制变量上提出了一种梯度下降方法，并为此方法显示了几个有希望的数值结果。
We study the problem of registering images. The framework we use is metamorphosis and we construct a variational Eulerian space-time setting and pose the registration problem as an infinite-dimensional optimisation problem. The geodesic equations correspond to a system of advection and continuity equations and are solved analytically. Well-posedness of a primal conforming finite element method is established and its convergence is investigated numerically. This provides a discrete forward operator for the matching parameterized by a space-time velocity field. We propose a gradient descent method on this control variable and show several promising numerical results for this approach.
