形状样条下随机二阶模型的无穷维推广
Extension to Infinite Dimensions of a Stochastic Second-Order Model associated with the Shape Splines
摘要：
我们引入了一个二阶随机模型来探索生物形状的变化与应用的医学成像的增长。我们的模型是一个随机力的哈密顿制定的测地线扰动。从有限维地标的情况下，我们证明了随机解不会在有限时间内爆破。然后，我们证明了模型的一致性，展示了强大的收敛结果从有限维近似的无限维设置的形状。为此，我们引入一个合适的希尔伯特空间接近Besov空间，导致我们的结果是有效的，在任何维度的环境空间和广泛的形状。
英文摘要：
We introduce a second-order stochastic model to explore the variability in growth of biological shapes with applications to medical imaging. Our model is a perturbation with a random force of the Hamiltonian formulation of the geodesics. Starting with the finite-dimensional case of landmarks, we prove that the random solutions do not blow up in finite time. We then prove the consistency of the model by demonstrating a strong convergence result from the finite-dimensional approximations to the infinite-dimensional setting of shapes. To this end we introduce a suitable Hilbert space close to a Besov space that leads to our result being valid in any dimension of the ambient space and for a wide range of shapes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
