Geodesic shooting and diffeomorphic matching via textured meshes
Geodesic shooting and diffeomorphic matching via textured meshes
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DOI：
10.1007/11585978_24
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发表时间：
2005-01-01
期刊：
影响因子：
--
通讯作者：
Younes, L
中科院分区：
文献类型：
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作者：
Allassonnière, S;Trouvé, A;Younes, L
本文提出了一种具有自由边界的微分同胚图像匹配的新方法。感兴趣的区域在模板上三角化，模板被认为是一个灰度纹理网格。然后用由三角形顶点位移驱动的分段仿射变形来近似微分同构变换。这为这种密集的图像比较问题提供了一个有限维的地标式简化。基于最优控制模型，我们分析和比较了两种基于初始动量的优化方法：通过梯度下降直接优化，或通过雅可比矩阵的预处理来增强横截方程的寻根。最后给出了一系列数字与人脸匹配的数值实验。
We propose a new approach in the context of diffeomorphic image matching with free boundaries. A region of interest is triangulated over a template, which is considered as a grey level textured mesh. A diffeomorphic transformation is then approximated by the piecewise affine deformation driven by the displacements of the vertices of the triangles. This provides a finite dimensional, landmark-type, reduction for this dense image comparison problem. Based on an optimal control model, we analyze and compare two optimization methods formulated in terms of the initial momentum: direct optimization by gradient descent, or root-finding for the transversality equation, enhanced by a preconditioning of the Jacobian. We finally provide a series of numerical experiments on digit and face matching.