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首页> 外文期刊>IEEE Transactions on Pattern Analysis and Machine Intelligence >A Stable Analytical Framework for Isometric Shape-from-Template by Surface Integration
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A Stable Analytical Framework for Isometric Shape-from-Template by Surface Integration

机译：通过表面集成的等距模板形状的稳定分析框架

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摘要

Shape-from-Template (SfT) reconstructs the shape of a deforming surface from a single image, a 3D template and a deformation prior. For isometric deformations, this is a well-posed problem. However, previous methods which require no initialization break down when the perspective effects are small, which happens when the object is small or viewed from larger distances. That is, they do not handle all projection geometries. We propose stable SfT methods that accurately reconstruct the 3D shape for all projection geometries. We follow the existing approach of using first-order differential constraints and obtain local analytical solutions for depth and the first-order quantities: the depth-gradient or the surface normal. Previous methods use the depth solution directly to obtain the 3D shape. We prove that the depth solution is unstable when the projection geometry tends to affine, while the solution for the first-order quantities remain stable for all projection geometries. We therefore propose to solve SfT by first estimating the first-order quantities (either depth-gradient or surface normal) and integrating them to obtain shape. We validate our approach with extensive synthetic and real-world experiments and obtain significantly more accurate results compared to previous initialization-free methods. Our approach does not require any optimization, which makes it very fast.
机译：模板形状（SfT）从单个图像，3D模板和先验变形中重建变形表面的形状。对于等轴测变形，这是一个恰当的问题。但是，以前的不需要初始化的方法在透视效果较小时会崩溃，这在对象较小或从较大距离查看时会发生。也就是说，它们不能处理所有投影几何形状。我们提出了稳定的SfT方法，可以为所有投影几何形状准确地重建3D形状。我们遵循使用一阶微分约束的现有方法，并获得深度和一阶量（深度梯度或表面法线）的局部解析解。先前的方法直接使用深度解来获得3D形状。我们证明，当投影几何形状趋于仿射时，深度解不稳定，而对于所有投影几何形状，一阶量的解都保持稳定。因此，我们建议通过首先估计一阶量（深度梯度或表面法线）并将其积分以获得形状来解决SfT。与以前的免初始化方法相比，我们通过大量的合成实验和实际实验验证了我们的方法，并获得了更为准确的结果。我们的方法不需要任何优化，因此非常快。

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