Toyota Technological Institute at Chicago, Chicago, IL 60637, USA.
IEEE Trans Pattern Anal Mach Intell. 2011 May;33(5):931-44. doi: 10.1109/TPAMI.2010.158.
Recovering the 3D shape of a nonrigid surface from a single viewpoint is known to be both ambiguous and challenging. Resolving the ambiguities typically requires prior knowledge about the most likely deformations that the surface may undergo. It often takes the form of a global deformation model that can be learned from training data. While effective, this approach suffers from the fact that a new model must be learned for each new surface, which means acquiring new training data, and may be impractical. In this paper, we replace the global models by linear local models for surface patches, which can be assembled to represent arbitrary surface shapes as long as they are made of the same material. Not only do they eliminate the need to retrain the model for different surface shapes, they also let us formulate 3D shape reconstruction from correspondences as either an algebraic problem that can be solved in closed form or a convex optimization problem whose solution can be found using standard numerical packages. We present quantitative results on synthetic data, as well as qualitative results on real images.
从单视点恢复非刚体表面的 3D 形状既具有歧义性，又极具挑战性。通常，要解决这些歧义需要事先了解表面可能经历的最可能的变形。这通常采用的是一种全局变形模型，可以从训练数据中学习得到。虽然这种方法很有效，但它存在一个问题，即对于每个新的表面都必须学习一个新的模型，这意味着需要获取新的训练数据，这可能不切实际。在本文中，我们用线性局部模型代替表面片的全局模型，只要它们是由相同的材料制成的，这些模型就可以被组装起来表示任意的表面形状。它们不仅消除了为不同的表面形状重新训练模型的需要，还让我们能够将对应点的 3D 形状重建表述为可以用封闭形式求解的代数问题，或者可以使用标准数值包找到解决方案的凸优化问题。我们在合成数据上给出了定量结果，以及在真实图像上的定性结果。
