PAVIS department, Istituto Italiano di Tecnologia, Genova, Italy.
IEEE Trans Pattern Anal Mach Intell. 2012 Aug;34(8):1496-508. doi: 10.1109/TPAMI.2011.238.
This paper presents a unified approach to solve different bilinear factorization problems in computer vision in the presence of missing data in the measurements. The problem is formulated as a constrained optimization where one of the factors must lie on a specific manifold. To achieve this, we introduce an equivalent reformulation of the bilinear factorization problem that decouples the core bilinear aspect from the manifold specificity. We then tackle the resulting constrained optimization problem via Augmented Lagrange Multipliers. The strength and the novelty of our approach is that this framework can seamlessly handle different computer vision problems. The algorithm is such that only a projector onto the manifold constraint is needed. We present experiments and results for some popular factorization problems in computer vision such as rigid, non-rigid, and articulated Structure from Motion, photometric stereo, and 2D-3D non-rigid registration.
本文提出了一种统一的方法来解决计算机视觉中存在测量缺失数据时的不同双线性分解问题。该问题被表述为一个约束优化问题，其中一个因子必须位于特定流形上。为了实现这一点，我们引入了一种等效的双线性分解问题的重新表述，将核心双线性方面与流形特异性解耦。然后，我们通过增广拉格朗日乘子法来解决由此产生的约束优化问题。我们方法的优势和新颖之处在于，该框架可以无缝处理不同的计算机视觉问题。该算法的特点是只需要一个到流形约束的投影器。我们为计算机视觉中的一些流行的分解问题（如刚性、非刚性和铰接运动结构、光度立体、2D-3D 非刚性配准）提供了实验和结果。
