用于等距与等面积 NRSfM 的凸松弛
Convex Relaxations for Isometric and Equiareal NRSfM
AI总结：
针对可伸展物体的 NRSfM 难题，本文提出等距模型的拟等距凸松弛，并首次引入等面积形变模型，通过与等距模型混合及新凸松弛克服歧义和四次非凸约束，且在真实与合成基准上验证有效。
摘要：
由于缺乏对点云具有充分约束的可伸展模型，可伸展物体构成了 NRSfM 的一个挑战性情形。我们通过提出以下两方面来应对该挑战：1）将等距模型凸松弛至拟等距；2）涉及等面积形变模型的凸松弛，该模型保持局部面积，且此前尚未用于 NRSfM。等面积模型颇具吸引力，因为它在物理上合理且应用广泛。然而，它存在两个主要困难：首先，单独使用时具有歧义；其次，它涉及四次约束，因而高度非凸。我们的方法通过将等面积模型与等距模型混合来处理第一个困难，并通过新的凸松弛来处理第二个困难。我们在多组真实和合成数据（包括知名基准）上验证了所提方法。
英文摘要：
Extensible objects form a challenging case for NRSfM, owing to the lack of a sufficiently constrained extensible model of the point-cloud. We tackle the challenge by proposing 1) convex relaxations of the isometric model up to quasi-isometry, and 2) convex relaxations involving the equiareal deformation model, which preserves local area and has not been used in NRSfM. The equiareal model is appealing because it is physically plausible and widely applicable. However, it has two main difficulties: first, when used on its own, it is ambiguous, and second, it involves quartic, hence highly nonconvex, constraints. Our approach handles the first difficulty by mixing the equiareal with the isometric model and the second difficulty by new convex relaxations. We validate our methods on multiple real and synthetic data, including well-known benchmarks.
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。
