Cyclical Fusion: Accurate 3D Reconstruction via Cyclical Monotonicity

The dense correspondence estimation is crucial to RGB-D reconstruction systems. However, the projective correspondences are highly unreliable due to sensor depth and pose uncertainties. To tackle this challenge, we introduce a geometry-driven fusion framework, Cyclical Fusion. It pushes the correspondence finding forward to the 3D space instead of searching for candidates on the 2.5D projective map. Moreover, it establishes precise correspondence in two phases, coarse to fine. 1) First, the local surface (represented by a voxel) is characterized by Gaussian distribution. The Karcher-Frechet barycenter is adapted to conduct the robust approximation of covariance. Then, the metric between distributions is calculated via the L2-Wasserstein distance, and the correspondence voxel can be discovered through the nearest distribution-to-distribution model. 2) Our method utilizes an effective correspondence verification scheme derived from cyclical monotonicity related to Rockafellar's theorem. The concept of cyclical monotonicity reveals the geometrical nature of correspondences. A substantial constraint prevents the correspondences from twisting during the fusion process. Accordingly, precise point-to-point correspondence can be discovered. 3) The advection between correspondences is used to form a smooth manifold under regularization terms. Finally, Cyclical Fusion is integrated into a prototype reconstruction system (utilize multiple streams: depth, pose, RGB, and infrared). Experimental results on different benchmarks and real-world scanning verify the superior performance of the proposed method. Cyclical Fusion accomplishes the most authentic reconstruction for which the original projective correspondence-based scheme failed (See Fig.1). Our new techniques make the reconstruction applicable for multimedia content creation and many others.