Space-time Surface Reconstruction
using Incompressible Flow
Andrei Sharf, Dan A. Alcantara, Thomas Lewiner, Chen Greif, Alla Sheffer, Nina Amenta, Daniel Cohen-Or
Reconstruction of a space-time surface. Left: A point cloud sequence of a running man containing holes due to self occlusions. Middle: Renderings of two iterations of our flow solver. As the solver progresses, mass (blue) accumulates inside the surface. Right: Final reconstruction from the flow solution.
We introduce a volumetric space-time technique for the reconstruction of moving and deforming objects from point data. The output of our method is a four-dimensional generalized cylinder in space-time, made up of spatial slices, each of which is a three-dimensional solid bounded by a watertight manifold. The motion of the object is described as an incompressible flow of material through time. We optimize the flow so that the distance material moves from one time frame to the next is bounded, the density of material remains constant, and the object remains compact. This formulation overcomes deficiencies in the acquired data, such as persistent occlusions, errors, and missing frames. We demonstrate the performance of our flow-based technique by reconstructing coherent sequences of watertight models from incomplete scanner data.
Reconstruction of a scanned moving hand puppet. Left: Input scan points to the flow solver (green points), with the initial inside cell labeling (dark blue cells). Center: Two flow solver iterations: mass cells is represented by a grayscale map. Cells determined to be inside by the solver are colored dark blue. Right: Our final reconstruction.
The 2D space-time surface of a single rounded box splitting into two distinct round objects. Left: Sampled space-time surface. Middle: Implicit surface reconstruction using RBF and FEM. Right: Results using flow. Table shows flow iterations. Despite poor sampling, mass estimation is able to separate and accumulate where the round objects are expected to be.
Excerpts from reconstruction sequences of various moving garments captured from multiple video cameras. Left: the captured points. We show zoom-ins of irregular sampling, holes and outliers on the leftmost column. Right: our reconstruction.