An Efficient Background Term for 3D Reconstruction and Tracking with Smooth Surface Models

We present a novel strategy to shrink and constrain a 3D model, represented as a smooth spline-like surface, within the visual hull of an object observed from one or multiple views. This new 'background' or 'silhouette' term combines the efficiency of previous approaches based on an image-plane distance transform with the accuracy of formulations based on raycasting or ray potentials. The overall formulation is solved by alternating an inner nonlinear minimization (raycasting) with a joint optimization of the surface geometry, the camera poses and the data correspondences. Experiments on 3D reconstruction and object tracking show that the new formulation corrects several deficiencies of existing approaches, for instance when modelling non-convex shapes. Moreover, our proposal is more robust against defects in the object segmentation and inherently handles the presence of uncertainty in the measurements (e.g. null depth values in images provided by RGB-D cameras).