4Deform: Neural Surface Deformation for Robust Shape Interpolation

Pipeline of 4Deform: Given a temporal sequence of inputs, we initialize a latent vector to each point cloud. Then the network takes pairs of point clouds \(P_0\) and \(P_1\) (with sparse correspondences), together with the concatenated latent vector \(\mathbf{z}_0\) and \(\mathbf{z}_1\) as input. At training time, we jointly optimize two neural fields: a time-varying implicit representation (Implicit Net \(\phi\)) and a velocity field (Velocity Net \(\mathcal{V}\)) with proposed geometric and physical constraints losses. Conditioning on a time stamp \(t\), we instantaneously obtain a continuous time-varying signed distance function (SDF), an offset of the input toward the target (velocity field).