ShapeFlow SupplementaryMaterial

Ford = 3,V isthe three-dimensional volume, and V is the surface boundary ofV. Given a deformation map ind spatial dimensions,Φ: Rd 7 Rd,induced via adivergence-free(i.e.solenoidal) spatio-temporal continuous flow functionf: Rd+1 7 Rd, f = 0, the volume within the deformed boundary Φ( V)remainsconstant. Figure6: Backboneflowarchitecture We employ a variant of the IM-NET [11] architecture as ourbackbone. In the case with no implicit regularization, we directly use the IM-NET backboneastheflowfunctionhη()(inEqn.6). We do not enforce isometry and volume conservation conditions since theydo not apply tothe shape categories inShapeNet.