Hamiltonian Dynamics for Real-World Shape Interpolation

NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go

“…correspondences for training. It is also on par with the axiomatic baseline Hamiltonian interpolation [11], which is remarkable since [11] requires dense correspondences even at test time.…”

“…However, building shape manifolds may be difficult in practice, especially if the input shapes are not in perfect correspondence. Therefore, also inspired by LIMP [7], for training NeuroMorph we follow approaches such as [12,11] that avoid building a shape manifold explicitly and instead directly construct geodesic paths that originate at the source shapes and terminate in the vicinity of the target shapes.…”

Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields

“…Eisenberger et al [14] interpolate shapes by constructing a volume-preserving flow and minimizing a reconstruction and ARAP energies. [13] improves [14] by introducing additional momentum conservation constraints. Among learning-based methods, Limp [12] trains a mesh deformation network given ground truth 3D correspondences.…”

“…Then, among these deformation fields, we seek the one that minimizes a geometric loss, consequently enforcing a geometric prior on the implicit neural representation f . We use in particular the as-rigid-as-possible energy, also known as Killing energy [6,37,36,14,13], due to its ability to encourage natural elastic or piece-wise rigid shape deformations.…”

Shortest Paths in Graphs with Matrix-Valued Edges: Concepts, Algorithm and Application to 3D Multi-Shape Analysis

“…In this experiment we consider the task of finding intermediate shapes between two given shapes. This is closely related to shape interpolation [35,27,20,19], which is typically based on the assumption that there exists a smooth deformation between two given shapes. The difference between an intermediate shape and shape interpolation is that intermediate shapes must be part of the shape collection.…”