Functional maps

By M. Ovsjanikov, Mirela Ben-Chen, Justin M. Solomon, Adrian Butscher, Leonidas J. Guibas. 2012

440 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Dynamic Graph CNN for Learning on Point Clouds (2018, background): “ng anisotropic diffusion [Boscaini et al. 2016] or Gaussian mixture models [Monti et al. 2017a; Veličković et al. 2017]. In [Halimi et al. 2018; Litany et al. 2017b], a differentiable functional map [Ovsjanikov et al. 2012] layer was incorporated into a geometric deep neural network, allowing to do ”
Taskonomy: Disentangling Task Transfer Learning (2018, background): “compositional modeling [33, 8, 11, 21, 53, 89, 87], homomorphic cryptography [40], lifelong learning [90, 13, 82, 81], functional maps [68], certain aspects of Bayesian inference and Dirichlet processes [52, 88, 87, 86, 35, 37], few-shot learning [78, 23, 22, 67, 83], transfer learning [72, 81, 27, ”
Dense Non-rigid Shape Correspondence Using Random Forests (2014, methodology): “) in order to constrain the solution optimally [14].”
Efficient Globally Optimal 2D-to-3D Deformable Shape Matching (2016, background): “A recent line of works builds upon the functional representation [18, 19, 22, 12, 23], where a point-wise map is replaced by a linear map between function spaces.”
PRNet: Self-Supervised Learning for Partial-to-Partial Registration (2019, background): “For example, functional maps [42] generalize to mappings between functions on shapes rather than points on shapes, expressing a map as a linear operator in the Laplace–Beltrami eigenbasis.”
DiffusionNet: Discretization Agnostic Learning on Surfaces (2020, methodology): “Functional maps compute a correspondence between a pair of shapes by finding a linear transformation between spectral bases, aligning some set of input features [Ovsjanikov et al. 2012].”
CaSpeR: Latent Spectral Regularization for Continual Learning (2023, methodology): “The comparison between G5 and G10 can be better understood in terms of the node-to-node bijection T : G5 → G10, which can be represented as a functional map matrix C [35] with elements ci,j ≜ ⟨φG5 i ,φ G10 j ◦ T ⟩ , where φG5 i is the i-th Laplacian eigenvector of G5 (similarly for G10), and ◦ denot”
3D-CODED: 3D Correspondences by Deep Deformation (2018, methodology): “The resulting functional maps only align basis functions and additional optimization is required to extract consistent point-to-point correspondences [33].”
Multi-directional geodesic neural networks via equivariant convolution (2018, methodology): “A similar technique, treating shapes as graphs, has been used for analyzing arbitrary shape collections [Yi et al. 2017], while synchronizing their laplacian eigenbases with functional maps [Ovsjanikov et al. 2012].”
ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds (2015, methodology): “Functional correspondence Following [Ovsjanikov et al. 2012], we estimate a linear operator T : L 2 ( X ) → L 2 ( Y ) representing the functional correspondence between shapes X and Y in the Fourier domain, from a set of knowingly corresponding functions on X and Y .”
Learning Program Embeddings to Propagate Feedback on Student Code (2015, positive): “The computer graphics community have represented pairings of nonlinear geometric shapes as linear maps between shape features, called functional maps (Ovsjanikov et al., 2012; 2013).”
Image Co-segmentation via Consistent Functional Maps (2013, methodology): “We remark that the obvious analog of [16] in the image domain is to use functions over the image pixels, but in our experience this works much less well (as shown in supplemental material).”