Deep orientation-aware functional maps: Tackling symmetry issues in Shape Matching

This is our implementation of Deep orientation-aware functional maps, a Shape Matching Network that builds comprehensive orientation-aware features from surfaces to compute accurate correspondence between pairs of shapes. Our method exploits both scalar-valued and vector-valued features to infer well-oriented maps between shapes, in a fully unsupervised manner.

We chose to call our network DUO-FM, for Deep Unsupervised Orientation-aware Functional Maps. Another reason for this name is that this network relies on the computation of two maps: the functional map for scalar-valued descriptors and the complex functional map for vector-valued descriptors. It is this joint estimation of both these maps that makes our method robust and able to retrieve orientation-preserving maps without supervision.

DUO-FM, Deep orientation-aware functional maps
Nicolas Donati, Etienne Corman, Maks Ovsjanikov
In CVPR 2022
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Outline

Feature Extractor

Our method is built upon DiffusionNet, a deep feature extractor for 3D surfaces which shows state-of-the-art results for many shape analysis tasks like classification or segmentation. We use DiffusionNet to build orientation-aware features that are in turn used for functional map estimation. The code for DiffusionNet is stored in diffusion_net/.

Complex Functional Maps

Our method uses Complex Functional Maps to link tangent vector field features between source and target shapes. This allows to efficiently impose an orientation-aware loss on the network, in order to get well-oriented maps. The code for Complex Functional Maps is stored in Tools/.

Prerequisites

Our code depends on pytorch (>1.8), as well as a handful of other fairly typical numerical packages, which can usually be installed manually.

How to use

To use our method, follow the following steps:

Configuration

Here is the training data we used. Specify your dataset and model parameters in a config/your_config.yaml file. Examples for the config file are displayed in config. The main requirements are the paths to your dataset and some parameters (e.g. number of eigenfunctions, number of output descriptors, number of epochs for training, ...).

More specifically, here are the main things you need to set in your config file :

├── dataset
│   ├── name         # the name of your dataset (e.g. scape)
│   ├── subset       # the category (e.g. type of remeshing, remeshed or anisotropic, etc...)
│   ├── type_        # vts (uses vts correspondence files) or gt (uses groundtruth files) are the two types supported
│   ├── root_train   # root to your data (e.g. data/SCAPE_r) do not include 'shapes_train'
│   ├── root_test    # same root to data (e.g. data/SCAPE_r) do not include 'shapes_test'
│   ├── root_geodist # root to geodesic distance matrices (only needed for geodesic error eval)
│   ├── cache_dir    # cache for geometric operator used by diffusion net
├── optimizer        # optimizer parameters (no need to change them for first tests)
├── training
│   ├── batch_size   # always 1 for now, because shapes have different numbers of points
│   ├── epochs       # number of training epochs (e.g. 30)
├── fmap
│   ├── n_fmap       # number of eigenvectors used for fmap (e.g. 50 in the paper)
│   ├── n_cfmap      # number of complex eigenvectors used for complex fmap (e.g. 20 in the paper)
│   ├── k_eig        # number of eigenvectors used for diffusion (e.g. 128 in the paper)
│   ├── n_feat       # dimension of output features (e.g. 128 in the paper)
│   ├── C_in: 128    # dimension of input features (e.g. 128 in the paper)
│                    # if C_in=3, xyz signal will be used; if C_in>3, WKS descs will be used
├── loss
│   ├── w_gt         # (default: False) if one wants to train as a supervised method, one should set w_gt=True.
│   ├── w_ortho      # (default: 1) orthogonal loss coefficient for functional map
│   ├── w_Qortho     # (default: 1) orthogonal loss coefficient for complex functional map
├── misc             # cuda parameters and checkpoint frequency

It is interesting to note that you can train a supervised version of the network with this code, by simply setting w_gt: True in the loss section of the config file. This implements Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence (find the paper here), with the difference that the feature extractor in this case is Diffusion Net.

The purpose of this paper is to propose an unsupervised deep shape matching method, which you get by simply setting w_gt: False in the loss section of the config file. This implements DUO-FM.

training

Run python train.py --config your_train_config to train DUO-FM on your train set with your parameters.

Images of a) the predicted functional map b) the predicted complex functional map c) the ground truth functional map for comparison are saved at img/. These images can be used to check that the model gets the maps right after some epochs.

testing

Run python eval.py --model_path path/to/your/model --config your_test_config to test DUO-FM on your test set with your parameters. If geodesic distance matrices are available (precise the path through the config file), the eval code will display geodesic errors after each test map is computed.

Citation

If you use our work, please cite our paper.

@article{donati2022DeepCFMaps,
  title={Deep orientation-aware functional maps: Tackling symmetry issues in Shape Matching},
  author={Donati, Nicolas and Corman, Etienne and Ovsjanikov, Maks},
  journal={CVPR},
  year={2022}
}

Thanks

Parts of this work were supported by the ERC Starting Grant No. 758800 (EXPROTEA) and the ANR AI Chair AIGRETTE.

Contact

If you have any problem about this implementation, please feel free to contact via:

nicolas DOT donati AT polytechnique DOT edu