Tensorflow Fourier Feature Mapping Networks

Tensorflow 2.0 implementation of Fourier Feature Mapping networks from the paper Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains.

Installation

• Pip install

$ pip install --upgrade tf_fourier_features

• Pip install (test support)

$ pip install --upgrade tf_fourier_features[tests]

Usage

from tf_fourier_features import FourierFeatureProjection
from tf_fourier_features import FourierFeatureMLP

# You should use FourierFeatureProjection right after the input layer.
ip = tf.keras.layers.Input(shape=[2])
x = FourierFeatureProjection(gaussian_projection = 256, gaussian_scale = 1.0)(ip)
x = tf.keras.layers.Dense(256, activation='relu')(x)
x = tf.keras.layers.Dense(3, activation='sigmoid')(x)
                                  
model = tf.keras.Model(inputs=ip, outputs=x)

# Or directly use the model class to build a multi layer Fourier Feature Mapping Network
model = FourierFeatureMLP(units=256, final_units=3, final_activation='sigmoid', num_layers=4,
                          gaussian_projection=256, gaussian_scale=10.0)

Results on Image Inpainting task

A partial implementation of the image inpainting task is available as the train_inpainting_fourier.py and eval_inpainting_fourier.py scripts inside the scripts directory.

Weight files are made available in the repository under the Release tab of the project. Extract the weights and place the checkpoints folder at the scripts directory.

These weights generates the following output after 2000 epochs of training with batch size 8192 while using only 10% of the available pixels in the image during training phase.

If we train for using only 20% of the available pixels in the image during training phase -

If we train for using only 30% of the available pixels in the image during training phase - .

Results on Multi Image Inpainting

It is possible to encode multiple images into a single network by using an augmented input latent vector. The latent vector can be of any size (here, set to 8) and conditions the model to predict the pixel of a certain image, even when given the same (x,y) coordinate for different images.

The code to train this type of model is available in the scripts directory - train_multi_inpainting_fourier.py and eval_multi_inpainting_fourier.py.

Below are the result of encoding 3 images in to a single model with 260K parameters, trained for 2000 epochs using 30% of the pixels per image as input training data at 800x800 pixel resolution. This is equivalent to training the model with 576K training samples.

Citation

@misc{tancik2020fourier,
    title={Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains},
    author={Matthew Tancik and Pratul P. Srinivasan and Ben Mildenhall and Sara Fridovich-Keil and Nithin Raghavan and Utkarsh Singhal and Ravi Ramamoorthi and Jonathan T. Barron and Ren Ng},
    year={2020},
    eprint={2006.10739},
    archivePrefix={arXiv},
    primaryClass={cs.CV}
}

Requirements

• Tensorflow 2.0+
• Matplotlib to visualize eval result