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Maxim Berman, Amal Rannen Triki, Matthew B. Blaschko

ESAT-PSI, KU Leuven, Belgium.

Published in CVPR 2018. Seeproject page,arxiv paper,paper on CVF open access.

Files included:

• lovasz_losses.py: Standalone PyTorch implementation of the Lovász hinge and Lovász-Softmax for the Jaccard index
• demo_binary.ipynb: Jupyter notebook showcasing binary training of a linear model, with the Lovász Hinge and with the Lovász-Sigmoid.
• demo_multiclass.ipynb: Jupyter notebook showcasing multiclass training of a linear model with the Lovász-Softmax

The binarylovasz_hinge expects real-valued scores (positive scores correspond to foreground pixels).

The multiclasslovasz_softmax expect class probabilities (the maximum scoring category is predicted). First use aSoftmax layer on the unnormalized scores.

Files included:

• lovasz_losses_tf.py: Standalone TensorFlow implementation of the Lovász hinge and Lovász-Softmax for the Jaccard index
• demo_binary_tf.ipynb: Jupyter notebook showcasing binary training of a linear model, with the Lovász Hinge and with the Lovász-Sigmoid.
• demo_multiclass_tf.ipynb: Jupyter notebook showcasing the application of the multiclass loss with the Lovász-Softmax

Warning: the losses values and gradients have been tested to be the same as in PyTorch (see notebooks), however we have not used the TF implementation in a training setting.

See the demos for simple proofs of principle.

• How should I use the Lovász-Softmax loss?

The loss can be optimized on its own, but the optimal optimization hyperparameters (learning rates, momentum) might be different from the best ones for cross-entropy. As discussed in the paper, optimizing the dataset-mIoU (Pascal VOC measure) is dependent on the batch size and number of classes. Therefore you might have best results by optimizing with cross-entropy first and finetuning with our loss, or by combining the two losses.

See for example how the workLand Cover Classification From Satellite Imagery With U-Net and Lovasz-Softmax Loss by Alexander Rakhlin et al. used our loss in theCVPR 18 DeepGlobe challenge.

• Inference in Tensorflow is very slow...

Compiling from Tensorflow master (or using a future distribution that includes committensorflow/tensorflow@73e3215) should solve this problem; seeissue #6.

Please cite

@inproceedings{berman2018lovasz,  title={The Lov{\'a}sz-Softmax loss: A tractable surrogate for the optimization of the intersection-over-union measure in neural networks},  author={Berman, Maxim and Rannen Triki, Amal and Blaschko, Matthew B},  booktitle={Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition},  pages={4413--4421},  year={2018}}