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https://github.com/bermanmaxim/LovaszSoftmax

Code for the Lovász-Softmax loss (CVPR 2018)
https://github.com/bermanmaxim/LovaszSoftmax

image-segmentation loss-functions neural-networks pytorch

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Code for the Lovász-Softmax loss (CVPR 2018)

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# The Lovász-Softmax loss: A tractable surrogate for the optimization of the intersection-over-union measure in neural networks






Maxim Berman, Amal Rannen Triki, Matthew B. Blaschko



ESAT-PSI, KU Leuven, Belgium.



Published in CVPR 2018. See [project page](http://bmax.im/LovaszSoftmax), [arxiv paper](https://arxiv.org/abs/1705.08790), [paper on CVF open access](http://openaccess.thecvf.com/content_cvpr_2018/html/Berman_The_LovaSz-Softmax_Loss_CVPR_2018_paper.html).



## PyTorch implementation of the loss layer (*pytorch* folder)

**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 binary `lovasz_hinge` expects real-valued scores (positive scores correspond to foreground pixels). 



The multiclass `lovasz_softmax` expect class probabilities (the maximum scoring category is predicted). First use a `Softmax` layer on the unnormalized scores.



## TensorFlow implementation of the loss layer (*tensorflow* folder)

**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.*



## Usage

See the demos for simple proofs of principle.



## FAQ

* 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 work [*Land Cover Classification From Satellite Imagery With U-Net and Lovasz-Softmax Loss* by Alexander Rakhlin et al.](http://openaccess.thecvf.com/content_cvpr_2018_workshops/w4/html/Rakhlin_Land_Cover_Classification_CVPR_2018_paper.html) used our loss in the [CVPR 18 DeepGlobe challenge](http://deepglobe.org/).



* Inference in Tensorflow is very slow...



Compiling from Tensorflow master (or using a future distribution that includes commit [tensorflow/tensorflow@73e3215](https://github.com/tensorflow/tensorflow/commit/73e3215c3a2edadbf9111cca44ab3d5ca146c327)) should solve this problem; see [issue #6](https://github.com/bermanmaxim/LovaszSoftmax/issues/6).



## Citation

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}

}

```