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

arXiv: https://arxiv.org/abs/1705.08790 · HTML: https://mlsanity.com/paper/1705.08790/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2017.

## Built on by (most cited first, 4 of 4)

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- [Effect of the output activation function on the probabilities and errors in medical image segmentation](https://mlsanity.com/paper/2109.00903/) (2021)
- [Loss function to optimise signal significance in particle physics](https://mlsanity.com/paper/2412.09500/) (2024)

## Abstract (arXiv)

The Jaccard index, also referred to as the intersection-over-union score, is commonly employed in the evaluation of image segmentation results given its perceptual qualities, scale invariance - which lends appropriate relevance to small objects, and appropriate counting of false negatives, in comparison to per-pixel losses. We present a method for direct optimization of the mean intersection-over-union loss in neural networks, in the context of semantic image segmentation, based on the convex Lov'asz extension of submodular losses. The loss is shown to perform better with respect to the Jaccard index measure than the traditionally used cross-entropy loss. We show quantitative and qualitative differences between optimizing the Jaccard index per image versus optimizing the Jaccard index taken over an entire dataset. We evaluate the impact of our method in a semantic segmentation pipeline and show substantially improved intersection-over-union segmentation scores on the Pascal VOC and Cityscapes datasets using state-of-the-art deep learning segmentation architectures.