Papers › The Lovász-Softmax loss: A tractable surrogate for the optimization of the...
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
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.
Code
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Real-Time Semantic Segmentation | Cityscapes test | ENet + Lovász-Softmax | Frame (fps) | 76.9 | #36 of 39 | Archive leaderboard | report |
| Real-Time Semantic Segmentation | Cityscapes test | ENet + Lovász-Softmax | Time (ms) | 13 | #36 of 39 | Archive leaderboard | report |
| Real-Time Semantic Segmentation | Cityscapes test | ENet + Lovász-Softmax | mIoU | 63.1% | #36 of 39 | Archive leaderboard | report |
| Semantic Segmentation | Cityscapes test | ENet + Lovász-Softmax | Mean IoU (class) | 63.06% | #99 of 105 | Archive leaderboard | report |
| Semantic Segmentation | PASCAL VOC 2012 test | Deeplab-v2 with Lovasz-Softmax loss | Mean IoU | 79.00% | #34 of 51 | Archive leaderboard | report |
| Semantic Segmentation | PASCAL VOC 2012 test | Deeplab-v2 + Lovász-Softmax | Mean IoU | 79.0% | #35 of 51 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
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