The Lovasz-Softmax Loss: A Tractable Surrogate for the Optimization of the Intersection-Over-Union Measure in Neural Networks

TLDR

The Jaccard index, or intersection‑over‑union, is widely used to evaluate image segmentation because it is perceptually meaningful, scale‑invariant, and penalizes false negatives. The authors propose a method to directly optimize the mean intersection‑over‑union loss in neural networks for semantic segmentation. They achieve this by applying the convex Lovász extension of submodular losses, enabling tractable optimization of the IoU metric. The Lovász‑Softmax loss yields higher IoU scores than cross‑entropy, shows distinct behavior when optimizing per image versus over the whole dataset, and substantially improves segmentation results on Pascal VOC and Cityscapes with state‑of‑the‑art architectures.

Abstract

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 Lovász 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.