# Use square root affinity to regress labels in semantic segmentation Source: [Use square root affinity to regress labels in semantic segmentation]() Collection index: [llms.txt]() Data updated: 2025-10-28T13:56:46.727Z Authors: Lumeng Cao, Zhouwang Yang Published: 2021-03-07T12:49:27.000Z ## Abstract Semantic segmentation is a basic but non-trivial task in computer vision. Many previous work focus on utilizing affinity patterns to enhance segmentation networks. Most of these studies use the affinity matrix as a kind of feature fusion weights, which is part of modules embedded in the network, such as attention models and non-local models. In this paper, we associate affinity matrix with labels, exploiting the affinity in a supervised way. Specifically, we utilize the label to generate a multi-scale label affinity matrix as a structural supervision, and we use a square root kernel to compute a non-local affinity matrix on output layers. With such two affinities, we define a novel loss called Affinity Regression loss (AR loss), which can be an auxiliary loss providing pair-wise similarity penalty. Our model is easy to train and adds little computational burden without run-time inference. Extensive experiments on NYUv2 dataset and Cityscapes dataset demonstrate that our proposed method is sufficient in promoting semantic segmentation networks. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()