In many computer vision tasks, for example saliency prediction or semantic
segmentation, the desired output is a foreground map that predicts pixels where
some criteria is satisfied. Despite the inherently spatial nature of this task
commonly used learning objectives do not incorporate the spatial relationships
between misclassified pixels and the underlying ground truth. The Weighted
F-measure, a recently proposed evaluation metric, does reweight errors
spatially, and has been shown to closely correlate with human evaluation of
quality, and stably rank predictions with respect to noisy ground truths (such
as a sloppy human annotator might generate). However it suffers from
computational complexity which makes it intractable as an optimization
objective for gradient descent, which must be evaluated thousands or millions
of times while learning a model's parameters. We propose a differentiable and
efficient approximation of this metric. By incorporating spatial information
into the objective we can use a simpler model than competing methods without
sacrificing accuracy, resulting in faster inference speeds and alleviating the
need for pre/post-processing. We match (or improve) performance on several
tasks compared to prior state of the art by traditional metrics, and in many
cases significantly improve performance by the weighted F-measure.

本文提出了一种可微分而高效的算法来逼近加权 F - 测量度量函数，通过引入空间信息，不牺牲准确性的情况下可以使用比现有方法更简单的模型，加快推断速度并减轻前 / 后处理的需要，对于许多任务可以比传统指标的先进状态匹配（或提高）性能，且在加权 F - 测量方面显著提高了性能。