标题： RankSEG-RMA：一种通过互反矩近似实现的高效分割算法 显示英文标题

标题： RankSEG-RMA: An Efficient Segmentation Algorithm via Reciprocal Moment Approximation

摘要： 语义分割为图像中的每个像素分配其对应的类别，并通常使用交并比（IoU）和Dice度量来量化预测分割掩码与真实分割掩码之间的重叠。在文献中，大多数现有方法估计像素级的类别概率，然后应用argmax或阈值处理以获得最终预测。这些方法已被证明通常会导致不一致或次优的结果，因为它们不直接最大化分割度量。为了解决这个问题，提出了一种新颖的一致性分割框架RankSEG，其中包含专门设计用于优化Dice和IoU度量的RankDice和RankIoU。尽管RankSEG几乎保证性能提升，但它存在两个主要缺点。首先，它的计算成本高——RankDice的复杂度为O(d log d)，具有较大的常数因子（其中d表示像素数量），而RankIoU表现出更高的复杂度O(d^2)，因此限制了其实际应用。例如，在LiTS中，使用RankSEG进行预测需要16.33秒，而使用argmax规则只需0.01秒。其次，RankSEG仅适用于重叠分割设置，其中多个类别可以占据同一像素，这与通常假设非重叠分割的标准基准相矛盾。在本文中，我们通过RankSEG的互反矩近似（RMA）克服了这两个缺点，具体贡献如下：(i) 我们使用RMA改进RankSEG，即RankSEG-RMA，将两种算法的复杂度降低到O(d)，同时保持相当的性能；(ii) 受RMA的启发，我们开发了一个像素级得分函数，使其能够在非重叠分割设置中高效实现。 显示英文摘要

摘要： Semantic segmentation labels each pixel in an image with its corresponding class, and is typically evaluated using the Intersection over Union (IoU) and Dice metrics to quantify the overlap between predicted and ground-truth segmentation masks. In the literature, most existing methods estimate pixel-wise class probabilities, then apply argmax or thresholding to obtain the final prediction. These methods have been shown to generally lead to inconsistent or suboptimal results, as they do not directly maximize segmentation metrics. To address this issue, a novel consistent segmentation framework, RankSEG, has been proposed, which includes RankDice and RankIoU specifically designed to optimize the Dice and IoU metrics, respectively. Although RankSEG almost guarantees improved performance, it suffers from two major drawbacks. First, it is its computational expense-RankDice has a complexity of O(d log d) with a substantial constant factor (where d represents the number of pixels), while RankIoU exhibits even higher complexity O(d^2), thus limiting its practical application. For instance, in LiTS, prediction with RankSEG takes 16.33 seconds compared to just 0.01 seconds with the argmax rule. Second, RankSEG is only applicable to overlapping segmentation settings, where multiple classes can occupy the same pixel, which contrasts with standard benchmarks that typically assume non-overlapping segmentation. In this paper, we overcome these two drawbacks via a reciprocal moment approximation (RMA) of RankSEG with the following contributions: (i) we improve RankSEG using RMA, namely RankSEG-RMA, reduces the complexity of both algorithms to O(d) while maintaining comparable performance; (ii) inspired by RMA, we develop a pixel-wise score function that allows efficient implementation for non-overlapping segmentation settings.