提出统一的形状优化损失MGIoU，高效精准计算任意凸形相似度。
Marginalized Generalized IoU (MGIoU): A Unified Objective Function for Optimizing Any Convex Parametric Shapes
- 将凸形投影到法线方向，用一维NGIoU实现可微近似
- 在多个基准上性能超越现有损失，计算速度提升10-40倍
- 适用于目标检测、轨迹预测等任务，支持复杂形状优化
参数化形状的相似性优化对众多计算机视觉任务至关重要，交并比（IoU）是经典度量。然而现有方法存在显著缺陷：基于回归的损失（如L1/L2）与IoU无关，基于IoU的损失不稳定且仅限于简单形状，特定任务方法计算开销大且泛化能力差。为此，本文提出边缘化广义交并比（MGIoU），通过将结构化凸形投影至其唯一形状法线方向，计算一维归一化广义交并比（NGIoU），实现一种简单、高效、完全可微的近似，与真实IoU高度相关。进一步扩展为支持非结构化凸形的MGIoU+。两者统一了多种应用场景下的参数化形状优化目标。在标准基准上的实验表明，MGIoU和MGIoU+持续优于现有损失，同时降低10-40倍的损失计算延迟。此外，二者满足度量性质与尺度不变性，确保作为目标函数的鲁棒性。我们还提出MGIoU-用于最小化重叠任务，如无碰撞轨迹预测。代码已公开于https://ldtho.github.io/MGIoU
原文摘要 · Abstract (English)
Optimizing the similarity between parametric shapes is crucial for numerous computer vision tasks, where Intersection over Union (IoU) stands as the canonical measure. However, existing optimization methods exhibit significant shortcomings: regression-based losses like L1/L2 lack correlation with IoU, IoU-based losses are unstable and limited to simple shapes, and task-specific methods are computationally intensive and not generalizable accross domains. As a result, the current landscape of parametric shape objective functions has become scattered, with each domain proposing distinct IoU approximations. To address this, we unify the parametric shape optimization objective functions by introducing Marginalized Generalized IoU (MGIoU), a novel loss function that overcomes these challenges by projecting structured convex shapes onto their unique shape Normals to compute one-dimensional normalized GIoU. MGIoU offers a simple, efficient, fully differentiable approximation strongly correlated with IoU. We then extend MGIoU to MGIoU+ that supports optimizing unstructured convex shapes. Together, MGIoU and MGIoU+ unify parametric shape optimization across diverse applications. Experiments on standard benchmarks demonstrate that MGIoU and MGIoU+ consistently outperform existing losses while reducing loss computation latency by 10-40x. Additionally, MGIoU and MGIoU+ satisfy metric properties and scale-invariance, ensuring robustness as an objective function. We further propose MGIoU- for minimizing overlaps in tasks like collision-free trajectory prediction. Code is available at https://ldtho.github.io/MGIoU
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