The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computer vision is the optimal transport framework. Its ability to model geometric displacements across an image's support gives it attractive qualities similar to optical flow methods that are effective at capturing visual motion, but are restricted to operate in significantly smaller state-spaces. Despite this advantage, two major drawbacks make it unsuitable for general deployment: (i) it suffers from exorbitant computational costs due to a quadratic optimization-variable complexity, and (ii) it has a mass-balancing assumption that limits applications with natural images. We tackle these issues simultaneously by proposing a novel formulation for an unbalanced optimal transport regularizer that has linear optimization-variable complexity. In addition, we present a general proximal method for this regularizer, and demonstrate superior empirical performance on novel dynamical tracking applications in synthetic and real video.

中文翻译：

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成像问题的不平衡最优传输正则化

现象学结构的建模是逆成像问题中的一个关键方面。计算机视觉中一种新兴的建模工具是最佳传输框架。它在图像支持下对几何位移进行建模的能力使其具有类似于光流方法的吸引力，这些方法可有效捕捉视觉运动，但仅限于在显着更小的状态空间中运行。尽管有这个优势，但有两个主要缺点使其不适合一般部署：（i）由于二次优化变量的复杂性，它遭受过高的计算成本，以及（ii）它具有质量平衡假设，限制了自然图像的应用。我们通过为具有线性优化变量复杂度的不平衡最优传输正则化器提出一种新的公式来同时解决这些问题。此外，我们为该正则化器提出了一种通用的近端方法，并在合成和真实视频中的新型动态跟踪应用中展示了卓越的经验性能。