🤖 AI Summary
This paper addresses two key challenges in point-supervised density regression: (1) difficulty in modeling pixel-to-annotation correspondences, and (2) high computational cost of optimal transport (OT) computation. To this end, we propose the Gaussian Spatial Transport (GST) framework—the first to introduce Gaussian lattice discretization into point-supervised learning. GST models both the image coordinate space and the annotation map as probability measures and directly solves for the transport plan via closed-form Bayesian inference, bypassing iterative OT optimization. Furthermore, we design a differentiable loss function grounded in measure transport, enabling end-to-end network training. GST is non-iterative, computationally efficient, and fully differentiable. Experiments on crowd counting and keypoint detection demonstrate substantial acceleration in training speed while maintaining state-of-the-art accuracy, validating both its effectiveness and cross-task generalizability.
📝 Abstract
This paper introduces Gaussian Spatial Transport (GST), a novel framework that leverages Gaussian splatting to facilitate transport from the probability measure in the image coordinate space to the annotation map. We propose a Gaussian splatting-based method to estimate pixel-annotation correspondence, which is then used to compute a transport plan derived from Bayesian probability. To integrate the resulting transport plan into standard network optimization in typical computer vision tasks, we derive a loss function that measures discrepancy after transport. Extensive experiments on representative computer vision tasks, including crowd counting and landmark detection, validate the effectiveness of our approach. Compared to conventional optimal transport schemes, GST eliminates iterative transport plan computation during training, significantly improving efficiency. Code is available at https://github.com/infinite0522/GST.