Counting objects in crowded scenes remains a challenge to computer vision. The current deep learning based approach often formulate it as a Gaussian density regression problem. Such a brute-force regression, though effective, may not consider the annotation displacement properly which arises from the human annotation process and may lead to different distributions. We conjecture that it would be beneficial to consider the annotation displacement in the dense object counting task. To obtain strong robustness against annotation displacement, generalized Gaussian distribution (GGD) function with a tunable bandwidth and shape parameter is exploited to form the learning target point annotation probability map, PAPM. Specifically, we first present a hand-designed PAPM method (HD-PAPM), in which we design a function based on GGD to tolerate the annotation displacement. For end-to-end training, the hand-designed PAPM may not be optimal for the particular network and dataset. An adaptively learned PAPM method (AL-PAPM) is proposed. To improve the robustness to annotation displacement, we design an effective transport cost function based on GGD. The proposed PAPM is capable of integration with other methods. We also combine PAPM with P2PNet through modifying the matching cost matrix, forming P2P-PAPM. This could also improve the robustness to annotation displacement of P2PNet. Extensive experiments show the superiority of our proposed methods.

翻译：密集场景中的物体计数仍是计算机视觉领域的挑战。当前基于深度学习的方法常将其建模为高斯密度回归问题。这种暴力回归虽然有效，但未能妥善处理由人工标注过程产生的标注偏移，这种偏移可能导致不同的分布。我们推测在密集物体计数任务中考虑标注偏移将具有积极意义。为获得对标注偏移的强鲁棒性，我们采用具有可调带宽和形状参数的广义高斯分布函数构建学习目标——点标注概率图（PAPM）。具体而言，我们首先提出手工设计的PAPM方法（HD-PAPM），基于广义高斯分布设计函数以容忍标注偏移。由于手工设计的PAPM可能不适用于特定网络和数据集进行端到端训练，我们进一步提出自适应学习的PAPM方法（AL-PAPM）。为提升对标注偏移的鲁棒性，我们基于广义高斯分布设计了一种高效的运输成本函数。所提出的PAPM可与其他方法集成。我们还通过修改匹配成本矩阵将PAPM与P2PNet结合，形成P2P-PAPM，这同样能提升P2PNet对标注偏移的鲁棒性。大量实验证明了我们提出方法的优越性。