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.

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