Point Annotation Probability Map: Towards Dense Object Counting by Tolerating Annotation Noise

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 noise 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 noise in the dense object counting task. To obtain strong robustness against annotation noise, 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 noise. 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 noise, we design an effective transport cost function based on GGD. With such transport cost constraints, a better PAPM presentation could be adaptively learned with an optimal transport framework from point annotation in an end-to-end manner. Extensive experiments show the superiority of our proposed methods.