Abstract:  Object counting gains an important role in many fields, such as estimating the number of cells in a microscopic image or predicting the number of pedestrians in surveillance video frames. Many researches have been done to accurately estimate the count, among which the density estimation framework first estimates the density image, then integrates probability over the whole density image to get the counting number. Under this framework, this paper proposes an algorithm based on minimizing square error to infer the density image. This algorithm has an analytical solution, and can reduce training time in a computationally efficient and stable manner. The prediction result has a competitive error rate to other density estimation algorithms. Combined with the technique of neighbor feature smoothing, the estimated density image is very similar to ground truth density in human vision.

Key words: object counting, cells counting, density estimation

摘要： 物体计数在医学领域的细胞计数、智能交通领域的行人计数问题中都有着广泛的应用。目前有大量的算法针对物体计数问题展开研究，其中基于密度图像估计的计数算法首先通过学习得到密度图像，然后将密度图像所有位置上的概率求和得到物体的数量。采用基于密度图像估计的算法框架对物体计数进行研究，提出了一种最小化平方误差的密度估计算法。该算法具有解析解，在最终错误率相近甚至更优的前提下，可以有效节省训练时间。与另一种近邻特征加权技术进行对比，估计出的密度图像在视觉效果上与真实密度图像非常接近。

关键词: 物体计数, 细胞计数, 密度估计