For crowded scenes, the accuracy of object-based computer vision methods declines when the images are low-resolution and objects have severe occlusions. Taking counting methods for example, almost all the recent state-of-the-art counting methods bypass explicit detection and adopt regression-based methods to directly count the objects of interest. Among regression-based methods, density map estimation, where the number of objects inside a subregion is the integral of the density map over that subregion, is especially promising because it preserves spatial information, which makes it useful for both counting and localization (detection and tracking). With the power of deep convolutional neural networks (CNNs) the counting performance has improved steadily. The goal of this paper is to evaluate density maps generated by density estimation methods on a variety of crowd analysis tasks, including counting, detection, and tracking. Most existing CNN methods produce density maps with resolution that is smaller than the original images, due to the downsample strides in the convolution pooling operations. To produce an original-resolution density map, we also evaluate a classical CNN that uses a sliding window regressor to predict the density for every pixel in the image. We also consider a fully convolutional (FCNN) adaptation, with skip connections from lower convolutional layers to compensate for loss in spatial information during upsampling. In our experiments, we found that the lower-resolution density maps sometimes have better counting performance. In contrast, the original-resolution density maps improved localization tasks, such as detection and tracking, compared to bilinear upsampling the lower-resolution density maps. Finally, we also propose several metrics for measuring the quality of a density map, and relate them to experiment results on counting and localization.
The concept of an object density map , where the integral (sum) over any subregion equals the number of objects in that region, was first proposed in @cite_25 . The density values are estimated from low-level features, thus sharing the advantages of general regression-based methods, while also maintaining location information. @cite_25 uses a linear model to predict a pixel's density value from extracted features, and proposed the Maximum Excess over Sub Array (MESA) distance, which is the maximum counting error over all rectangular subregions, as a learning objective function. @cite_12 uses ridge regression (RR), instead of the computationally costly MESA, in their interactive counting system. Both @cite_25 and @cite_12 use random forest to extract features from several modalities, including the raw image, the difference image (with its previous frame), and the background-subtracted image.
@cite_25 @cite_12
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We propose a new supervised learning framework for visual object counting tasks, such as estimating the number of cells in a microscopic image or the number of humans in surveillance video frames. We focus on the practically-attractive case when the training images are annotated with dots (one dot per object). Our goal is to accurately estimate the count. However, we evade the hard task of learning to detect and localize individual object instances. Instead, we cast the problem as that of estimating an image density whose integral over any image region gives the count of objects within that region. Learning to infer such density can be formulated as a minimization of a regularized risk quadratic cost function. We introduce a new loss function, which is well-suited for such learning, and at the same time can be computed efficiently via a maximum subarray algorithm. The learning can then be posed as a convex quadratic program solvable with cutting-plane optimization. The proposed framework is very flexible as it can accept any domain-specific visual features. Once trained, our system provides accurate object counts and requires a very small time overhead over the feature extraction step, making it a good candidate for applications involving real-time processing or dealing with huge amount of visual data. Our objective is to count (and localize) object instances in an image interactively. We target the regime where individual object detectors do not work reliably due to crowding, or overlap, or size of the instances, and take the approach of estimating an object density.