An approach to the problem of estimating the size of inhomogeneous crowds, composed of pedestrians that travel in different directions, without using explicit object segmentation or tracking is proposed. Instead, the crowd is segmented into components of homogeneous motion, using the mixture of dynamic textures motion model. A set of holistic low-level features is extracted from each segmented region, and a function that maps features into estimates of the number of people per segment is

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... with Bayesian regression. Two Bayesian regression models are examined. The first is a combination of Gaussian process regression (GPR) with a compound kernel, which accounts for both the global and local trends of the count mapping, but is limited by the real-valued outputs that do not match the discrete counts. We address this limitation with a second model, which is based on a Bayesian treatment of Poisson regression that introduces a prior distribution on the linear weights of the model. Since exact inference is analytically intractable, a closedform approximation is derived that is computationally efficient and kernelizable, enabling the representation of non-linear functions. An approximate marginal likelihood is also derived for kernel hyperparameter learning. The two regression-based crowd counting methods are evaluated on a large pedestrian dataset, containing very distinct camera views, pedestrian traffic, and outliers, such as bikes or skateboarders. Experimental results show that regression-based counts are accurate, regardless of the crowd size, outperforming the count estimates produced by stateof-the-art pedestrian detectors. Results on two hours of video demonstrate the efficiency and robustness of regression-based crowd size estimation over long periods of time.