Bayesian Poisson regression for crowd counting

By Antoni B. Chan, Nuno Vasconcelos. 2009

463 citations recorded by the source corpus.

Poisson regression models the noisy output of a counting function as a Poisson random variable, with a log-mean parameter that is a linear function of the input vector. In this work, we analyze Poisson regression in a Bayesian setting, by introducing a prior distribution on the weights of the linear function. Since exact inference is analytically unobtainable, we derive a closed-form approximation to the predictive distribution of the model. We show that the predictive distribution can be kernelized, enabling the representation of non-linear log-mean functions. We also derive an approximate marginal likelihood that can be optimized to learn the hyperparameters of the kernel. We then relate the proposed approximate Bayesian Poisson regression to Gaussian processes. Finally, we present experimental results using Bayesian Poisson regression for crowd counting from low-level features.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Transportation, Probabilistic & Bayesian Methods

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Citations in the corpus

DeepSetNet: Predicting Sets with Deep Neural Networks (2016, background): “It is important to bear in mind that unlike many existing approaches that learn to count [1, 5, 12, 20, 24, 35, 50, 51], our main goal is not object counting.”
Representation Learning by Learning to Count (2017, background): “The counting prediction can be provided as an object density map [15, 39, 23] or simply as the number of counted objects [5, 6].”
Assumed Density Filtering Methods for Learning Bayesian Neural Networks (2016, methodology): “Here, we use an accurate approximation which induces an exponential family posterior predictive distribution (Chan and Vasconcelos 2009; El-Sayyad 1973).”
Crowd Counting and Density Estimation by Trellis Encoder-Decoder Networks (2019, background): “The successes of regression-based methods [3, 34, 10, 51, 15] can thus be attributed to their ability of circumventing explicit detection and directly mapping the input images to scalar values.”
JHU-CROWD++: Large-Scale Crowd Counting Dataset and A Benchmark Method (2020, background): “Consequently, computer vision-based crowd analytics and surveillance [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] have received increased interest.”
Generating High-Quality Crowd Density Maps Using Contextual Pyramid CNNs (2017, methodology): “To overcome the issues of occlusion and high background clutter, researchers attempted to count by regression where they learn a mapping between features extracted from local image patches to their counts [3, 27, 6].”
Salient Object Subitizing (2015, background): “…objects can also facilitate applications like image retrieval, iconic image detection (Berg and Berg, 2009), image thumbnailing (Choi et al., 2014), robot vision (Scharfenberger et al., 2013), egocentric video summarization (Lee et al., 2012), snap point prediction (Xiong and Grauman, 2014), etc .”
Learning to Detect Partially Overlapping Instances (2013, background): “by recovering the overall realvalued count of objects in the scene [5, 12, 16, 22] or by estimating the local real-valued density of the objects in each location of interest [11, 15].”
Counting in the Wild (2016, background): “As a consequence, models emerged which cast the problem as one where image features were mapped into a global object count [2, 3, 7], or local features mapped into pixel-wise object densities [4, 6, 8, 16, 24, 26] which can be integrated into the object count over”
Context-Aware Crowd Counting (2018, methodology): “The regressors can be based on Random Forests [18], Gaussian Processes [7], or more recently Deep Nets [41, 42, 26, 31, 40, 36, 32, 24, 19, 30, 33, 22, 15, 28, 5], with most state-of-the-art approaches now relying on the latter.”
DecideNet: Counting Varying Density Crowds Through Attention Guided Detection and Density Estimation (2017, methodology): “Different binary classifiers including Naive Bayes [4], Random Forest [23] and their variations [40, 11] are trained with these features.”
Leveraging Unlabeled Data for Crowd Counting by Learning to Rank (2018, background): “To address these issues, researchers proposed to map features learned from the crowded scene or patches to the number of people [4, 6].”
Counting People With Low-Level Features and Bayesian Regression (2012, methodology): “In this paper, we take a different approach and directly analyze Poisson regression from a Bayesian perspective, by imposing a Gaussian prior on the weights of the linear log-arrival rate [24].”
Multi-scale Deep Learning Architectures for Person Re-identification (2017, background): “It plays an important role in a number of applications in video surveillance, including multicamera tracking [2, 41], crowd counting [3, 10], and multicamera activity analysis [54, 53].”
Scale Aggregation Network for Accurate and Efficient Crowd Counting (2018, methodology): “Researchers attempted regression-based methods to directly learn a mapping from the feature of image patches to the count in the region [18,19,20].”
CSRNet: Dilated Convolutional Neural Networks for Understanding the Highly Congested Scenes (2018, methodology): “such as foreground and texture features, have been used for generating low-level information [30].”
Crowd Analysis Using Computer Vision Techniques (2010, methodology): “It is also interesting to note that techniques that somehow explore camera information (such as [33], [28], and [29]) are more flexible regarding the camera setup used to monitor the scene, being also able to correct perspective distortions.”
Iterative Crowd Counting (2018, methodology): “To handle images of dense crowds, some meth-ods [2,3] proposed to use a regression approach to avoid the harder detection problem.”
Single-Image Crowd Counting via Multi-Column Convolutional Neural Network (2016, methodology): “Arguably the most extensively used method for crowd counting is feature-based regression, see [4, 7, 5, 27, 15, 20].”