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Marked Point Processes for Crowd Counting

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Learning Intrinsic Shape Classes

- Bayesian approach

determine location, scale, orientation

Estimating Extrinsic Parameters

Original image

Foreground blobs

Blob orientation axes in a frame

determine body shape

Blob orientation axes of a sequence

Inliers found by RANSAC

Vertical vanishing point

Binary mask

“Soft” mask

A rectangular covering

A shape covering

MPP prior

Combined with likelihood

Marked Point Processes for Crowd Counting

Weina Ge and Robert T. CollinsComputer Science and Engineering Department, The Pennsylvania State University, USA

MOTIVATION

We consider a crowd scene as a realization of an MPP

- Delineate pedestrians in a fg mask using shape coverings

- Model the shapes using a mixture of Bernoulli distributions

- Automatically determine the number of mixture components by Bayesian EM

EM iterations

Bayesian EM with Dirichlet prior

- Adapt to different videos by learning the shape models

Training samples

Automatically learned shapes

- Our MPP combines a stochastic point process with a conditional mark process to model prior knowledge on the spatial distribution of an unknown number of pedestrians

RESULTS

π(θi|pi)

π(wi, hi|pi)

robust regression

- Estimating the MPP Configurations by RJMCMC

RJMCMC: stochastic mode seeking procedure with two different types of proposals

1. update shape/location

local updates to a current configuration

2. birth/death

jumps between two configurations of different

dimensions

- CONTRIBUTIONS
- An MPP with a conditional mark process to model known correlations between bounding box size/orientation and image location
- Bayesian EM for automatic learning of Bernoulli shapes

For more info: http://vision.cse.psu.edu/projects/mpp/mpp.html