1. J. Mike McHugh,Janusz Konrad, Venkatesh Saligrama and Pierre-Marc Jodoin Signal Processing Letters, IEEE Professor: Jar-Ferr Yang Presenter: Ming-Hua Tang

2.  Introduction  Background subtraction as a hypothesis test  Foreground modeling  Makov modeling of change labels  Experimental results

3.  Change detection based on thresholding intensity differences.  We adapt the threshold to varying video statistics by means of two statistical models.  In addition to a nonparametric background model, we introduce a foreground model based on small spatial neighborhood to improve discrimination sensitivity.

4.  We also apply a Markov model to change labels to improve spatial coherence of the detections.  Our approach is using a spatially-variable detection threshold, offers an improved spatial coherence of the detections.

5.  Involves two distinct processes that work in a closed loop: 1. Background modeling: a model of the background in the field of view of a camera is created and periodically updated. 2. foreground detection: a decision is made as to whether a new intensity fits the background model; the resulting change label field is fed back into background modeling.

6.  At each background location n of k frame, this model uses intensity from recent N frames to estimate background PDF:  is a zero-mean Gaussian with variance that, for simplicity, we consider constant throughout the sequence.

7.  Change labels can be estimated by evaluating intensity in a new frame at each pixels in current image.  Without an explicit foreground model, is usually considered uniform.  This test is prone to randomly-scattered false positives, even for low θ.

8.  We propose a foreground model based on small spatial neighborhood in the same frame.  Let be a change label at n  Define a set of neighbors belonging to the foreground:  Calculate the foreground probability using the kernel-based method

9.  At iteration, this results in a refined likelihood ratio test  Since we introduce a positive feedback, the threshold θ must be carefully selected to avoid errors compound.  False negatives will be corrected by Markov model if several neighbors are correctly detected.

10.  A pixel surrounded by foreground labels should be more likely to receive a foreground label than a pixel with background neighbors.  Suppose that the label field realization is known for all m except n. Then the decision rule at n is :  By mutually independent spatially on the label field

11.  Since E is a MRF, the a priori probabilities on the right-hand side are Gibbs distributions characterized by the natural temperature γ, cliques c, and potential function V defined on c.

12.  Z and T(γ) are normalization and natural temperature constants respectively.  The potential function, V(c), in the set of all cliques in the image C. In this work, we take C to include all 2-element cliques of the second-order Markov neighborhood.

13.  Since the labels are binary, we choose to use the Ising potential function  With Z canceled, the ratio of Gibbs priors becomes

14.  denote the number of foreground and background neighbors of n  γ is selected by the user to control the nonlinear behavior  smaller values of γ strengthen the influence of MRF model on the estimate, while larger values weaken it.

18.  (b)Probabilities:  (c) followed by  (d) labels computed using additional MRF model.