J. Mike McHugh,Janusz Konrad, Venkatesh Saligrama and Pierre-Marc Jodoin Signal Processing Letters, IEEE Professor: Jar-Ferr Yang Presenter: Ming-Hua Tang
Introduction Background subtraction as a hypothesis test Foreground modeling Makov modeling of change labels Experimental results
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.
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.
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.
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.
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.
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
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.
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
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.
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.
Since the labels are binary, we choose to use the Ising potential function With Z canceled, the ratio of Gibbs priors becomes
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.
(b)Probabilities: (c) followed by (d) labels computed using additional MRF model.