Foreground-Adaptive Background Subtraction

J. Mike McHugh,Janusz Konrad, Venkatesh Saligrama and Pierre-Marc Jodoin Signal Processing Letters, IEEE

Professor: Jar-Ferr YangPresenter: Ming-Hua Tang

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

Outline

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.

Introduction(1/2)

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.

Introduction(2/2)

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.

Background subtraction

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.

Background modeling

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.

Foreground detection

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

Foreground modeling(1/2)

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.

Foreground modeling(2/2)

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

Makov modeling of change labels

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.

Makov modeling of change labels

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.

*Makov modeling of change labels

Since the labels are binary, we choose to use the Ising potential function

With Z canceled, the ratio of Gibbs priors becomes

*Makov modeling of change labels

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.

Makov modeling of change labels

Experimental results

Experimental results(1/3)

Experimental results(2/3)

(b)Probabilities:

(c) followed by

(d) labels computed using additional MRF model.

Experimental results(3/3)