Background detection work in progress
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Background Detection work in progress. Roger S. Gaborski. Main Reference Papers. “Robust Tracking of Human Motion” – Dan Buzan, Boston University “Adaptive Background Mixture Model for Real-time Tracking,” Stauffer and Grimson, MIT

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Background Detection work in progress

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Background Detectionwork in progress

Roger S. Gaborski

Roger S. Gaborski

Main Reference Papers

  • “Robust Tracking of Human Motion” – Dan Buzan, Boston University

  • “Adaptive Background Mixture Model for Real-time Tracking,” Stauffer and Grimson, MIT

  • Both of these papers operate on the premise that each pixel in an image can be modeled with a Gaussian distribution(s)

  • The parameters of the distribution change with changes in the background environment

Roger S. Gaborski

Approach- develop understand of current methods

  • First, implement Buzan’s approach

  • Evaluate approach under wide range of conditions

  • Implement Stauffer and Grimson’s approach

  • Evaluate approach under wide range of conditions

  • Read the literature

  • Propose, implement and test new algorithms

Roger S. Gaborski

Test Video'Test1Sidewalk3.avi';

Roger S. Gaborski

Consider Two Locations:no movement in white locationmovement in yellow location

Roger S. Gaborski

White Dot Region

Consider pixel in upper right corner ( white circle, brick area).

No motion in this area.

Mean of RED 124.7700 STD of RED 2.3044

Mean of GREEN 88.2700 STD of GREEN 2.1736

Mean of BLUE 78.4900 STD of BLUE 2.2133

Roger S. Gaborski

Data for 100 frames

Roger S. Gaborski

Consider area where there is motion (yellow circle, student with dark jacket walks through this point.

Roger S. Gaborski

Red, Green and Blue Data

Roger S. Gaborski

Opening an avi Video File in MATLAB

% Read in the avi file

fname = 'Test1Sidewalk3.avi';

%fname = 'sidewalk10_09.avi';

a = aviread(fname);

% Get the information for the avi

frameInfo = aviinfo(fname);

totalFrames = frameInfo.NumFrames

height = frameInfo.Height

width = frameInfo.Width

Roger S. Gaborski

Computing Statistics

Use 100 frames of data to calculate statistics:

First smooth data to reduce noise:

Smoothing each frame by [1 1 1; 1 1 1; 1 1 1]/9 reduces the std

deviation of a non moving region by a factor of 2.

filterLP=[1 1 1;1 1 1;1 1 1]/9;

For each frame in image:




Roger S. Gaborski


For each pixel in the image, calculate its red, green and blue mean

using the first 100 frames

redAvg=zeros(height,width); greenAvg=zeros(height,width);


redAvg(:,:)= a(1,1).cdata(:,:,1); %initial values, redAvg is an array

greenAvg(:,:)= a(1,1).cdata(:,:,2);%initial values, greenAvg is an array

blueAvg(:,:)= a(1,1).cdata(:,:,3);%initial values, blueAvg is an array

numberFrames = 100;

for i=2:100 %process 100 images for mean, first frame in initial array from above

for k=1:width

for j=1:height

redAvg(j,k)= redAvg(j,k)+double(a(1,i).cdata(j,k,1));

greenAvg(j,k)= greenAvg(j,k)+double(a(1,i).cdata(j,k,2));

blueAvg(j,k)= blueAvg(j,k)+double(a(1,i).cdata(j,k,3));







Roger S. Gaborski

Covariance for Each Pixel

Covariance for each pixel is estimated using N frames (say, 100)

Let up = (redAvgp, greenAvgp,blueAvgp)T , where p is pixel p and

T is transpose

I(p.t) is the intensity of pixel p at frame t

Kp = (1/N-1)  (I(p,t)-up) (I(p,t)-up)T

Dimensions of K

I(p,t) and up is 3x1 , so (I(p,t)-up) is 3x1

(I(p,t)-up)Tis 1x3, soKp is 3x3

Each pixel in the image has a red, green and blue mean

And a 3x3 covariance matrix



(MATLAB has a cov function for calculating covariance)

Roger S. Gaborski


  • Because of changes in the scene (environmental, shadows, etc.) it is necessary to update the background model.

  • One approach is to only update the mean of the model

  • Assume we have a binary map Mt associate with frame t. 1’s in the map represent foreground objects

  •  is a learning rate indicates how much of current background should be maintained

  •  is a learning rate indicates how much of current background occupied by foreground pixels in the current frame should be maintained

  •  and  are close to 1

Roger S. Gaborski


u(t) = [ (1- ) I(t-1) +  u(t-1) ] Mt-1

+ [ (1- ) I(t-1) + u(t-1) (1- Mt-1)

Roger S. Gaborski

Blob Detection

We now have a background model. We will compute the distance

Between the current frame and the background using the

log-likelihood measure:

dp(t)= -.5 [ (I(p,t)-up(t)) Kp-1 (I(p,t)-up(t))T +ln | Kp | +n*ln(2) ]

n is dimension of color space

(note: MATLAB has functions for determinants, transpose and matrix inverse)

The magnitude of the distance determines if the pixel p belongs to the

background or the foreground

Roger S. Gaborski

Set of all dp(t) distances generates a gray level image

We apply morphological operations to eliminate small

holes and regions

First threshold gray level difference image to obtain

a binary image

Apply closing operation

Perform connected component analysis to generate a

set of blobs

b(t)= ConnCompAnalysis(U[dp(t) < thres]

Remove small blobs with size filter

Result is binary map M

Roger S. Gaborski

Movies- sidewalk10_09.avi

Note: first 100 frames (approx) contain motion. Exclude these frames

When calculating means and covariance matrices

Roger S. Gaborski

Processed: oct11thres15meanA90

Roger S. Gaborski

Processed: oct10thres15.avino mean update

Roger S. Gaborski


  • Background recovered as foreground

  • Loose portions of walking individuals

  • Analysis:

    • Analyze individual pixels – why are background pixels being labeled as foreground?

    • Why are foreground pixels being labeled as background

    • Is dp(t) being calculated as you would expect, is threshold ok?

    • Is the mean update formula working correctly?

Roger S. Gaborski

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