Revision as of 01:01, 24 January 2008

The Lucas-Kanade algorithm iteratively tries to minimise the difference between the image and a warped template. The technique can be used for image alignment, tracking, optic flow analysis, and motion estimation. In this example a texture patch in a Space Shuttle video is tracked over 324 frames. A 2-D affine transform was used as a model.

For the documentation of the mathematics have a look at the web-page of the CMU-project "Lucas-Kanade 20 years on" and at the publication by Baker and Matthews.

Implementation

The crucial parts of the implementation (here: isometric model) are only a few lines of code. An initial parameter vector p, an image img and a template tpl are required. The tracking algorithm (inverse compositional Lucas-Kanade) is initialised as follows:

p = Vector[ xshift, yshift, rotation ]
w, h = *tpl.shape
x, y = xramp( w, h ), yramp( w, h )
sigma = 5.0
gx = tpl.gauss_gradient_x( sigma )
gy = tpl.gauss_gradient_y( sigma )
c = Matrix[ [ 1, 0 ], [ 0, 1 ], [ -y, x ] ] * Vector[ gx, gy ]
hs = ( c * c.covector ).collect { |e| e.sum }

A tracking step then is done by applying the following piece of code to each image img. Usually the tracking step is performed multiple times on each image to improve the tracking estimate.

field = MultiArray.new( MultiArray::LINT, w, h, 2 )
field[ 0...w, 0...h, 0 ] = x * cos( p[2] ) - y * sin( p[2] ) + p[0]
field[ 0...w, 0...h, 1 ] = x * sin( p[2] ) + y * cos( p[2] ) + p[1]
diff = img.warp_clipped( field ).to_type( MultiArray::SFLOAT ) - tpl
s = c.collect { |e| ( e * diff ).sum }
d = hs.inverse * s
p += Matrix[ [  cos(p[2]), -sin(p[2]), 0 ],
             [  sin(p[2]),  cos(p[2]), 0 ],
             [          0,          0, 1 ] ] * d

A full implementation (more sophisticated) is available as an example application with HornetsEye. You can find a listing of the source code here.

See Also

• HornetsEye
• Gradient Based Motion Estimation

External Links

• Hornetseye implementation
• CMU project: "Lucas-Kanade 20 years on"
  • S. Baker, I. Matthews: Lucas-Kanade 20 Years On: A Unifying Framework, International Journal of Computer Vision, Vol. 56, No. 3, March, 2004, pp. 221-255.
• NASA high definition videos