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					                            Kanade Lucas Tomasi Tracker




                                 Ankit Gupta (1999183)
                                  Vikas Nair (1999219)
                            Supervisor Prof M. Balakrishnan
                           Electrical Engineering Department
                                        IIT Delhi



ASSET Group Seminar, 25/02/2002           http://www.cse.iitd.ac.in/esproject   Slide 1
Tracking and its Applications



 Tracking is to follow features from one frame to another
  in an image sequence
      • The definition of a feature depends from implementation to
        implementation


 Tracking finds many real time applications
      • Survelliance systems
      • Defence applications
      • Robotic arm



ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 2
A Tracking Example




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 3
Kanade Lucas Tomasi Tracker



 Algorithm proposed by Kanade and Lucas



 Definition of a good feature extended by Lucas and
  Tomasi

 Implementation of the algorithm by vision group at
  Stanford


ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 4
KLT Control Graph


                                  A    Start If sequence                              Take stored
             A                    Smoothening                                           image

                                   Take new image
                                    Windows Smoothen
                                    measured                                                        B
                                     Select Good
                                  for tractability
                                        FeaturesSubsampling

                           N best features                   If lost   Yes Replace features
                             Track Features
                                 Yes
         Newton Raphson selected                            features
                                                           No                        Write image
                         ensuring minimum   If n>3
             Tracking
                              distance                            No
                                                 Yes                    No
                       Yes      If images
  Replace features                                       Store Image
     No                      Yesremaining
              If feature               If subsampled          No                      Yes
                              If write                               If write image B
                                                           Write image
               tracked                    levels left
                                 No
                                                      Stop

ASSET Group Seminar, 25/02/2002                     http://www.cse.iitd.ac.in/esproject                 Slide 5
KLT Control Graph

                                        Start


                                    Take new image

                                     Select Good
                                       Features

                                                                           If lost          Yes   Replace features
                                     Track Features                       features

                                                                                  No
                              Yes      If images
  Replace features                                                   Store Image
                                       remaining

                                        No
                                                               Stop

ASSET Group Seminar, 25/02/2002                       http://www.cse.iitd.ac.in/esproject                            Slide 6
Select Good Features



 Features are dependent on the method

 We select those features that can be tracked well

 Optimal by Construction




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 7
Select Good Features



 The image is smoothened by convolving with a
  Gaussian function

 The gradient of each window is calculated by convolving
  it with derivative of Gaussian of sigma

 A list of the windows is made




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 8
Selection



 Feature windows sorted according to eigenvalues of G
  matrix calculated as
                  G = (ggTw)da

 Required top features are selected

 Minimum distance between features is maintained




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 9
Properties of G



 Above the Image noise level

 Well Conditioned

 These properties map onto the eigenvalues
  characteristics




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 10
Eigenvalue Characteristics



 Small, small : Constant intensity profile

 Large, small : Unidirectional Pattern

 Large, large : Corners, salt-and-pepper textures




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 11
Constant Intensity Profile




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 12
Unidirectional pattern




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 13
Salt-and-pepper features




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 14
Tracking Mathematically


             Solution of the equation

                             Gd=e
                            G = (ggTw)da
Where
 G : second order weighted gradient matrix (22)
  e : weighted intensity error (21)
  d : Displacement Vector(21)
  g : Gradient matrix(21)


ASSET Group Seminar, 25/02/2002             http://www.cse.iitd.ac.in/esproject   Slide 15
The Pyramid of Images




                                         Sub Sampled 1/4




                                          Sub sampled 1/2




                                  The original Window w/o sampling




ASSET Group Seminar, 25/02/2002                http://www.cse.iitd.ac.in/esproject   Slide 16
Tracking



 Coarsest resolution tracked first

 Starting point for subsequent resolutions

 Newton-Raphson iterative minimization between
  intensities of two windows




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 17
Tracking stops when


 Feature moves by no more than mindist

 λ is less than λmin

 Number of iterations exceed the limit

 Feature is out of bounds

 Residue is too large




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 18
Replace Good Features



 On the same principle as Select Good Features.

 Retains existing features i.e. those being tracked well.

 Keeps a minimum distance between the features.




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 19
Parallelism



 The windows can be threaded

 The calculation of the G and e

 The convolution with Gaussian function




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 20
Tracking Video




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 21
Tracking Video




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 22
Thanks




ASSET Group Seminar, 25/02/2002   http://www.cse.iitd.ac.in/esproject   Slide 23

				
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