Kanade Lucas Tomasi Tracker

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Kanade Lucas Tomasi Tracker

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

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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

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A Tracking Example
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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

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KLT Control Graph
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KLT Control Graph
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Select Good Features

• Features are dependent on the method
• We select those features that can be tracked well
• Optimal by Construction

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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

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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

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Properties of G

• Above the Image noise level
• Well Conditioned
• These properties map onto the eigenvalues
  characteristics

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Eigenvalue Characteristics

• Small, small Constant intensity profile
• Large, small Unidirectional Pattern
• Large, large Corners, salt-and-pepper textures

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Constant Intensity Profile
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Unidirectional pattern
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Salt-and-pepper features
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Tracking Mathematically

• Solution of the equation
• G d 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)

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The Pyramid of Images
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Tracking

• Coarsest resolution tracked first
• Starting point for subsequent resolutions
• Newton-Raphson iterative minimization between
  intensities of two windows

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Tracking stops when

• Feature moves by no more than mindist
• ? is less than ?min
• Number of iterations exceed the limit
• Feature is out of bounds
• Residue is too large

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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.

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Parallelism

• The windows can be threaded
• The calculation of the G and e
• The convolution with Gaussian function

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Tracking Video
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Tracking Video
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Thanks