Optical flow (motion vector) computation

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Optical flow (motion vector) computation

• Course Computer Graphics and Image Processing
• Semester Fall 2002
• Presenter Nilesh Ghubade (nileshg_at_temple.edu)
• Advisor Dr Longin Jan Latecki
• Dept Computer and Information Science,
• Temple University, Philadelphia, PA-19122

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Motion Analysis

• Three groups of motion-related problems
• Motion detection
• Registers any detected motion.
• Single static camera.
• Used for security purposes.
• Moving object detection and location
• Determination of object trajectory.
• Static camera, moving objects OR Moving camera,
  static objects OR Both camera and objects moving.
• Deriving 3D properties
• Use of set of 2D projections acquired at
  different time instants of object motion.

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Object motion assumptions

• Maximum velocity.
• Small acceleration.
• Common motion of object points.
• Mutual correspondence.

Cmax dt
t2
t1
t0
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Differential motion analysis

• Simple subtraction of images acquired at
  different instants in time makes motion detection
  possible, assuming stationary camera position and
  constant illumination.
• Difference image is a binary image ? subtract two
  consecutive images.
• Cumulative difference image
• Reveals motion direction.
• Time related motion properties.
• Slow motion and small object motion.
• Constructed from sequence of n images taking
  first image as the reference image.

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Example
Motion in front of a security camera. Sobel
filter edge detection.
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Motion Detection- Sobel filter
10 frames/second
15 frames/second
15 frames/second
25 frames/second
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Optical Flow

• Optical Flow reflects the image changes due to
  motion during a time interval dt.
• Optical flow field is the velocity field that
  represents the 3D motion of object points across
  a 2D image.
• It should not be sensitive to illumination
  changes and motion of unimportant objects (e.g.
  shadows)
• Exceptions
• Non-zero optical flow? fixed sphere illuminated
  by a moving source.
• Zero optical flow ? smooth sphere under constant
  illumination, although there is rotational motion
  and true non-zero motion field.

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Optical Flow (continued)

• Aim is to determine optical flow that corresponds
  with true motion field.
• Necessary pre-condition of subsequent higher
  level motion processing ? stationary or moving
  camera.
• Provides tools to determine motion parameters,
  relative distances of objects in the image etc..
• Example

t2
t1
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Assumptions

• Optical flow computation is based on two
  assumptions
• The observed brightness of any object point is
  constant over time.
• Nearby points in the image plane move in a
  similar manner (the velocity smoothness
  constraint).

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Optical flow computation

• The optical flow field represented in the form of
  Velocity vector
• Length of the vector determines the magnitude of
  velocity.
• Direction of the vector determines the direction
  of motion.
• Global optical flow estimation
• Local constraints are propagated globally.
• But errors also propagate across the solution.
• Local optical flow estimation
• Divide image into smaller regions.
• But inefficient in the areas where spatial
  gradients change slowly ? here use global method,
  neighboring image parts contribute.

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Forms of motion
Translation at constant distance from the observer. Set of parallel motion vectors.
Translation in depth relative to the observer. Set of vectors having common focus of expansion.
Rotation at constant distance from view axis. Set of concentric motion vectors.
Rotation of planar object perpendicular to the view axis. One or more sets of vectors starting from straight line segments.
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Representation
Locate the position of a pixel (row,col) in the
current image by computing shortest Euclidean
distance with respect to 5-by-5 neighborhood in
the next consecutive frame.
16 15 14 13 12
17 4 3 2 11
18 5 0 1 10
19 6 7 8 9
20 21 22 23 24
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Experiments
3-by-3 neighborhood
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Experiments (contd)
5-by-5 neighborhood
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Experiments (contd)
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Experiments (contd)
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Applications of optical flow

• Object motion detection.
• Action recognition.
• Active vision or structure of motion
• Reconstruction of 3D object by computing depth
  information.
• If you have distance (depth) maps, you can
  reconstruct surface of the object.
• Facial expression recognition reference?
• http//athos.rutgers.edu/decarlo/pubs/ijcv-face.p
  df

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• Thank you ?