Motion Analysis using Optical flow

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Motion Analysis using Optical flow
CIS750 Presentation Student Wan Wang Prof
Longin Jan Latecki Spring 2003 CIS Dept of
Temple
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Contents

• Brief discussion to Motion Analysis
• Introduction to optical flow
• Application of Detect and tracking people in
  complex scenes using optical flow

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Part 1 Motion Analysis

• Usual input of a motion analysis system is a
  temporal image sequence
• Motion analysis is often connected with real-time
  analysis

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Three main groups of motion analysis problem

• Motion detection
• - register any detected motion
• - single static camera
• Moving object detection and location
• - moving object detection only
  motion_based segmentation methods
• - detection of a moving object, detection of
  the trajectory of its motion, prediction of its
  future trajectory image object_matching
  techniques are often used to solve these tasks
  (direct matching of image data, matching of
  object features, specific representative object
  points (corner etc.),represent moving object as
  graphs and mathing these graphs) another useful
  method is optical flow
• Derivation of 3D object properties from a set
  of 2D projections of acquired at different time
  instants of object motion

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Part2 Optical flow

• Reflects the image changes due to motion during a
  time interval dt, which is short enough to
  guarntees small inter-frame motion changes
• The immediate objective of optical flow is to
  determine a Velocity fieldA 2D representation of
  a (generally) 3D motion is called a motion
  field(velocity field) Whereas each point is
  assigned avelocity vector corresponding the
  motion direction, velocity and distance from an
  observer at an appropriate image location
• Based on 2 assumptions
• - The observed brightness of any object
  point is constant over time
• - Nearby points in the image plane move in a
  similar manner(velocity smoothness constraint)

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Optical flow

Eghttp//www.ai.mit.edu/people/lpk/mars/temizer_2
001/Optical_Flow/index.html
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Computation Rationale

• Let us suppose we have a continuous image, the
  image intensity is given by f(x,y,t), where the
  intensity is now a function of time t, as well as
  of x and y.
• If this point(x,y) moves to a point (xdx,ydy)
  at time tdt, the following equation holds
•  
• Taylor expansion of the right side of the
  equation (1) is
• Where fx(x,y,t),fy(x,y,t),ft(x,y,t) denote the
  partial derivation of f.
• And e is the high-order term in Tylor series.

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Computation Rationale
Assuming that e is negligible, we obtain the next
equation   That means
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Computation Method
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Optical flow in motion analysis
Motion, as it appears in dynamic images, is
usually some combination of 4 basic
elements (a)Translation at constant distance
from the observer. ---parallel motion
vectors (b)Translation in depth relative to the
observer. ---Vectors having common focus of
expansion. (c) Rotation at constant distance from
view axis. ---concentric motion vectors. (d)
Rotation of planar object perpendicular to the
view axis. ---- vectors starting from
straight line segments.
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Optical flow in motion analysis

• Mutual velocity of an observer and an object
• Let mutual velocities be (u,v,w) at
  direction x,y,z.(z represent the depth) if
  (x0,y0,z0) is the position at time t00.then the
  position of the same point at time t can be
  determined as
• FOE (focus of expansion) determination
• Distance(depth) determination
• Collision Prediction

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Part 3
Experiment of detecting and tracking people in
complex scenes using optical flow (by saitama
univ)
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Demand

• Automatic visual surveillance systems are
  strongly demanded for various applications. We
  have several systems commercially available, most
  of which are based on subtraction between
  consecutive frames or that between a current
  image and a stored background image. They can
  work as expected if environmental conditions do
  not change, such as indoors.
• However, they cannot work outdoors because there
  are various disturbances such as changes of
  lighting and movements of background objects.

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First step compute the optical flow

• By applying two different spatial filters g,h to
  the input image , the following two constraint
  equations are derived.
•   Two orientation_selective spatial Gaussian
  filters g, h applied to the original image
  f(x,y,t) one is sensitive to vertical edges, one
  is to horizental edges.
• (u,v) denotes an optical flow vector and
  subscript denotes partial differentiation

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Second step Region Segmentation

• segment the flow image into uniform flow regions
  in a split-and-merge fashion. First, we divide
  the image into 16 (4 X 4) regions, calculating
  the mean flow vector in each region. If the
  region has any outlier subregions whose flow
  vectors are different from the mean, the region
  is further split into 4 (2 X 2) regions. If the
  region has no outlier subregion, that is, the
  region has a uniform flow, it will not be split.
  The above process is repeated to each region
  until it becomes too small to be split

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Third step Predicted Path Voting

• We prepare a four-dimensional voting space (
  )For each uniform flow region detected in
  the previous process, we predict a path of the
  region in a certain time interval of future. Fig.
  shows the predicted path(only x-y-t are shown).
  We assume that the region continues to move in
  the direction of the mean flow vector ( u,v ) at
  its speed. We approximate each region by an
  ellipse whose center coincides with the region
  centroid. Every point inside the ellipse is given
  weight, according to the two dimensional Gaussian
  as shown in Fig. 3(a). This weight is voted at
  the predicted position (x,y) at the time (t) in
  the direction ( ).
• The voted result is compared with a threshold. If
  there is any region whose number of votes is over
  the threshold, the region is detected as a
  target.

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Reference

• Image processing, analysis, and machine vision
• Detecting and tracking people in complex scenes
• http//www-cv.mech.eng.osaka-u.ac.jp/research/trac
  king_group/iketani/research_e/node1.html