Tracking is the problem of estimating the trajectory of an object as it moves around a scene. Motion tracking involves collecting data on human movement using sensors to control outputs like music or lighting based on performer actions. Motion tracking differs from motion capture in that it requires less equipment, is less expensive, and is concerned with qualities of motion rather than highly accurate data collection. Optical flow estimates the pixel-wise motion between frames in a video by calculating velocity vectors for each pixel.

1. Moving Object Detection

2. Tracking
 Tracking is the problem of estimating the trajectory of
an object in the image plane as it moves around a
scene.
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3. What is Motion Tracking…?
• Technologies that collect data on human movement
(input) used to control sounds, music, recorded or
projected text, video art, stage lighting (output) via
performer actions / gestures / movements / bio-data.
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4. What is Motion Tracking…?
• other uses:
• Animation modeling (motion capture)
• Scientific research
(musicology, semantics, ergonomics, medicine, sports
medicine, architecture)
• Therapy for physically and mentally handicapped
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5. Motion tracking vs. Motion capture
Motion capture Motion tracking
•Tracks location of fixed •less equipment, less data,
positions on body
•less cost ($1k-2k)
•Highly
accurate, expensive •concerned with motion
($200k-2m) qualities like
dynamic, direction of motion
•Generally not realtime
•real time
•Used for data collection
(research) and for making •used for live applications:
human or animal motion in installation
animations art, dance, theater and
(films, games, etc.) more
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6. Motion capture
 Motion capture is defined as "The creation of a 3D representation of
a live performance."
 Tracks location of fixed positions on body with reflective markers
 12-24 cameras, each lens is ringed with infrared lights
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7. Motion capture
 Motion capture is used to be considered a tool for
creating animation.
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8. Motion capture
 Typical uses
 Human movement research
(sports, musicology, ergonomics, medicine,...)
 Film and Animation -- often used with 3-D animation (modeling)
programs to make animations
 maya (http://www.animationarena.com)
 houdini (http://www.sidefx.com)
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9. Motion capture
 Vicon is a leading company in motion capture
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10. Motion tracking
media output
sounds, musi
input c, text, projec
physical tions, lighting
human action
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11. Motion tracking
sensor output device
(e.g. video computer (e.g. loud media output
camera) speakers)
input sounds, musi
physical c, text, projec
human action tions, lighting
analogue to digital to
digital analogue
conversion conversion
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12. Digital vs. Analogue
Digital data
Analogue data
• easy to reproduce
• hard to reproduce
• "rich data" (infinite values) • lower resolution, less human-
• very high resolution feel.
• more details • easy to store
• contaminated data (becomes • easy to process
noisy, but rarely fails • contaminated data remains
completely) clean (errors can be filtered) or
signal fails altogether
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13. What you need to track motion
Computer needs video input
Digital video (Firewire, USB2)
+ digital cameras (camcorder, webcams)
+ low noise
+ works with laptops
- latency issues
- image resolution issues (smaller chip sizes)
- limited cable length
Analog video
+ "unlimited" cable length
+ lower latency
+ even digital cams usually have analog output
- cost more (although many older cameras work quite well)
- works less well with laptops i.e. need an external or internal
framegrabber
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14. Who is using motion tracking?
 Palindrome Intermedia Performance Group
 Krisztina de Chatel
 Igloo
 Ventura Dance (Pablo Ventura)
 Robert Lepage
 André Werner
 Marlon Barrios Solano
 La la la Human Steps
 Georg Hobmeier
 Leine Roebana Dans Kompanie
 Troika Ranch
 Blue Man Group
 you
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15. The Problem in Motion Tracking
 Given a set of images in time which are similar but not
identical, derive a method for identifying the motion
that has occurred (in 2d) between different images.

16. Motion Detection and Estimation
in Literature
 Image differencing
 based on the threshold difference of successive images
 difficult to reconstruct moving areas
 Background subtraction
 foreground objects result by calculating the difference between
an image in the sequence and the background image
(previously obtained)
 remaining task: determine the movement of these foreground
objects between successive frames
 Block motion estimation
 Calculates the motion vector between frames for sub-blocks of
the image
 mainly used in image compression
 too coarse

17. What Is Optical Flow?
 Optical flow is the displacement field for each of the
pixels in an image sequence.
 For every pixel, a velocity vector dx , dy
is found which says: dt dt
 how quickly a pixel is moving across the
image
 the direction of its movement.

18. Optical Flow Examples
Image #1 Optical Flow Field Image #2
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19. Optical Flow Examples
Translation Rotation Scaling

20. Estimation of the optical flow
 Sequences of ordered images allow the estimation
of motion as either instantaneous image velocities or
discrete image displacements.
 The optical flow methods try to calculate the motion
between two image frames which are taken at times
t and
t + δt at every voxel position.
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21. Voxel Position
 A voxel (volumetric pixel or Volumetric Picture
Element) is a volume element, representing a value
on a regular grid in three dimensional space.
A series of voxels in a stack with a single voxel
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22. Estimation of the optical flow
 Optical Flow methods are called differential since they
are based on local Taylor series approximations of the
image signal; that is, they use partial derivatives with
respect to the spatial and temporal coordinates.
 In mathematics, a Taylor series is a representation of a
function as an infinite sum of terms that are calculated
from the values of the function's derivatives at a single
point.
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23. Taylor series
 The Taylor series of a real or complex function ƒ(x) that is infinitely
differentiable in a neighborhood of a real or complex number a is the
power series
which can be written in the more compact sigma notation as
where n! denotes the factorial of n and ƒ (n)(a) denotes the nth derivative of ƒ
evaluated at the point a. The zeroth derivative of ƒ is defined to be ƒ itself and (x −
a)0 and 0! are both defined to be 1. In the case that a = 0, the series is also called
a Maclaurin series.
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24. Estimation of the optical flow
 For a 2D+t dimensional case (3D or n-D cases are similar) a voxel at
location (x,y,t) with intensity I(x,y,t) will have moved by δx, δy and δt
between the two image frames, and the following image constraint
equation can be given:
I(x,y,t) = I(x + δx,y + δy,t + δt)
Assuming the movement to be small, the image constraint at I(x,y,t)
with Taylor series can be developed to get:
H.O.T
(higher-order terms)
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25. Estimation of the optical flow
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26. Estimation of the optical flow
where Vx,Vy are the x and y components of the velocity or optical flow of
I(x,y,t) and are the derivatives of the image at (x,y,t)
in the
corresponding directions. Ix,Iy and It can be written for the derivatives in
the following.
Thus:
IxVx + IyVy = − It
or
This is an equation in two unknowns and cannot be solved as such. This is
known as the aperture problem of the optical flow algorithms. To find the
optical flow another set of equations is needed, given by some additional
constraint. All optical flow methods introduce additional conditions for
estimating the actual flow.
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27. Our Solution
 Optical flow: maximum one pixel large movements
 Optical flow: larger movements
 Morphological filter
 Contour detection (demo purposes)

28. Optical Flow: maximum one pixel large
movements
 The optical flow for a pixeli, j given 2 successive
images and k : k 1
mk (i, j ) ( x, y) so that
I k (i, j) I k 1 (i x, j y) (1)
is minimum for 1 x 1, 1 y 1
k k+1

29. Optical Flow: maximum one pixel
large movements
 More precision: consider a 3×3 window
around the pixel:
 Optical flow for pixel i, j becomes:
mk (i, j ) ( x, y) so that
1 1 1 1
I k (i u, j v) I k 1 (i u x, j v y) (2)
u 1v 1 u 1v 1
is minimum for 1 x 1, 1 y 1

30. Optical Flow: larger movements
 Reduce the size of the image
=> reduced size of the movement
 Solution: multi-resolution analysis of the images
 Advantages: computing efficiency, stability

31. Multi-resolution Analysis
 Coarse to fine optical flow estimation:
32 32
64 64
128 128
256 256
Original image k Original image k+1

32. Optical Flow: Top-down Strategy
Algorithm (1/4 scale of resolution reduction):
 Step 1: compute optical flow vectors for the highest
level of the pyramid l (smallest resolution)
 Step 2: double the values of the vectors
 Step 3: first approximation: optical flow vectors for the
(2i, 2j), (2i+1, 2j), (2i, 2j+1), (2i+1, 2j+1) pixels in the l-
1 level are assigned the value of the optical flow
vector for the (i,j) pixel from the l level
Level l Level l-1

33. Optical Flow: Top-down Strategy
 Step 4:
 adjustment of the vectors of the l-1(one) level in the
pyramid
 method: detection of maximum one pixel
displacements around the initially approximated
position
 Step 5:
smoothing of the optical flow field (Gaussian
filter)

34. Filtering the Size of the Detected Regions
 Small isolated regions of motion detected by the
optical flow method are classified as noise and are
eliminated with the help of morphological
operations:
 Step 1: Apply the opening:
 Step 2: Apply the  B
X closing: B
X B
X B X B B

35. Contour Detection
 For demonstration purposes, the contours of the moving
regions detected are outlined
 Method: the Sobel edge detector:
 Compute the intensity gradient: f f
f x, y , fx, f y (5)
x y
using the Sobel masks: 1 0 1 1 2 1
1 1
Gx 2 0 2 , Gy 0 0 0 (6)
4 4
1 0 1 1 2 1
 Compute the magnitude of the gradient:
M x, y f x, y fx
2
fy
2
(7)
 if M x, y threshold edge pixel
then
else non-edge pixel

36. A Block Diagram of the System

37. Conclusions
 What we did:
 We managed to estimate the motion with a certain
level of accuracy
 The results might be good enough for some
applications, while other applications might require
better accuracy
 What remains to be done:
 Reduce computational complexity
 use the computed background image to separate
foreground objects
 Parallelism of the algorithms
 Experiment with specific problems, calibrate the
parameters of the algorithms

38. Thanks
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