# Tracking: Why? How?

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```					Using Multi-Modality to Guide
Visual Tracking
Jaco Vermaak
Cambridge University Engineering
Department
Patrick Pérez, Michel Gangnet, Andrew Blake
Microsoft Research Cambridge

Paris, December 2002
Introduction
 Visual tracking difficult: changes in pose and illumination,
occlusion, clutter, inaccurate models, high-dimensional state
spaces, etc.
 Tracking can be aided by combining information in multiple
measurement modalities
 Illustrated here on head tracking using:
 Sound and contour measurements
 Colour and motion measurements
General Tracking
Tracking Equations
 Objective: recursive estimation of the filtering distribution:

p xt | y1:t ,     y1:t   y1 ,, yt 
 General solution:
 Prediction step:

p xt | y1:t 1    p xt | xt 1  p xt 1 | y1:t 1  dxt 1
   
  
dynamical prior    previous filtering

 Filtering/update step:

pxt | y1:t   Ly t | xt  pxt | y1:t 1 
 
            
likelihood       prediction

 Problem: generally no analytic solutions available
Particle Filter Tracking
 Monte Carlo implementation of general recursions.
 Filtering distribution represented by samples/particles with
associated importance weights:
N
p N x t | y1:t     ti  x i  dx t 
t
i 1
 Proposal step: new particles proposed from a suitable proposal
distribution:

x ti  simulated from q x t | x ti1 , y t                 
 Reweighting step: particles reweighted with importance weights:

 ti    t1 Ly t | x ti   p x ti  | x ti1  / q x ti  | x ti1 , y t 
i

 Resampling step: multiply particles with high importance weights
and eliminate those with low importance weights.
Particle Filter Building Blocks
 Sampling from conditional density    q x | x 

p x 
q       q x '| x  pdx 
 xi ,  i                    xi,  i 
 Resampling

p x                                     p x 
 xi ,  i             x j (i) ,1, p j(i)  MN 1  N 
 Reweighting with positive function   h x   0

p x 
h

h x  p x   h x  pdx   1

 xi ,  i                       xi , h xi  i 
Particle Filter Implementation
Requires specification of:
 System configuration and state space
 Likelihood model
 Dynamical model for state evolution
 State proposal distribution
 Particle filter architecture
Contour Measurements
Problem Formulation
 Objective: track the head of a person in a video sequence using
audio and image cues
 Audio: time delay of arrival (TDOA) measurements at microphone
pair orthogonal to optical axis of camera
 Image: edge events along normal lines to a hypothesised contour
 Complimentary modalities: audio good for (re)initialisation; image
good for fine localisation
System Configuration

camera

microphone pair

image plane
Model Ingredients
 Low-dimensional state space: similarity transform applied to a
reference template
x  x, y, , 
 Dynamical prior: integrated Langevin equation, i.e. second-order
Markov kernel
pxt x0:t 1   pxt xt 1, xt 2 
 Multi-modal data likelihoods:

p  y x   L x 
 LTDOA x LEDGE rx 
 Sound based likelihood: TDOA at mic. pair
 Contour based likelihood: edge events                 rx
Contour Likelihood
 Input: maxima of projected luminance gradient along normals
( N j such events on j  th normal)

LEDGE

d1, j d 2 , j      d 3, j

     1  q0                  
           
Nj

LEDGE
rx    q0            N di, j ;0, 
2
c
j 
       Nj     i 1           

Contour Likelihood
 Low computational cost
 Robust to illumination changes
 Drawbacks
 Fragile because of narrow support (especially with only
similarity transform on a fixed shape space)
 Sensitive to background clutter
 Extension
 Multiply gradient by inter-frame difference to reduce influence
of background clutter

I
I             I
I max
Inter-Frame Difference

Without frame difference   With frame difference
Audio Likelihood
 Input: positions of peaks in generalised cross-correlation function
(GCCF)
 Reverberation leads to multiple peaks

GCCF

x
 x 
d1      TDOA         dN

LTDOA

d1      TDOA         dN
Audio Likelihood
 Deterministic mapping from Time Delay of Arrival (TDOA) to
bearing angle (microphone calibration) to X-coordinate in image
plane (camera calibration)

G:d   x
 Audio likelihood follows in similar manner to contour likelihood

1  q0
                     
N
L TDOA
 x   q0            N d i ; G 1  x ,  s2
N      i 1

 Likelihood assumes a uniform clutter model
Particle Filter Architecture
LTDOA p X
 qX                                   pY p p    LEDGE
qX

 Layered sampling: first X-position and sound likelihood; then rest
 X-position proposal: mixture of diffusion dynamics and sound
proposal:
q X x   p X x   1   q X x 
LANG               TDOA

                   
N
TDOA
x            1
 N G 1 x ; d i ,  s2
q   X
 x N
G G   1
i 1

 To admit “jumps” from proposal X-dynamics have to be
augmented with an uniform component:

p X x   p X x   1   U x 
LANG
Examples
 Effect of inter-frame difference:

 Conversational ping-pong:
Examples
 Conversational ping-pong and sound based reinitialisation:
Motion Measurements
Problem Formulation
 Objective: detect and track the head of a single person in a
video sequence taken from a stationary camera
 Modality fusion:
 Motion and colour measurements are complementary
 Motion: when the object is moving colour is unreliable
 Colour: when the object is stationary motion information
disappears
 Automatic object detection and tracker initialisation using motion
measurements
 Individualisation of the colour model to the object:
 Initialised with a generic skin colour model
 Adapted to object colour during periods of motion: motion
model acts as “anchor”
Object Description and Motion
 Head modelled as an ellipse that is free to translate and scale in
the image
 Binary indicator variable to signal whether object is present in the
image or not, so object state becomes: x  x, y, s, r 
 State components assumed to have independent motion models
 Indicator: discrete Markov chain
 Position and scale: Langevin motion with uniform initialisation:
undefined if rt  0

pxt | xt 1 , rt , rt 1    pL xt | xt 1  if rt  1 and rt 1  1
U x             if rt  1 and rt 1  0
 Rx t
Image Measurements
 Measurements taken on a regular filter grid:

hue image
saturation image
frame-difference image

isotropic Gaussian filters

y i  H i , Si , Di 

 Measurement vector: y  y1  y G 
Observation Likelihood Model
 Measurements at gridpoints assumed to be independent
 Unique background (object absent) likelihood model for each
gridpoint
 All gridpoints covered by the object share the same foreground
likelihood model:
G
Ly | x    Li y i | x       LF y i      LB y i 
 i
i 1                iF  x        iB  x 
 At each gridpoint the measurements are also assumed to be
independent:
LF y i   LFH H i LFS Si LFM Di 
LB y i   LBH H i LBS Si LBM Di 
i           i         i

 Note that the background motion model is shared by all the
gridpoints
Colour Likelihood Model
 Normalised histograms for both foreground and background
colour likelihood models:
Lc    c 
c : colour measuremen   t
c : bin index correspond to measurement
ing
 i : normalised count for bin i  1 B
 Background models trained on a sequence without objects
 Foreground models trained on a set of labelled face images
 Histogram models supplied with a small uniform component to
prevent numerical problems associated with empty bins
Motion Likelihood Model
 Background frame-difference measurements empirically found to
be gamma distributed:

LBM Di   Dia 1 exp  bDi 

 Foreground frame-difference depends on magnitude of motion,
number and orientation of foreground edges, etc.
 Modelling these effects accurately is difficult
 In general: if the object is moving foreground frame-difference
measurements are substantially larger than those for background
 Thus a two-component uniform distribution is adopted for the
foreground frame-difference measurements (outlier model)
Particle Proposal
 Three stages of operation:
 Birth: object first enters scene; proposal should detect object
and spawn particles in the object region
 Alive: object persists in scene; proposal should allow object to
be tracked, whether it is stationary or moves around
 Death: object leaves scene; proposal should kill particles
associated with the object
 Form of particle proposal:
qx | x' , y, P'  qr | r ' , P'qz | z ' , r , r ' , y 
z   x, y , s 
N
P    (i ) r (i ) empirical probability of
i 1                object being alive
Particle Proposal
 Indicator proposal:
 Pbirth if P'  0
qr  1 | r '  0, P'  
0       otherwise
qr  0 | r '  1  Pdeath
 Birth only allowed if there is no object currently in the scene
 All particles alive are subjected to a fixed death probability
 State proposal:
undefined if r  0

qz | z ' , r , r ' , y    pL z | z ' if r  1 and r '  1


ˆ ˆ
 N z; μ, Σ if r  1 and r '  0
 Langevin dynamics if object is alive
 Gaussian birth proposal: parameters from detection module
Object Detection
 Object region detected by probabilistic segmentation of the
horizontal and vertical projections of the frame-difference
measurements:

 Region location and size determine parameters for birth proposal
distribution
 Why:
 Generic skin colour model may be too broad for accurate
localisation
 Model sensitive to colour changes due to changes in pose and
illumination
 When:
 Object present and moving: largest variations in colour
expected
 Motion likelihood “anchors” particles around moving object
 How:
 Gradual: avoid fitting to the background: enforced with prior
 Stochastic EM: contribution of particles proportional to
likelihood
 Unknown parameters: normalised bin values for object hue and
saturation histograms
 EM Q-function for MAP estimation:

    ˆ  
Q θt , θt  E p x |y
t
ˆ
1:t ,θ1:t    log Ly t | xt , θt   log θtθt
p  | ˆ 1
 
prior
dy nam ical

 No analytic solution but particle approximation yields:

                                                                     
N
QN θ t , θ t    ti  log L y t | x ti  , θ t  log p θ t | θ t 1
ˆ                                                       ˆ
i 1

 Monte Carlo approximation only performed over particles that
are currently alive
 Dirichlet prior used for parameter updates:

pθt | θt 1   Di θt | Cθt 1 
 Prior centred on old parameter values
 Variance controlled by multiplicative constant
 Update rule for normalised bin counts becomes:
ni   i  1
i 
 n           j  B
B

j
j 1
N
ni     j ni j 
j 1

ni j  : i - th bin count for j - th particle
 i : Dirichlet prior parameter
What Happens?

 1

     particle
histograms

 2

weighted average
histogram
Implementation
 Colour model adaptation iterations occur between particle
prediction and particle reweighting in standard particle filter
 Stochastic EM algorithm initialised with parameters from previous
time step
 A single stochastic EM iteration is sufficient at each time step
 Number of particles is fixed to 100
 Non-optimised algorithm runs at 15fps on standard desktop PC
Examples

No adaptation: tracker gets stuck on skin-
coloured carpet in the background

changes in pose and illumination and lock is
maintained

No motion likelihood: tracker fails, illustrating
need for “anchor” likelihood
Examples

Tracking is successful despite substantial variations
in pose and illumination and the subject
temporarily leaving the scene

Particles are killed when the subject leaves the
scene; upon re-entering the individualised
colour model allows lock to be re-established
within a few frames
The End

```
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