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Formation et Analyse d’ImagesSession 8

Daniela Hall

14 November 2005

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Course Overview

• Session 1 (19/09/05)– Overview– Human vision – Homogenous coordinates– Camera models

• Session 2 (26/09/05)– Tensor notation– Image transformations– Homography computation

• Session 3 (3/10/05)– Camera calibration– Reflection models– Color spaces

• Session 4 (10/10/05)– Pixel based image analysis

• 17/10/05 course is replaced by Modelisation surfacique

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Course overview

• Session 5 + 6 (24/10/05) 9:45 – 12:45– Contrast description– Hough transform

• Session 7 (7/11/05)– Kalman filter

• Session 8 (14/11/05)– Tracking of regions, pixels, and lines

• Session 9 (21/11/05)– Gaussian filter operators

• Session 10 (5/12/05)– Scale Space

• Session 11 (12/12/05)– Stereo vision – Epipolar geometry

• Session 12 (16/01/06): exercises and questions

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Session overview

1. Tracking of objects

2. Architecture of the robust tracker

3. Tracking using Kalman filter

4. Tracking using CONDENSATION

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Robust tracking of objects

Trigger regions

Detection New targets

List of targets

PredictList of predictions

Correct

Detection

Measurements

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Tracking system

• Tracking system: detects position of targets at each time instant (using i.e. background differencing)

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Tracking system

• Supervisor– calls image acquisition, target observation and detection in a cycle

• Target observation module– ensures robust tracking by prediction of target positions using a Kalman

filter• Detection module

– verifies the predicted positions by measuring detection energy within the search region given by the Kalman filter

– creates new targets by evaluating detection energy within trigger regions• Parameters

– noise threshold, detection energy threshold, parameters for splitting and merging

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Detection by background differencing

• I=(IR,IG,IB) image, B=(BR,BG,BB) background • Compute a binary difference image Id, where all pixels that have a

difference diff larger than the noise threshold w are set to one.

• Then we compute the connected components of Id to detect the pixels that belong to a target.

• For each target, we compute mean and covariance of its pixels. The covariance is transformed to width and height of the bounding box and orientation of the target.

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Real-time target detection

• Computing connected components for an image is computationally expensive.

• Idea:– Restrict search of targets to a small number of search

regions.

• These regions are:– Entry regions marked by the user– Search region obtained from the Kalman filter that

predicts the next most likely position of a current target.

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Background adaption to increase robustness of detection

• In long-term tracking, illumination of a scene changes. Image differencing with a static background causes lots of false detections.

• The background is updated regularily by

• t time, α=0.1 background adaption parameter• Background adaption allows that the background

incorporates slow illumination changes.

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Example• Detection module

• Parameters: detection energy threshold– energy threshold too high: targets are missed or targets are split– energy threshold too low: false detections

• Problem: energy threshold depends on illumination and target appearance

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Session overview

1. Tracking of objects

2. Architecture of the robust tracker

3. Tracking using Kalman filter

4. Tracking using CONDENSATION

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Tracking

• Targets are represented by position (x,y) and covariance.

• A first order Kalman filter is used to predict the position of the target in the next frame.

• The Kalman filter provides a ROI where to look for the target. ROI is computed from the a posteriori estimate xk and from the a posteriori error covariance Pk

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Example

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Example: Tracking bouncing ball

• Specifications:– constant background– colored ball

• Problems:– noisy observations– motion blur– rapid motion changes

Thanks to B. Fisher UEdin for providing slides and figures of this example. http://homespages.inf.ed.ac.uk/rbf/AVAUDIO/lect8.pdf

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Ball physical model

• Position zk = (x, y)

• Position update zk = zk-1 + vk-1Δt

• Velocity update vk = vk-1+ak-1Δt

• Acceleration (gravity down) ak=(0,g)T

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Robust tracking of objects

• Measurement

• State vector

• State equation

• Prediction

• State control

Tk

kkk

kkk

Tk

k

tgBu

BuxAx

HvHxz

yxyxx

y

xz

),0,0,0(

,ˆˆ

0010

0001,

',',,

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Robust Tracking of objects

• Measurement noise error covariance

• Temporal matrix

• Process noise error covariance

• a affects the computation speed (large a increases uncertainty and therefore the search regions)

IQ

t

t

A

R

k

k

01.0

1000

0100

010

001

046.0005.0

005.0285.0

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Kalman filter successes

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Kalman filter failures

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Kalman filter analysis

• smoothes noisy observations

• dynamic model fails at bounce and stop

• could estimate ball radius

• could plot a boundary of 95% likelihood of ball position (the boundary would grow when the fit is bad).

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Session overview

1. Tracking of objects

2. Architecture of the robust tracker

3. Tracking using Kalman filter

4. Tracking using CONDENSATION

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Tracking by CONDENSATION

• CONDENSATION: Conditional Density Propagation. Also known as Particle Filtering.

Ref: M.Isard and A. Blake: CONDENSATION for visual tracking, Int Journal of Computer Vision, 29(1),1998.http://www.robots.ox.ac.uk/%7Econtours/

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CONDENSATION tracking

• Keeps multiple hypotheses

• updates using new data

• selects hypotheses probabilistically

• copes with very noisy data and process state changes

• tunable computation load (by choosing number of particles).

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CONDENSATION algorithm

• Given a set of N hypotheses at time k Hk={x1,k, ... , xN,k} with associated probabilities {p(x1,k), ..., p(xN,k)}

• Repeat N times to generate Hk+1– 1. randomly select a hypothesis xu,k from Hk with p(xu,k)– 2. generate a new state vector sk from a distribution centered at xu,k

– 3. get new state vector using dynamic model xk+1=f(sk) and kalman filter.

– 4. evaluate probability p(zk+1|xk+1) of observed data zk+1 given state xk

– 5. use bayes rule to get p(xk+1|zk+1)

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CONDENSATION algorithm

Figure from book Isard, Blake: Active Contours

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Why does condensation tracking work?

• many slightly different hypotheses suggests that maybe we find one that fits better.

• dynamic model allows to switch between different motion models – Motion models of bouncing ball: bounce,

freefall, stop

• sampling by probability weeds out bad hypotheses

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Tracking of bouncing ball

1. Select 100 hypotheses xk with probabilities p(xk)

2. use estimated covariance P() to create state samples sk

3. define a situation switching model

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Tracking of bouncing ball

• If in STOP situation: y'=0• If in BOUNCE: x'=-0.7x', also add some random

y' motion, y'=y'+r.• If in FREEFALL: use freefall motion model.

y'=gΔt and x'=x'+r• then use Kalman filter for predicting ^xk

• 4. estimate hypothesis goodness by 1/||Hxk – zk||2

• p(xk) is estimated from the goodness by normalization.

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Example of sampling effects

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Kalman filter failures fixed

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Comparison Kalman vs condensation

• Kalman: – assumes Gaussian motion model.

– Easy to parametrize.

– Fast.

• Condensation:– can track objects with non-gaussian motion.

– very good for multi-modal motion models

– simple algorithm

– reasonably fast