Principal Axis-Based Correspon-dence between Multiple Cameras

for People Tracking

Dongwook Seoseodonguk@islab.ulsan.ac.kr

2012.04.07

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Overview

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Detection of principal axes in a single cameraMotion segmentation and object classification

Using the vertical projection histogram to distinguish people from vehicles

1, , 1,height

yh x I x y x width

- I(x,y): binary image- height, width: the height and width of motion region

The spread of a vertical projection histogram

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1

1

1width

xwidth

x

h x h xSpread

h x

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Detection of Principal Axes

2argmin ,i ilL median D X l

Principal axis of an isolated personUsing the Least Median of Squares to determine the princi-pal axis of an isolated person

- : the perpendicular distance between the ith foreground pixel and axis

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Detection of Principal Axes(Cont.)Principal axes of people in group

(a) input image

(b) Detected foreground region

(c) Vertical projection histogram

(d) segmented individuals

(e) Principal axes

 

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Detection of Principal Axes(Cont.)Principal axes of people under occlusion

Using the color template-based method to segment people

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i i

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M X t M X t I X if X

P M X t if XP M X

P M X t if X

F

FF

- : color model of object i consist of a color variable - : the rgb color of each pixel X of object i- : the likelihood of object i being observed at pixel X

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TrackingThe construction of correspondence relationships between “tracked objects” in previous frames and “detected objects” in the current frame

To track people using Kalman filter: the state of a person

: the position of a person in the image plane: the velocity of a person

Using “ground-point” on the image plane for the position of individual

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Correspondence between multiple camerasHomography recovery

A homography is a 3 by 3 matrix H.

Consider a point in one image and in another image

11 12 13

21 22 23

31 32 1

h h hh h hh h

H

'11 12 13

'21 22 23

31 321 1 1

i i

i i

x h h h xy h h h y

h h

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Correspondence between multiple cameras(Cont.)

Geometrical relationship and correspondence likeli-hood

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Correspondence between multiple cameras(Cont.)

The function of correspondence likelihood

1/2 1

1/2 1

, | |

1| 2 exp21| 2 exp2

i j i ji i ijs k s ks k sk

Ti ji i i ji i i jis ks s s ks s s ks

Ti ij j j ij j j ijk sk k k sk k k sk

L L p X Q p X Q

p X Q X Q X Q

p X Q X Q X Q

- : covariance matrixes (diagonal matrix-)- : covariance matrixes (diagonal matrix-)

The correspondence distance () for principal axis pairs

1

1

,

i Tij i ji i jisk s ks s ks

j Tj ij j ijk sk k sk

i i j js k

D X Q X Q

X Q X Q

where

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Correspondence between multiple cameras(Cont.)

Correspondence between multiple camerasStep1. A list() of all possible correspondence pairs of princi-pal axes is created.Step2. For each pair in the pair list , it is checked whether pair satisfies the constraint

: Threshold to classify true or false correspondence pairsStep3. To find all possible pairing modes

, k: index of a paring mode Step4. The minimum sum of correspondence distance

All principal axis pairs in pair mode are the matched one.Step5. The pairs in pair set are labeled.

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ExperimentsResults on NLPR Database

Tracking and correspondence of multiple people with two cameras

# 3286

# 3297

# 3380

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Experiments(Cont.)Results on PETS2001 Database

Tracking and correspondence of multiple people with three cameras

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Experiments(Cont.)Tracking and correspondence

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Experiments(Cont.)Comparison

(a) Trajectory acquired using this paper and true data. E=3.2(b) Centroid trajectory and true data. E=5.8

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Experiments(Cont.)Comparison

- The white ones are acquired using this paper, and the black ones are centroid trajectories.(a) Trajectories in view 1.(b) Trajectories in view 2.

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ConclusionsFor matching people across multiple cameras

Using principal axis-based methodCamera calibration is not needed and there is less sensitivity to errors in motion detection.

Future workApplying this algorithms for non-planar ground surfaces

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Thank you!!!