Counting Crowded Moving Objects Vincent Rabaud and Serge Belongie Department of Computer Science and Engineering University of California, San Diego {vrabaud,sjb}@cs.ucsd.edu

Counting Crowded Moving Objects

Vincent Rabaud and Serge BelongieDepartment of Computer Science and Engineering

University of California, San Diego{vrabaud,sjb}@cs.ucsd.edu

Presentation by: Yaron KoralIDC, Herzlia, ISRAEL

AGENDA

• Motivation• Challenges• Algorithm• Experimental Results

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AGENDA


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Motivation

• Counting crowds of people• Counting herds of animals• Counting migrating cells

• Everything goes as long as the crowdis homogeneous!!

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AGENDA


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Challenges

• The problem of occlusion– Inter-object– Self occlusion

• Large number of independent motions– Dozens of erratically moving objects– Require more than two successive

frames

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Surveillance camera viewing a crowd from a distant viewpoint, but zoomed in, such that the effects of perspective are minimized.

AGENDA


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Algorithm Highlights

• Feature Tracking with KLT• Increased Efficiency• Feature Re-Spawning• Trajectory Conditioning• Trajectory Clustering

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Harris Corner Detector – What are Good Features? C.Harris, M.Stephens. “A Combined Corner and Edge Detector”. 1988

• We should easily recognize a corner by looking through a small window

• Shifting a window in any direction should give a large change in intensity

Harris Detector: Basic Idea

“flat” region:no change in all directions

“edge”:no change along

the edge direction

“corner”:significant

change in all directions

Harris Detector: Mathematics

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,

( , ) ( , ) ( , ) ( , )x y

E u v w x y I x u y v I x y

Change of intensity for shift in [u,v] direction:

IntensityShifted intensity

Window function

orWindow function w(x,y)=

Gaussian1 in window, 0 outside


2

,

( , ) ( , ) ( , ) ( , )x y

E u v w x y I x u y v I x y

yx vIuIyxIvyuxI ,,

v

uMvu

v

u

III

IIIyxwvu

v

uyxIyxIyxwvuE

yyx

yxx

yxyx

2

2

,

2

),(

,,,,

For small [u,v]:

We have:


( , ) ,u

E u v u v Mv

For small shifts [u,v] we have a bilinear approximation:

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2,

( , ) x x y

x y x y y

I I IM w x y

I I I

where M is a 22 matrix computed from image derivatives:

Harris Detector: MathematicsDenotes by ei the ith eigen-vactor of

M whose eigen-value is i:

Conclusions:

0 iiTi M ee

max1, ,maxarg e vuEvu

maxmax eE


( , ) ,u

E u v u v Mv

Intensity change in shifting window: eigenvalue analysis

1, 2 – eigenvalues of M

direction of the slowest change

direction of the fastest change

)max(-1/2

)min(-1/2

Ellipse E(u,v) = const


1

2

“Corner”1 and 2 are large,

1 ~ 2;

E increases in all directions

1 and 2 are small;

E is almost constant in all directions

“Edge” 1 >> 2

“Edge” 2 >> 1

“Flat” region

Classification of image points

using eigenvalues of M:

Sum of Squared Differences – Tracking FeaturesTracking Features

• SSD is optimal in the sense of ML when1. Constant brightness assumption2. i.i.d. additive Gaussian noise

Ayx

tyxtvyuxvu,

2,,1,,,SSD RI

Exhaustive Search

• Loop over all parameter space• No realistic in most cases

– Computationally expensive• E.g. to search 100X100 image in 1000X1000

image using only translation~1010 operations!

– Explodes with number of parameters– Precision limited to step size

The Problem

Find (u,v) that minimizes the SSD

over region A.

Assume that (u,v) are constant over all A

Ayx

yxvyuxvuSSD,

2,,, RI

Iterative Solution

• Lucas Kanade (1981)– Use Taylor expansion of I (the optical

flow equation)

– Find

Ayx

tyxvuvu

vuvuSSD,

2

,,min,min III

0 tyx vu III

Feature Tracking with KLT(We’re back to crowd counting…)• KLT is a feature tracking algorithm• Driving Principle:

– Determine the motion parameter oflocal window W from image I to consecutive image J

– The center of the window defines the tracked feature

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Feature Tracking with KLT

• Given a window W– the affine motion parameters A and d

are chosen to minimize the dissimilarity

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Feature Tracking with KLT

• It is assumed that only d matters between 2 frames. Therefore a variation of SSD is used

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• A window is accepted as a candidate feature if in the center of the window, both eigenvalues exceed a predefined threshold t

min(min(λλ11,, λ λ22) > t) > t



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Increased Efficiency #1• Associating only one window with

each feature– Giving a uniform weight function that

depends on 1/(window area |w|)– Determining quality by comparing:

• Computation of different Z matrices is accelerated by “integral image”[1]

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|| w

z

[1] Viola & Jones 2004

Increased Efficiency #2

• Run on sample training frames first– Determine parameters that lead to the

optimal windows sizes– Reduces to less than 5% of the possible

parameter set– All objects are from the same class

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Feature Re-Spawning

• Along time, KLT looses track:– Inter-object occlusion– Self occlusion– Exit from picture– Appearance change due to perspective

and articulation

• KLT recreates features all the time– Computationally intensive– Weak features are renewed

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Feature Re-Spawning

• Re-Spawn features only at specific locations in space and time

• Propagate them forward and backward in time– Find the biggest “holes”– Re-spawn features

in frame with theweighted average oftimes

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Trajectory Conditioning

• KLT tracker gives a set of trajectories with poor homogeneity– Don’t begin and end at the same times– Occlusions can result in trajectory

fragmentation– Feature can lose its strength resulting in

less precise tracks

• Solution: condition the data– Spatially and temporally

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Trajectory Conditioning

• Each trajectory is influenced by its spatial neighbors

• Apply a box to each raw trajectory• Follow all neighbor trajectories from

the time the trajectory started

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Trajectory Clustering

• Determine number of object at time tt by clustering trajectories

• Since at time tt objects may be close, focus attention on a time interval (half-width of 200 frames)

• Build connectivity graph– At each time step, the present features form the

nodes of a connectivity graph G – Edges indicate possible membership to a common

object.

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Trajectory Clustering• Connectivity Graph

– Bounding Box: as small as possible, able to contain every possible instance of the object

– If two features do not stay in a certain box, they do not belong to the same object.

– The 3 parameters of this box are learned from training data.

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Articulation factor

Trajectory Clustering• Rigid parts merging

– Features share similar movement during whole life span, belong to a rigid part of an objectrigid part of an object, and consequently to a common objectcommon object

– RANSAC is applied to sets of trajectories • Within time window • Connected in graph G

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Trajectory Clustering

• Agglomerative Clustering– At each iteration, the two closest sets are

considered – If all features are linked to each other in the

connectivity graph, they are merged together.

– Otherwise, the next closest sets are considered

– Proceed until all possible pairs are analyzed

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AGENDA


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Experimental results

• Datasets– USC: elevated view of a crowd

consisting of zero to twelve persons– LIBRARY: elevated view of a crowd of

twenty to fifty persons– CELLS: red blood cell dataset consisting

of fifty to hundred blood cells

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Estimated

Ground Truth


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Conclusion

• A new way for segmenting motions generated by multiple objects in crowd

• Enhancements to KLT tracker• Conditioning and Clustering

techniques

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Thank You!Thank You!

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Documents

Counting Crowded Moving Objects Vincent Rabaud and Serge Belongie Department of Computer Science and Engineering University of California, San Diego {vrabaud,sjb}@cs.ucsd.edu