Event Understanding of Human-Object Interaction: Object Movement Detection via Stable Changes - Intelligent Video Event Analysis and Understanding - page 199

3.1 Region-Level Background Subtraction for Object Movement

Detection

When the method detects changes caused by object movements, the method needs to
be robust for changes caused without object movements (e.g. shadows, background
clutters). In this work, we employ a region-level background subtraction method by
graph cuts (this method is mainly based on Shimosaka's method [11]).
Background subtraction by using only single pixels fails when background color
is similar to foreground object's and is weak for noises. To address these problems,
background subtraction methods based on region optimization via graph cuts [11,
12] are proposed. The background subtraction method via graph cut chooses the
label x r of each pixel ( x r = 0 if background , x r = 1 if foreground) with optimizing

energy function mentioned below:

)= r ∈ I D r ( x r )+ λ

∑

E ( X S rs ( x r , x s ) (1)

( r , s ) ∈ ε

where I is the input image and r is the target pixel, is the set of adjacent pixel

pairs. D r is the data term, encoding the cost when the label of r is x r ,and S rs is
the smoothing term, encoding the cost when the adjacent pixels r

ε

,

s have different

labels. The parameter controls the influence of the smoothing term. The energy in

eq.(1) is minimized by the min-cut / max-flow algorithm [13].
The data term is defined as follows:

λ

−

ln p B ( i r )( x r = 0 )

D r ( x r )= (2)

− ln p F ( i r )( x r = 1 )

where i r is RGB vector on pixel r , p B ( is

the foreground likelihood. We employ robust a color model for shadow changes
[14] as the background likelihood. This color model divides RGB difference into
the brightness difference and the chromatic difference. The elements of this color
model are defined as follows:

i r ) is the background likelihood, p F ( i r )

i r i r
|

α r = ,

i r |

2

(3)

r i r

= | − α |,

c r i r

where i r is the RGB vector of pixel r on the background image, α r is the ratio of the

brightness of the input image to the one of the background image on the pixel r , c r
is the chromatic difference.
The background likelihood p B (

i r ) is calculated as follows[11]:

0

v r − 1 v r − 1

( < τ l or > τ h )

η r η r

p B ( i r )= (4)

2
r

2
r N ( c r | 0 , α ξ ) ( ot herwise )

r r

where v r is α r − 1, N ( c r | 0 , α ξ ) is Gaussian distribution which mean is 0 and which

2
r

2
r ,

variance is α ξ η r is the standard deviation of c r , ξ r is the standard deviation of

v r ,and τ l and τ r are the fixed thresholds.