The document proposes a perceptual mixture-of-Gaussians approach to background subtraction that adapts dynamically based on principles of human visual perception. It models the relationship between detectable foreground pixels and background pixels based on Weber's law of just-noticeable differences. This results in piecewise linear relationships and different adaptation speeds for scotopic and photopic vision. An evaluation of 50 test sequences shows the proposed approach achieves more realistic background value prediction, higher stability across scenarios, and superior detection quality compared to other statistical methods.

1. Information Technology
Robust Background Subtraction Based on
Perceptual Mixture-of-Gaussians with
Dynamic Adaptation Speed
Mahfuzul Haque and Manzur Murshed

2. Agenda
 Background Subtraction
 Statistical Background Subtraction
 Perception Inspired Background Subtraction
 Dynamic Adaptation Speed
 Experiments
 Summary
 Q&A
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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3. Background Subtraction
Input
Output
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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4. Background Subtraction: Challenges
Basic Background Subtraction (e.g., BBS)
-
Current frame
Challenges
=
Background
Foreground Blob
Dynamic Background Subtraction(e.g., MOG)
Background




Illumination variation
Local background motion
Camera displacement
Shadow and reflection
Model
Current frame
Foreground Blob
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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5. Statistical Background Subtraction
ω1
ω2
ω3
σ12
σ22
σ32
µ1
µ2
µ3
road
car
shadow
65%
20%
Statistical Approaches
x
x
P(x)
Our Hypothesis (Perception Inspired)
x
BBS: x = c
MOG: x = c1σ
μ
15%
x
x = c2b
P(x)
Te b
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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6. Perception Inspired Background Subtraction
x = c2 b
Current
Frame
Detection with
Low x
Detection with
High x
x
x
P(x)
b
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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7. Weber’s Law
How human visual system perceives noticeable intensity
deviation from the background?
Ernst Weber, an experimental psychologist in the 19th
century, observed that the just-noticeable increment ΔI
is linearly proportional to the background intensity I.
ΔI = c2I
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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8. Weber’s Law
Ernst Weber, an experimental psychologist in the
19th century, observed that the just-noticeable
increment ΔI is linearly proportional to the
background intensity I.
?
x
x
ΔI = c2I
x
x = c2 b
P(x)
b
Te
b
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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9. Perceptual tolerance of HVS
What is the perceptual tolerance level in distinguishing
distorted intensity measures?
p dB
Method 1
Reference
q dB
Method 2
Image
Distorted
Images
|p – q| < 0.5 dB
Not perceivable
by human visual
system
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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10. Our Problem: c2 = ?
x = c2 b
x
x
P(x)
Weber’s Law
x = c2b
Perceptual Threshold, TP (0.5 dB)
 255
20 log10 
 bx



  20 log  255
10  b  x




 1
 2TP

b
Te
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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11. Linear Relationship
x
b
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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12. Rod and Cone
 Rods and Cones are two different types of
photoreceptor cells in the retina of human eye
 Rods
– Operate in less intense light
– Responsible for scotopic vision (night vision)
 Cones
– Operate in relatively bright light
– Responsible for photopic (color vision)
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13. Error Sensitivity in Darker Background
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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14. Piece-wise Liner Relationship
Scotopic Vision (R)
Photopic Vision (C)
Te
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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15. Dynamic Adaptation Speed
•Sleeping person problem
•Walking person problem
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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16. Dynamic Adaptation Speed
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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17. Dynamic Adaptation Speed
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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18. Dynamic Adaptation Speed
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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19. Experiments
Test Sequences
 Total 50 test sequences from 8 different sources
 Scenario distribution





Indoor
Outdoor
Multimodal
Shadow and Reflection
Low background-foreground contrast
False Classification
Evaluation
 Qualitative and quantitative comparison:
 MOG (S&G) (TPAMI, 2000)
False Positive (FP)
False Negative (FN)
 MOG (Lee) (TPAMI, 2005)
 ViBe (TIP, 2011)
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20. Test Sequences
PETS (9) Wallflower (7) UCF (7)
IBM (11)
CAVIAR (7)
Te
VSSN06 (7)
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
Other (2)
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21. Experiments
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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22. Experiments
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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23. Experiments
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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24. First
Frame
Test
Frame
Ground
Truth
MOG
(S&G)
MOG
(Lee)
ViBe
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
Proposed
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25. Summary
 Realistic background value prediction: high model agility
and superior detection quality at fast learning rate.
 No context related information: high stability across
changing scenarios.
 Perception based detection threshold: superior detection
quality in terms of shadow, noise, and reflection.
 Perceptual model similarity: optimal number of models
throughout the system life cycle.
 Parameter-less background subtraction: ideal for realtime video analytics.
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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26. Q&A
Perceptual Mixture-of-Gaussians with Dynamic Adaptation Speed
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