1. Visual Perception, Image Formation, Math Concepts
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Visual Perception, Image Formation, Math Concepts

2. Visual Perception, Image Formation, Math Concepts
References
Gonzalez and Woods, “ Digital Image Processing,” 2nd Edition, Prentice Hall, 2002.
Jahne, “Digital Image Processing,” 5th Edition, Springer 2002.
Jain, “Fundamentals of Digital Image Processing,” Prentice Hall 1989
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Visual Perception, Image Formation, Math Concepts

3. Visual Perception, Image Formation, Math Concepts
Overview
Human Visual System
Visual Perception
Image Acquisition
Sampling and Quantization
Basic pixel relationships
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Visual Perception, Image Formation, Math Concepts

4. Visual Perception, Image Formation, Math Concepts
What are we looking for?
The Human Visual System is complex.
Need to find clues to “improve” image quality (from the viewpoint of the human).
Our focus is on math techniques to achieve an objective. Which techniques are most appropriate?
What is the impact of illumination?
11/20/2018
Visual Perception, Image Formation, Math Concepts

5. Cross Section of the Eye
Two kinds of receptors
Cones ~ 6 to 7 million Primarily in fovea Sensitive to color One cone per nerve end Bright light vision (photopic)
Rods ~ 75 to 100 million Several rods / nerve end General overall picture of field of view Sensitive to low levels of illumination Dim light vision (scotopic)
From [1]
11/20/2018
Visual Perception, Image Formation, Math Concepts

6. Some questions that helps Image Processing
How many sensors are needed to “see” well?
How does the eye adjust to brightness?
What is the eye’s ability to discriminate between light intensity changes?
11/20/2018
Visual Perception, Image Formation, Math Concepts

7. Cones and Rods Distribution
From [1]
Rod, cone distribution is symmetric around the center of fovea, except the blind spot.
Fovea is a circular indentation that is about 1.5mm diameter.
Most sensing elements are rectangular, so to draw lessons treat the fovea to be 1.5 mm x 1.5 mm.
Cone density is about 150K per mm2. Cones in fovea: 150K*1.5*1.5=337.5K.
Modern 5mm x 5mm imaging sensors accommodate 300K detectors.
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Visual Perception, Image Formation, Math Concepts

8. Visual Perception, Image Formation, Math Concepts
From [1]
Eye lens is flexible – the focal length (distance between lens and the retina) varies from 17 to 14 mm.
From similarity of triangles (h=height of image):
h/17 = 15/100; h = 2.55 mm d f h x
x = f h / d
Object Pin-hole Image
11/20/2018
Visual Perception, Image Formation, Math Concepts

9. Brightness Adaptation
HVS adapts to a 1010 range of light intensity.
Subjective brightness (intensity as perceived by HVS) is log of the light incident on the eye.
Gradual transition from Scotopic to Photopic.
HVS does not operate over the entire range simultaneously. Small variations about an operating point.
From [1]
11/20/2018
Visual Perception, Image Formation, Math Concepts

10. Visual Perception, Image Formation, Math Concepts
Discrimination
If ΔI is small, no change perceived.
ΔIc/I is Weber ratio; where ΔIc is the change that is detected 50% of the time.
From [1]
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Visual Perception, Image Formation, Math Concepts

11. Visual Perception, Image Formation, Math Concepts
Mach bands
From [1]
11/20/2018
Visual Perception, Image Formation, Math Concepts

12. Another example of contrast
From [1]
11/20/2018
Visual Perception, Image Formation, Math Concepts

13. Electromagnetic Spectrum
From [1]
C = λν = 3 * 1010 cm/second
The wavelength of the EM wave used to “see” must be smaller than the object size being detected.
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Visual Perception, Image Formation, Math Concepts

14. Visual Perception, Image Formation, Math Concepts
Measures of light
Gray level is used to define monochromatic intensity. Black to white.
Radiance: Light source measured in watts
Luminance: Perceived amount of energy from light source
Brightness: Subjective measure
For IR: Radiance maybe high, but Luminance is zero.
11/20/2018
Visual Perception, Image Formation, Math Concepts

15. Different types of Sensors
Filters are used to reduce the range of colors, e.g. green filters will only pass green incident energy.
Used in Aerial sensors like FLIRS
From [1]
11/20/2018
Visual Perception, Image Formation, Math Concepts

16. Linear and Circular sensors
From [1]
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Visual Perception, Image Formation, Math Concepts

17. Visual Perception, Image Formation, Math Concepts
Sampling Rate?
What is a good sampling rate?
High rate will require more storage and communication cost
Low rate – we may miss something
Sampling rate should enable adequate reconstruction
How to interpolate between samples – this figures into the sampling rate selection
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Visual Perception, Image Formation, Math Concepts

18. Visual Perception, Image Formation, Math Concepts
Reconstruction?
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Visual Perception, Image Formation, Math Concepts

19. Visual Perception, Image Formation, Math Concepts
Image Acquisition
Quantized
From [1]
Sampled
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Visual Perception, Image Formation, Math Concepts

20. Image Formulation Model
An image is represented as f (x, y, s)
f is the value at the spatial co-ordinate x, y using a spectral frequency s (suppressed in the further analysis)
0 < f (x, y) < ∞
f (x, y) = illumination * reflectance
= i (x, y) * r (x, y)
0 < i (x, y) < ∞
0 < r (x, y) < 1 : 0 = absorption; 1=total reflectance
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Visual Perception, Image Formation, Math Concepts

21. Visual Perception, Image Formation, Math Concepts
Typical values
i (x, y):
Sun produces 90K lumens/sq.m. on a sunny day, and 10K on a cloudy day.
Full moon yields about 0.1 lumens/sq.m
Commercial building 1K lumens/sq.m.
r (x, y):
.01 for black velvet
0.65 for stainless steel
0.85 for flat white wall paint
0.91 for silver plated metal
0.93 for snow
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Visual Perception, Image Formation, Math Concepts

22. Steps in Digitizing an Image
From [1]
Quantization
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Visual Perception, Image Formation, Math Concepts

23. Visual Perception, Image Formation, Math Concepts
Quantization
From [1]
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Visual Perception, Image Formation, Math Concepts

24. Representing Digital Images
From [1]
f(0,0) f(0,1) f(0, N-1)
f(1,0) f(1,1) f(1, N-1)
f(x,y) =
f(M,0) f(M,1) f(M, N-1)
f(i,j) = integer
0 <= f(i,j) <= 2k
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Visual Perception, Image Formation, Math Concepts

25. Visual Perception, Image Formation, Math Concepts
Impact of sub sampling (zoom)
From [1]
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Visual Perception, Image Formation, Math Concepts

26. Impact of reduced gray levels
From [1]
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Visual Perception, Image Formation, Math Concepts

27. Zooming using interpolation
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Visual Perception, Image Formation, Math Concepts

28. Basic Relationships between pixels1
Neighborhoods of pixel p
N4(p) = 4 nearest neighbors
ND(p) = 4 diagonal neighbors
N8(p) = 8-neighbors of p
Connectivity
4, 8 and m connectivity
Adjacency: if p, q are connected they are adjacent
Distance metrics
Euclidean, city-block, chess board 1
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Visual Perception, Image Formation, Math Concepts

29. Visual Perception, Image Formation, Math Concepts
Adjacency
Neighboring pixels are connected only if their value is similar, i.e. belongs to a set V
If p and q have values in V, and
4-adjacent: q is in the set N4(p)
8-adjacent: q is in the set N8(p)
m-adjacent:
q is in the set N4(p) or
q is in the set ND(p) and {N4(p) AND N4(q) = null (i.e. no pixels in V)}
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Visual Perception, Image Formation, Math Concepts

30. Visual Perception, Image Formation, Math Concepts
M-adjacency
m-adjacent:
1. q is in the set N4(p), or
2. q is in the set ND(p) and {N4(p) AND N4(q) = null (i.e. no pixels in V)} X
[1]
11/20/2018
Visual Perception, Image Formation, Math Concepts