Digital Image Fundamentals
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Human visual system
A simple image model
Sampling and quantization
Color models and Color imaging
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Human Visual System
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Brightness adaptation
Brightness discrimination
Weber ratio
Mach band pattern
Simultaneous contrast
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Human Visual System
 Elements of visual perception
The amount of light entering the
eye is controlled by the pupil, which
dilates and contracts accordingly.
The cornea and lens, whose shape
is adjusted by the ciliary body,
focus the light on the retina, where
receptors convert it into nerve
signals that pass to the brain.
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Human Visual System
 Elements of visual perception
 Cones
 6 – 7 million in each eye
 Photopic or bright-light vision
 Highly sensitive to color
 Rods
 75 – 150 million
 Not involved in color vision
 Sensitive to low level of illumination (scotopic or dim-light
vision)
 An object appears brightly colored in daylight will be seen
colorless in moonlight (why)
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Human Visual System
Image formation in the eye
 Distance between center of lens and retina
(focal length) vary between 14-17 mm.
 Image length h = 17(mm) x (15/100)
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Human Visual System
Human simultaneous luminance vision range
(5 orders of magnitude)
log (cd/m2)
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Human Visual System
Brightness adaptation
HVS can adapt to light intensity range
on the order of 1010
Subjective brightness is a logarithmic
function of the light intensity incident
on the eye
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Human Visual System
Brightness adaptation
The lambert (symbol L) is a unit of
luminance named for Johann
Heinrich Lambert (1728 - 1777), a
German mathematician, physicist
and astronomer. A related unit of
luminance, the foot-lambert, is
used in the lighting, cinema and
flight simulation industries. The SI
unit is the candela per square
metre (cd/m²).
Source: Wikipedia
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Human Visual System
 Brightness adaptation
 The HVS cannot operate on such range (10 orders of
magnitude) simultaneously
 It accomplishes this through (brightness) adaptation
 The total intensity level the HVS can discriminate
simultaneously is rather small in comparison (about 4
orders of magnitude)
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Human Visual System
 Brightness adaptation
Sensitivity of the HVS
for the given
adaptation level
Anything below Bb will
be perceived as
indistinguishable
blacks
For a given
observation
condition, the
current sensitivity
level is call the
brightness
adaptation level
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Human Visual System
 Brightness discrimination
 Perceivable changes at a given adaptation
level
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Human Visual System
 Brightness discrimination
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Human Visual System
 Perceived brightness is not a simple function
of intensity – Mach band pattern
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Human Visual System
 Perceived brightness is not a simple function
of intensity – Simultaneous contrast
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A simple image model
Two-dimensional light-intensity
function
f(x,y) = l(x,y) r(x,y)
l(x,y) - illumination component
r(x,y) – reflectance component
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A simple image model
 l(x,y) - illumination range
log (cd/m2)
 r(x,y) – typical reflectance indixes
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black velvet (0.01)
stainless steel (0.65)
white paint (0.80)
silver plate (0.90)
snow (0.93)
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Sampling
 Digitization of the spatial coordinates, sample (x, y) at
discrete values of (0, 0), (0, 1), ….
 f(x, y) is 2-D array
 f (0,0)
 f (1,0)
f ( x, y )  
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 f ( N  1,0)
f (0,1)
f (1,1)
f ( N  1,1)
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f (0, M  1) 
f (1, M  1) 
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f ( N  1, M  1)
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Quantization
 Digitization of the light intensity function
 Each f(i,j) is called a pixel
 The magnitude of f(i,j) is represented digitally
with a fixed number of bits - quantization
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Image Sensor
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Image Acquisition
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Image Acquisition
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Sampling and Quantization
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Sampling and Quantization
 How many samples to take?
 Number of pixels (samples) in the image
 Nyquist rate
 How many gray-levels to store?
 At a pixel position (sample), number of levels of
color/intensity to be represented
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Sampling and Quantization
 How many samples to take?
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Sampling and Quantization
 How many samples to take?
 The Nyquist Rate
 Samples must be taken at a rate that is twice the
frequency of the highest frequency component to be
reconstructed.
 Under-sampling: sampling at a rate that is too
coarse, i.e., is below the Nyquist rate.
 Aliasing: artefacts that result from under-sampling.
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Sampling and Quantization
 How many gray-levels to store?
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Sampling and Quantization
 Non-uniform sampling
 Non-uniform quantization
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Basic relationships between pixels
 Neighbors
 Connectivity
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Simple intensity processing
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Color Imaging
 Light
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Color Imaging
 Visible light spectrum
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Color Imaging
 Trichromacy and human color vision
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Color Imaging
 Color image formation (acquisition)
Observer (Camera)
RGB Camera Output
Light
l ( )
Reflected Light  l ( )  i( )
Object Reflectanc e i( )
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Color Imaging
 Power spectrum of standard illuminants
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Color Imaging
 Color image formation
(acquisition)
R( x, y )   l ( )  i ( x, y,  )  FR  d
G ( x, y )   l ( )  i ( x, y,  )  FG  d
B( x, y )   l ( )  i ( x, y,  )  FB  d
Color filters
Of the sensor
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Color Imaging
 Color image formation
(acquisition)
R ( x, y )   l ( )  i ( x, y,  )  FR  d
G ( x, y )   l ( )  i ( x, y,  )  FG  d
B ( x, y )   l ( )  i ( x, y,  )  FB  d
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Color Imaging
 The RGB Color Model
 R, G, B at 3 axis ranging in [0 1] each
 Gray scale along the diagonal
 If each component is quantized into 256 levels
[0:255], the total number of different colors that
can be produced is (28)3 = 224 =16,777,216 colors.
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Color Imaging
 The RGB Color Model
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Color Imaging
 The YIQ Color Model
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Video (NTSC) standard
Y encodes luminance; I and Q encode chrominance (“color”)
Black and white TV shows only the Y channel
Backward compatibility; efficiency
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Color Imaging
 Color Models, YCbCr
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Color Imaging
 More Color Models, see e.g.,
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Color Imaging
 More Color Models, see e.g.,
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Color Imaging
 Color image representation (in RGB space)
=
Red
Green
Blue
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Color Imaging
 Color image representation (in RGB space)
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