Holography

1
The Properties of Images and Imaging
Devices Group II of the Imaging Chain
2
Think of an image mathematically.
A simple black white image is a volume of
information! Two dimensions are spatial
dimensions (cm for example) The other dimension
is lightness/darkness
y
gray level
y
x
x
3
Three dimensional graphs are hard to understand.
y
gray level
y
x
x
4
Contour Plot Another way to represent 3
dimensional information
y
x
Lines are regions of constant gray level
5
The 3D graph and the contour plot are not used
much in imaging science. Other graphical
representations are more often used. One that is
commonly used is the "Histogram"
6
The Histogram A statistical way of looking at an
image
Step 1 Sample the image Divide it up into
"pixels"
7
Step 2 Look at the gray value of each "pixel"
Gray Scale
R 1 is white R 0 is black
Gray Value R 0.653
8
Step 3 Take the gray pixels out of the image.
We have cut the image into lots of pieces, called
"pixels". We measure the gray value, R, for each
patch.
9
Step 4 Sort the pixels from darkest to
lightest.
There are many pixels at this gray level.
Only a few at these gray levels.
10
Each pixel in the image has its place in the
stacks of rearranged pixels.
11
Step 5 Form a graph to represent the sorted
pixels.
Number of pixels at a given R
R
Each pixel in the image has its place in the
stacks of rearranged pixels.
12
If you use very small pixels, the graph becomes
sharper.
This is called the image Histogram.
13
The Image Histogram Has Many Uses Use 1 A
way to describe Properties of an Image
14
The Image Histogram Has Many Uses Use 1 A way
to describe Image "Brightness"
Average R 0.2
Average R 0.47
Average R 0.78
15
Range 1
Same Average R0.47 Different Ranges
Range 0.7
Range 0.2
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Vary Both Brightness AND Contrast A graph of
graphs!!
C o n t r a s t
Contrast Range of R
Brightness
Brightness (Average R)
17
A Summary of Brightness Contrast 1. These are
properties of the image. 2. The Histogram is a
way of quantifying Brightness and Contrast.
18
The Image Histogram Has Many Uses Use 2 A way
to describe Imaging Devices.
19
The Image Histogram Has Many Uses Use 2 A way
to describe Imaging Devices.
For example, a camera
Original
Photo-copy
Average R 0.2
Average R 0.78
20
Imaging Devices Change Brightness and Contrast
The image you want to make
The image you have
Input
Output
An Imaging Device
Camera, scanner, transmission line, computer,
display monitor, printer, etc. Anything in Group
II of the Imaging Chain
21
Example Adobe Photoshop Program
The image you want to make
The image you have
Input
Output
An Imaging Device
22
Think of the imaging device as something that
changes the histogram.
An Imaging Device
Input
Output
The image you have
The image you want to make
23
The Imaging Device is described by the way it
transforms gray levels in histograms.
An Imaging Device
Input
Output
Original gray levels, Ro
Copy gray levels Rc.
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This graph is called the Tone Transfer Function
(TTF). The TTF is a characteristic of the Imaging
Device.
Different shape curves will produce output
different histograms.
25
How to measure a TTF
An Imaging Device
Input
Output
Original gray levels, Ro
Copy gray levels Rc.
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How to measure a TTF
Use an image with a very simple histogram. A gray
scale has the same number of pixels at each gray
level.
An Imaging Device
Ro
Ro
Input
Output
Original
Compare the output values, Rc, versus the input
values, Ro.
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How to measure a TTF
Pair up the input values, Rc, with the output
values, Ro.
Output
Original
Plot the output values, Rc, versus the input
values, Ro.
The graph is the TTF of the device.
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Device Property 1 Location of the TTF Curve
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Property 1 Location of the TTF Curve
Device 1
Device 2
Device 1
Device 3
Device 2
Device 3
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Location Controls the brightness of the copy
image.
Device 1
Device 2
Device 1
Device 3
Device 2
Device 3
Device 1 is most sensitive to brightness. It
makes the copy brighter. Device 3 is least
sensitive to brightness. It makes the copy
darker.
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A Useful Metric of Device Sensitivity
Device
Locate the middle gray for the output copy Rc
0.5
1
Devices 1 2 3
Rc
0.5
0
1
0
Ro
32
A Useful Metric of Device Sensitivity
Device
Next, locate the corresponding input values Ros
1
Devices 1 2 3
Rc
0.5
0
1
0
0.3
0.5
0.68
Ro
33
A Useful Metric of Device Sensitivity
Device
It is useful to define an index of "sensitivity"
S.
1
S
1
2Ros
Devices 1 2 3
S11.67
S21.00
S30.74
Rc
0.5
0
1
0
0.3
0.5
0.68
Ro
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Sensitivity (location) Controls the brightness
of the copy image.
Device 1
S11.67
3
2
Device 1
S21.00
Device 2
S30.74
Device 3
S gt 1 increases brightness. S 1 gives the same
brightness. S lt 1 decreases brightness.
35
Device Property 2 Slope of the TTF Curve
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Property 2 Slope of the TTF Curve
Device 1
1
Device 1
Device 2
Rc
Device 3
0
1
Ro
Device 3
0
37
A Useful Metric of Device Slope
Device
Locate the middle gray for the output copy Rc
0.5
1
Devices TTF
Rc
0.5
0
1
0
Ro
38
A Useful Metric of Device Slope
Device
Next, Draw a straight line through the point so
that it matches the slope at that point.
1
Devices TTF
Rc
0.5
0
1
0
Ro
39
A Useful Metric of Device Slope
Device
Locate the points where the straight line crosses
Rc0 and Rc1. Find the corresponding values of
Ro. Call these Ro0 and Ro1.
1
Devices TTF
Ro0 0.40 Ro1 0.60
Rc
1
0.5
Slope
Ro1 - Ro0
1
Slope
0.6 - 0.4
0
1
Slope 5.0
0
0.4
0.6
Ro
40
A Useful Metric of Device Slope
Device
Call this slope the "Contrast" of the
device, symbolized by Greek letter "gamma", g.
1
Devices TTF
Slope 5.0
Or,
g 5.0
Rc
0.5
g 5.0
0
1
0
Ro
41
1
Device 1
Rc
Device 1
Device 3
0
1
Ro
0
Device 2
Device 3
g gt 1 increases brightness. g 1 gives the same
brightness. g lt 1 decreases brightness.
42
A Summary of the Device TTF
Device
S1 and g 1 Output copy Input Copy Sgt1
Output copy is brighter Slt1 Output copy is
darker g gt 1 Output copy has higher
contrast g lt 1 Output copy has less contrast
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A Summary of the Device TTF
Slt1 ggt1
Sgt1 ggt1
S1 ggt1
Sgt1 g1
Slt1 g1
S1 glt1
Sgt1 glt1
Slt1 glt1
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A Summary of
Sensitivity Gamma
Sgt1 ggt1
S1 ggt1
Slt1 ggt1
Sgt1 g1
S1 glt1
Sgt1 glt1
Slt1 glt1
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A Cautious Note There are many ways to define
indices of sensitivity and slope. There are many
other names used instead of sensitivity and
slope. For example, Adobe Photoshop
uses, Brightness -100 to 0 to 100 (instead
of sensitivity lt 1 to 1 to gt 1)
Sensitivity
Gamma
For example, Adobe Photoshop uses, Contrast -100
to 0 to 100 (instead of gamma lt 1 to 1 to gt
1) In general, however, the TTF of most imaging
devices are characterized by some index of
location (sensitivity, brightness, etc.) and by
some index of slope (gamma, contrast, etc.)
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Properties of the Image (I) The Histogram A.
Brightness (average R) B. Contrast (Range of
R) (II) Others to be discussed
later (sharpness, granularity, etc.) Note
Don't confuse the terms "brightness" and
"contrast" as used here for the terms used by
Adobe and others for location and slope of the
TTF. We are using the terms as properties of
the image, not properties of the imaging device.
47
Properties of the Imaging Device (I) The TTF
(Transforms the histogram) A. Sensitivity B.
Gamma (II) Others to be discussed
later (sharpening/blurring, noise, etc.)
Note All imaging devices are described by the
TTF. Most devices are given an index of location
defined from the TTF. Most devices are given an
index of slope defined from the TTF. However
Different organizations use different definitions
for location and slope. They also use different
names for the TTF, the location, and the
slope. Also, terms like "sensitivity", "gamma",
"brightness", and "contrast" are in common use,
but there is no universal agreement about how
these terms should be applied. Thus, all four
are used by different groups to mean many
different things, both as device properties and
as image properties. Be cautious and ask for
clarification if you are not sure what is meant.