1. © University of Wisconsin, CS559 Spring 2002
Last Time
Course introduction
Assignment 1 (not graded, but necessary)
View is part of Project 1
Image and film basics
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2. © University of Wisconsin, CS559 Spring 2002
Today
More on Digital Images
Introduction to color
Homework 1
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3. © University of Wisconsin, CS559 Spring 2002
Digital Images
Computers work with discrete pieces of information
How do we digitize a continuous image?
Break the continuous space into small areas, pixels
Use a single value for each pixel - the pixel value (no color, yet)
No longer continuous in space or intensity
This process is fraught with danger, as we shall see
Continuous
Discrete
Pixels: Picture Elements
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Digital Cameras
CCD stores a charge each time a photon hits it
“Bins” have discrete area, one per pixel
Spatially discrete
Camera “reads” the charges out of the bins at some frequency
Convert charges to discrete value
Discrete in intensity
Store values in memory - the image
Still have issues of motion blur, depth of field, dynamic range, etc
Light in
Lens
CCD
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5. Alternative Imaging Methods
We obviously don’t have to use a digital camera to generate a digital image
You can write the pixels directly, or use a paint program, or describe a 3D scene and have a computer render it into an image, or …
This course is all about these other methods
However, it still helps to think of any digital image as a sample of some ideal image
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6. Discretization Issues
Can only store a finite number of pixels
Resolution: Pixels per inch, or dpi (dots per inch from printers)
Storage space goes up with square of resolution
600dpi has 4× more pixels than 300dpi
Can only store a finite range of intensity values
Typically referred to as depth - number of bits per pixel
Directly related to the number of colors available
Also concerned with the minimum and maximum intensity – dynamic range
Both film and digital cameras have highly limited dynamic range
The big question is: What is enough resolution and enough depth?
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Perceptual Issues
Humans can discriminate about ½ a minute of arc
At fovea, so only in center of view, 20/20 vision
At 1m, about 0.2mm (“Dot Pitch” of monitors)
Limits the required number of pixels
Humans can discriminate about 8 bits of intensity
“Just Noticeable Difference” experiments
Limits the required depth for typical dynamic ranges
Actually, it’s 9 bits, but 8 is far more convenient
BUT, while perception can guide resolution requirements for display, when manipulating images much higher resolution may be required
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Intensity Perception
Humans are actually tuned to the ratio of intensities, not their absolute difference
So going from a 50 to 100 Watt light bulb looks the same as going from 100 to 200
So, if we only have 4 intensities, between 0 and 1, we should choose to use 0, 0.25, 0.5 and 1
Most computer graphics ignores this, giving poorer perceptible intensity resolution at low light levels, and better resolution at high light levels
It would use 0, 0.33, 0.66, and 1
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Dynamic Range
Image depth refers to the number of bits available, but not how those bits map onto intensities
We can use those bits to represent a large range at low resolution, or a small range at high resolution
Common display devices can only show a limited dynamic range, so typically we fix the range at that of the display device and choose high resolution
Low range, high res
High range, low res
All possible
intensities
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More Dynamic Range
Real scenes have very high and very low intensities
Humans can see contrast at very low and very high light levels
Can’t see all levels all the time – use adaptation to adjust
Still, high range even at one adaptation level
Film has low dynamic range ~ 100:1
Monitors are even worse
Many ways to deal with the problem, but no great solution
Way beyond the scope of this course
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Display on a Monitor
When images are created, a linear mapping between pixels and intensity is assumed
For example, if you double the pixel value, the displayed intensity should double
Monitors, however, do not work that way
For analog monitors, the pixel value is converted to a voltage
The voltage is used to control the intensity of the monitor pixels
But the voltage to display intensity is not linear
Same problem with digital monitors, they just do the pixel to intensity conversion differently
The outcome: A linear intensity scale in memory does not look linear on a monitor!
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Gamma Control
The mapping from voltage to display is usually an exponential function:
To correct the problem, we pass the pixel values through a gamma function before converting them to the monitor
This process is called gamma correction
The parameter, , is controlled by the user
It should be matched to a particular monitor
Typical values are between 2.2 and 2.5
The mapping can be done in hardware or software
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Some Facts About Color
So far we have only discussed intensities, so called achromatic light (black and white)
Accurate color reproduction is commercially valuable - e.g. Kodak yellow, painting a house
Of the order of 10 color names are widely recognized by English speakers - other languages have fewer/more, but not much more
Color reproduction problems have been increased by the prevalence of digital imaging - eg. digital libraries of art
Color consistency is also important in user interfaces, eg: what you see on the monitor should match the printed version
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Light and Color
The frequency of light determines its “color”
Frequency, wavelength, energy all related
Describe incoming light by a spectrum
Intensity of light at each frequency
Just like a graph of intensity vs. frequency
We care about wavelengths in the visible spectrum: between the infra-red (700nm) and the ultra-violet (400nm)
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White
# Photons
Wavelength (nm)
400
500
600
700
White
Less Intense White (grey)
Note that color and intensity are technically two different things
However, in common usage we use color to refer to both
For example, dark red vs. light red
You will have to use context to extract the meaning
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Helium Neon Laser
# Photons
Wavelength (nm)
400
500
600
700
Lasers emit light at a single wavelength, hence they appear colored in a very “pure” way
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Normal Daylight
# Photons
Wavelength (nm)
400
500
600
700
The sky is blue, so what should this look like?
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Normal Daylight
# Photons
Wavelength (nm)
400
500
600
700
Note the hump at short wavelengths - the sky is blue
Other bumps came from solar emission spectra and atmospheric adsorption
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Tungsten Lightbulb
# Photons
Wavelength (nm)
400
500
600
700
Most light sources are not anywhere near white
It is a major research effort to develop light sources with particular properties
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Red Paint
# Photons
Wavelength (nm)
400
500
600
700
Red paint absorbs green and blue wavelengths, and reflects red wavelengths, resulting in you seeing a red appearance
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Frequency Response
Any sensor is defined by its response to a frequency distribution
Expressed as a graph of sensitivity vs. wavelength, ()
For each unit of energy at the given wavelength, how much voltage/impulses/whatever the sensor provides
To compute the response, take the integral
E() is the incoming energy at the particular wavelength
The integral multiplies the amount of energy at each wavelength by the sensitivity at that wavelength, and sums them all up
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A “Red” Sensor
Sensitivity
Wavelength (nm)
400
500
600
700
This sensor will respond to red light, but not to blue light, and a little to green light
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23. The “Red” Sensor Response
Sensitivity, 
Sensitivity, 
400
500
600
700
400
500
600
700
#photons, E
#photons, E
Red
Blue
400
500
600
700
400
500
600
700
High response
Low response
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Changing Response
How can you take a “white” sensor and change it into a “red” sensor?
Hint: Think filters
Can you change a “red” sensor into a “white” sensor?
Assume for the moment that your eye is a “white” sensor. How is it that you can see a “black light” (UV) shining on a surface?
Such surfaces are fluorescent
Your eye isn’t really a white sensor - it just approximates one
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Seeing in Color
The eye contains rods and cones
Rods work at low light levels and do not see color
That is, their response depends only on how many photons, not their wavelength
Cones come in three types (experimentally and genetically proven), each responds in a different way to frequency distributions
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Color receptors
Each cone type has a different sensitivity curve
Experimentally determined in a variety of ways
For instance, the L-cone responds most strongly to red light
“Response” in your eye means nerve cell firings
How you interpret those firings is not so simple …
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Color Perception
How your brain interprets nerve impulses from your cones is an open area of study, and deeply mysterious
Colors may be perceived differently:
Affected by other nearby colors
Affected by adaptation to previous views
Affected by “state of mind”
Experiment:
Subject views a colored surface through a hole in a sheet, so that the color looks like a film in space
Investigator controls for nearby colors, and state of mind
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The Same Color?
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The Same Color?
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Color Deficiency
Some people are missing one type of receptor
Most common is red-green color blindness in men
Red and green receptor genes are carried on the X chromosome - most red-green color blind men have two red genes or two green genes
Other color deficiencies
Anomalous trichromacy, Achromatopsia, Macular degeneration
Deficiency can be caused by the central nervous system, by optical problems in the eye, injury, or by absent receptors
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Trichromacy
Experiment:
Show a target color beside a user controlled color
User has knobs that add primary sources to their color
Ask the user to match the colors
By experience, it is possible to match almost all colors using only three primary sources - the principle of trichromacy
Sometimes, have to add light to the target
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32. The Math of Trichromacy
Write primaries as A, B and C
Many colors can be represented as a mixture of A, B, C: M=aA+bB+cC (Additive matching)
Gives a color description system - two people who agree on A, B, C need only supply (a, b, c) to describe a color
Some colors can’t be matched like this, instead, write: M+aA=bB+cC (Subtractive matching)
Interpret this as (-a, b, c)
Problem for reproducing colors
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33. Color matching functions
Choose primaries, say A, B, C
Given energy function, E(), what amounts of primaries will match it?
For each wavelength, determine how much of A, of B, and of C is needed to match light of that wavelength alone. Gives a(), b() and c()
Match is:
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