Image Acquisition
CS 450: Introduction to Digital Signal
and Image Processing
Acquisition Devices
• Aperture
• Scanning
• Sensor
• Quantizer
• Output storage medium
Aperture
• Point measurements are impossible
• Have to make measurements using a
(weighted) average over some aperture
• time window
• spatial area
• etc.
Aperture
• Size of aperture determines resolution
• Smaller apertures = better resolution
• Larger apertures = worse resolution
• Lenses allow a physically larger aperture to
act as an effectively smaller one
Lenses
Lens!
Effective
Aperture!
Sensor!
Sensor
• Converts light (photons) to chemical
and/or electrical response
• Examples
• Silver halide crystals (film)
• Photoreceptors in our eyes (rods, cones)
• Charge-coupled device (CCD), etc.
Noise
• Unavoidable random fluctuations
from “correct” value
• Can usually be modeled as a
statistical distribution with mean
at the “correct” value
µ
• A measured sample will vary
from that mean according to
the distribution std. dev.
Signal-To-Noise Ratio
• Measure of how “noise free” a signal is
SNR =
µ
Sources of Noise
• Quantum noise
• Sensor inhomogeneity
• Electrical fluctuations
• “Background” noise
May not be
random
Quantum Noise
•
Caused by the discrete
nature of light
•
•
Poisson distributed
•
Sometimes called
“shot noise”
Signal-to-noise ratio
thus increases with
increased light
2
SNR =
µ
=µ
µ
p
=p = µ
µ
Reducing Shot Noise
• The only way to reduce quantum noise is
to increase the photon count
• Turn up the source
• Larger aperture
• Collect for longer
• What are the tradeoffs involved in each of
these approaches?
Noise vs. Resolution
• Smaller apertures
• Better resolution
• Less area = fewer photons = more noise
• Larger apertures
• Worse resolution
• More area = more photons = less noise
Noise vs. Resolution
•
•
•
Example 1: Camera settings
•
•
F-stop: aperture
Shutter speed: collection time
Example 2: Film
•
Larger crystals mean less resolution
but more photon hits (faster)
•
Smaller crystals mean more resolution
but fewer photon hits (slower)
Example 3: CCD cameras
•
Physical limitations to “X megapixels”
Lenses
Physical
(Collecting)
Aperture!
Sensor!
Lens!
Effective
Aperture!
Ideal Sensor Response
• Multiplying the input by a constant
multiplies the output by the same constant
• Adding two input signals causes their
corresponding outputs to add
T (af (t) + bg(t)) = a T (f (t) + b T (g(t))
Linearity
Gain and Bias
• Gain = proportionality of input to output
• Offset / Bias = constant addition to output
Sensor Responses
• Most “approximately linear” devices are
linear over some range
• Below that range - little or no response
• Within that range - linear
• Above that range - saturation
• Example: H&D curve for film
Measuring Resolution
One common way is to use alternating black/
white lines with fixed spacing
• Increase the density until you can’t
resolve (discern) the separate lines
• Gradually blurs to grey
• Stop when half the original contrast
• Units: line pairs per millimeter
Transfer Functions
Another way of quantifying resolution
• Instead of using line-pairs, use sine waves
• Instead of just stopping when you have
half the original contrast, measure the
contrast as a function of frequency
contrast!
frequency!
Transfer Functions
Engineering Example
•
The Gigapxl project:
www.gigapxl.org
•
Built a gigapixel camera by using
the principles we’ve talked about
•
•
•
•
Sampling
Quantum (Shot) noise
Resolution/Transfer functions
“Mom and Pop operation”
now traveling all over the world
photographing scenes