1. Spatiochromatic Vision Models for Imaging
Jan P. Allebach
School of Electrical and Computer Engineering
Purdue University
West Lafayette, Indiana
CIC-17, Albuquerque, NM, 10 November 2009

2. What is a model? From dictionary.com:
A schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics.
Model is not a complete description of the phenomenon being modeled.
It should capture only what is important to the application at hand, and nothing more.
Its structure must be responsive to resource constraints.

3. Visual system components

4. Why do we need spatiochromatic models?
Imaging systems succeed by providing a facsimile of the real world
A few primaries instead of an exact spectral match
Spatially discretized and amplitude quantized representation of images that are continuous in both space and amplitude
These methods only succeed only because of the limitations of the human visual system (HVS)
To design lowest cost systems that achieve the desired objective, it is necessary to take into account the human visual system in the design and evaluation

5. Modeling context
Modeling process is very dependent on the intended application
Motivation for developing the models in the first place
Governs choice of features to be captured and computational structure of the model
Provides the final test of the success of the model
Tight interplay between models for imaging system components and the human visual system
Model usage may be either embedded or external

6. Pedagogical approach
Spatiochromatic modeling, in principle, builds on all of the following areas:
Color science
Imaging science
Psychophysics
Image systems engineering
As stated in course description, we assume only a rudimentary knowledge of these subjects
Start from basic principles, but move quickly to more advanced level
Focus on what is needed to follow the modeling discussion

7. The retinal image is what counts
Every spatiochromatic model has an implied viewing distance
What happens when this condition is not met?
Too far – image looks better than specification
Too close – may see artifacts

8. Basic spatiochromatic model structure

9. Impact of viewing geometry on spatial frequencies
Both arrows A and B generate same retinal image
For small ratio , the angle subtended at the retina in radians is

10. Spatial frequency conversion
To convert between (cycles/inch) viewed at distance (inches) and (cycles/degree) subtended at the retina, we thus have
For a viewing distance of 12 inches, this becomes

11. Spatial frequency filtering stage
Based on pyschophysical measurements of contrast sensitivity function
Use sinusoidal stimuli with modulation along achromatic, red-green, or blue-yellow axes
For any fixed spatial frequency, threshold of visibility is depends only on This is Weber’s Law.

12. Campbell’s contrast sensivity function on log-log axes

13. Dependence of sine wave visibility on contrast and spatial frequency

14. Models for achromatic spatial contrast sensitivty*
*Kim and Allebach, IEEE T-IP, March 2002
Author
Contrast sensitivity function
Constants
Campbell
1969
Mannos
1974
Nasanen
1984
Daly
1987

15. Achromatic spatial contrast sensitivity curves

16. Chrominance spatial frequency response
Based on Mullen’s data*
*K.T. Mullen, J. Physiol., 1985

17. Spatial Frequency Response of Opponent Channels
Luminance
[Nasanen]
Chrominance
[Kolpatzik and Bouman*]
cycles/sample
cycles/sample
cycles/sample
cycles/sample
*B. Kolpatzik, and C. A. Bouman, J. Electr. Imaging, July 1992

18. Illustration of difference in spatial frequency response of luminance and chrominance channels
Original image
O1- filtered

19. Illustration of difference in spatial frequency response of luminance and chrominance channels
Original image
O2- filtered

20. Illustration of difference in spatial frequency response of luminance and chrominance channels
Original image
O3- filtered

21. Application areas for spatiochromatic models
Color image display on low-cost devices
PDA
Cellphone
Color image printing
Inkjet
Laser electrophotographic
Digital video display
LCD
DMD
Plasma panel
Lossy color image compression
JPEG
MPEG