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

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.

Visual system components

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

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

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

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

Basic spatiochromatic model structure

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

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

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.

Campbell’s contrast sensivity function on log-log axes

Dependence of sine wave visibility on contrast and spatial frequency

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

Achromatic spatial contrast sensitivity curves

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

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

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

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

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

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