Download - [1990] Contrast in Complex Images

8/9/2019 [1990] Contrast in Complex Images

1/9

2032 J. Opt. Soc.Am. A/Vol. 7, No. 10/October 1990

Contrast in complex images

Eli PeliEye Research Institute, 20 Staniford Street, Boston, Massachusetts 02114

Received November30, 1989; accepted March 26, 1990

The physicalcontrast of simpleimagessuch as sinusoidalgratings or a singlepatch of lighton a uniformbackgroundis well defined and agrees with the perceivedcontrast,but this is not so for complex images. Most definitions assigna single contrast value to the whole image, but perceived contrast may vary greatly across the image. Humancontrast sensitivityis a function of spatial frequency; thereforethe spatial frequencycontent of an image shouldbeconsidered in the definition of contrast. In this paper a definition of local band-limited contrast in images isproposed that assignsa contrast value to every point in the image as a function of the spatial frequencyband. Foreach frequencyband, the contrast is definedas the ratioof the bandpass-filteredimage at that frequencyto the low-pass image filteredto an octave below the same frequency(local luminance mean). This definitionraises importantimplicationsregarding the perception of contrast in compleximages and is helpful in understanding the effects ofimage-processingalgorithms on the perceived contrast. A pyramidal image-contrast structure based on this

definition is useful in simulatingnonlinear, threshold characteristicsof spatial vision in both normal observers andthe visually impaired.

INTRODUCTIONApparent or perceived contrast is a basic perceptualattri-bute of an image. Many techniques of contrast manipula-tion and modificationhave been developed within the fieldof digital image processing. The study of contrast sensitiv-ityhas dominatedvisual perceptionresearch in the past twodecades. However,the measurementand evaluationof con-trast and contrast changes in arbitrary images are notuniquelydefined in the literature. In this paper I proposea

definitionof local band-limitedcontrast in complex imagesthat is closelyrelatedto thecommondefinitionof contrastinsimple pattern tests. The purpose of this new definitionisbetter to link measured physical contrast with visual con-trast perception. This definitionprovides new insights intothe perceptionofsuprathresholdcontrastin compleximagesand permitsbettersimulationsof the effectsof the thresholdnonlinearnatureof contrastsensitivityon the appearance ofimages.

Definitions of Contrast in Simple PatternsTwo definitionshave been commonlyused formeasuringthecontrastof test targets. The contrastC of a periodicpattern

such as a sinusoidalgrating is measuredwith the Michelsonformula'

C Lmax LminLmax Lmin

where Lmax and Lmin are the maximumand minimum lumi-nance values, respectively,in the gratings. The Weber frac-tion definitionof contrast [Eq. (2) below] is used to measurethe local contrast of a single target of uniform luminanceseen againsta uniform background:

C AL (2)

where AL is the increment or decrement in the target lumi-nance from the uniformbackgroundluminanceL. One usu-ally assumes a large backgroundwith a small test target, in

which case the average luminancewill be close to the back-groundluminance. If there are many targets, or if there is arepetitive target as in the case of a grating stimulus, theseassumptionsdo not hold. The processing of images in thevisual system is believed to be neither periodic nor local;thereforethe representation of contrast in images shouldbequasi-localas well.

The difference between the two definitionsbecomes ap-parent when the Michelsoncontrast is expressedsimilarlytothe Weber contrast:

= L=L + AL (3)

where AL = (Lmax Lmin)/2 and L = Lmin. These twomeasures of contrast do not coincideor even share a commonrange of values. The Michelson contrast value ranges from0 to +1.0, whereas the Weber contrast value ranges from-1.0 to +o. Other definitionsof contrast that share similarproblems [for example, C = 2AL/(2L + AL)] have beenpresented by Westheimer.2 However, all the definitionsrepresent the contrast as a dimensionlessratio of luminancechange to mean background luminance.

Previous Definitions of Contrast in ImagesBecause of the difficulties in defining contrast in images,many definitionsof contrast in a complex scene found in theliterature are restricted to the assessment of contrastchanges in the same image displayedin two different ways.One such definition of contrast change was given by Gins-burg.3 For an image spanning the full range of displayedgray levels (i.e., 0-255 gray levels), the contrast was definedas 100%, but when the same image was linearly compressedto span only half of the range (i.e., 0-127), the contrast wasreducedto 50%. With this definitionof contrast change, themean luminancedecreaseswith contrast and, thus, based on

some of the other definitions, the contrast should be leftunchangedby compression. More commonly, the contrastchange of images was evaluated by using the Michelson

0740-3232/90/102032-09$02.00 © 1990 Optical Societyof America

Eli Peli


2/9


3/9

2034 J. Opt. Soc. Am. A/Vol. 7, No. 10/October 1990

domain, the band-limited image can be represented in thefollowing way:

A(u, v) A r, 0) = F(r, 0)G(r), (7)

where u and v are the respective horizontal and verticalspatial frequency coordinatesand r and 0 represent the re-

spective polar spatial frequency coordinates: r = Vu2

+ v2

and 0 = tan'I(ulv), and F(r, 0) s the Fouriertransform of theimage f(x, y).

In the space domain the filtered image a x, y) can berepresented similarly, that is, as

a(x, y) = f(x, y) * g(x, y), (8)

where * represents the convolution operator and g(x, y) isthe inverse Fourier transform of the band-passfilter trans-form G(r). We can also define, for every bandpass-filteredimage, a(x, y), the correspondinglocal luminance mean im-age, 1(x, y), which is a low-pass-filteredversion of the imagecontaining all energy below the band. The contrast at the

band of spatial frequencies can be representedas a two-

dimensionalarray c(x, y):

c(xy) = a(Xy) (9)

where l(x, y) > 0. This definitionprovides a local contrastmeasure for every band that depends not only on the localenergy at that band but also on the local background lumi-nance as it varies from place to place in the image. SeeAppendix A for details of implementation of the contrastpyramid.

IMPLICATIONS OF THE CONTRASTDEFINITION

The contrast at a spatial frequency or a band of spatialfrequencies is usually considered to be dependent only onthe local amplitude at that frequency. The contrast in Eq .(9) depends also on the amplitude at lower spatial frequen-cies. The effect of this difference can be easily appreciatedwith a one-dimensional,two-frequencypattern (Fig. 1):

f x, y) = Io(l + a, cos wx + a2 cos 8wx), (10)

where Io is the mean luminance and ajlo and a IO are theamplitude of the first and eighthharmonics, respectively.

Although the amplitude of the eighth harmonic is con-

stant across the image, the apparent contrast is higher near

Fig. 1. Compound grating image as described in Eq. (10). Theapparent contrast of the high-frequencycomponentchanges acrossthe image although the amplitude is fixed.

Fig. 2. Comparison between bandpass amplitude image (left) andlocal band-limited contrast image (right) for two spatial frequen-cies, 16 (top) and 32 (bottom) cycles per picture. Note the relativeincrease of contrast around the eyes and over dark areas in theoriginal image (at left in Fig. 3below).

the troughs of the first harmonic than near the peaks, aspredicted by Eq. (9). This observationwas recentlyverifiedpsychophysically by Thomas.2 0 The contrast of the eighthharmonic c8 may vary in the range

a 2 a 2C8 a a, u l-a, (11)

For low-contrast patterns (i.e., a,


4/9

Vol. 7, No. 10/October 1990/J. Opt. Soc. Am.A 2035

The resultant simulated perceived image (Fig. 3) is muchsharper, has higher contrast, and enhances those detailsthatoccur againstdarker backgrounds. The details of the filtersused in the generationof the images in Fig.2 and the recon-struction in Fig. 3 are given in Appendix A.

Linear scaling of an image grayscale, a common image-enhancement technique,is frequently used to modifyimagesto study the effect of contrast.5 91 0 It is usually assumedthat linear resealing will change the contrast of all frequen-cies in the same way. Indeed, the amplitudesof allfrequen-cies will be modified linearly by the same amount, but thecontrast as defined by Eq. (9) will change differently fordifferent spatial frequencies. For example, ifin Eq. (10) wemultiply a, and a2 by k, the new contrast for the first har-monic will be kal, but the contrast of the eighth harmonicwill span a new range:

ka 2 ka21 +kaj 1 -ka l (12)

This effect is illustrated in Fig. 4. Each of the two imagesat the right has two sinusoidal componentsof the sameamplitude with the higher componentof equal spatial fre-quency on both images. The images at the left representequal linear resealingof the two images at the right butresult in a noticeable difference in the apparent contrast ofthe higher-frequency componentsin the two images. Thuslinear resealingof gray levelsactually increases the contrastof high spatial frequencies more over dark areas than it doesfor the same spatial frequency over light areas, and both arechanged differently from the amount of change inthe con-trast of low spatial frequencies.

Reverse scaling or polarity inversion of the display issometimes usedfor image enhancement.2 2 The fact thatsuch a process results in enhancementof details is usuallyattributed to the nonlinearityof the display. However, evenwith a linear display, an improvement in details may beobserved with such processing,while at the same time thevisibilityof other detailsis reduced. These resultsare clear-ly understandable within the frameworkof the contrast defi-nition proposed here. Reversingthe polarity of the displaywill not change the magnitude of the local high-frequencyinformation. Contrast, on the otherhand, will be increasedin areas transferred from higher to lower local luminancemean andwill be lower for areas transferred from low to highluminancemean.

Changingthe polarityof text from black on white to white

Fig. 3. Simulation of the perceived contrast image. This imagewas reconstructedby addingthe local band-limitedcontrast images(right) instead of the original bandpass-filtered images (left).

Fig. 4. Illustration of the different effects of linear resealing onpatterns of different spatial frequency composition. The com-pound gratings at the right were linearlyscaled equally(2X), result-ing in their respective gratingson the left. The amplitudes of thetwo sinusoidal componentsin each image pair are equal, and thehigh-frequency componentis of the sameperiod in all images. Notethe relative increase incontrast of this componentin the lower-left-hand image compared with the upper-left-hand image.

on black has little effect on normal reading. Legge et al . 2 3

have shown that some low-visionobservers read as much as50% faster with reversedcontrast text. These effects, whichhave been known clinically for many years, are usually at-tributed to abnormal lightscatter in eyes with cloudymedia.Part of the effect maybe explained by the change in contrastat the critical band of frequencies that occurs with change inpolarity. The contrast at a 1-octave-wide band of spatialfrequencies, extending upward from the fundamental fre-quency of the letters, has been shown to contain sufficientinformation for fast reading. The contrast of details at thisband will change substantially with a change of polarityfrom black-on-whiteto w hite-on-blacktext, accordingto ourdefinition. Thus a patient's reading performancethat de-clines with a decrease in contrast at high contrast levels willimprove withthe reversal of text polarity irrespectiveof thenature of the patient's disability. This indeed appearsto betrue for the two cases reported by Rubin andLegge.24 Sincefor many low-vision patients performance becomes depen-dent on contrast only at fairly low contrast levels, this effectis apparent only with a small portion of the population.Pelli25 analyzed similarlythe contrast of lines of text in thetwo polarities on a video display. His patterns, however,span different nonoverlappingluminance ranges andthushad different contrasts globally (defined byMichelson con-trast) as well as locally. Only this global difference wasconsidered in his case.

APPLICATION: SIMULATIONS OF THEAPPEARANCE OF IMAGES

In this section two applicationsof the pyramidal image con-trast structure described in Appendix A are illustrated.This type of processingenables us to implement thenonlin-

Eli Peli


5/9


ear response of the visual system locally. This applicationwas not possible until now.

The Fourier analysis of images in the context of imageperceptionhas frequently been interpreted to imply that thecontrast sensitivityfunctionmeasured at various spatial fre-quencies can be implementedas a modulation transfer func-tion of the system in the Fourier domain for filtration ofimages.3 26 -28 In most cases, such applications were limitedto increasing or decreasing the amplitudesat various spatial

frequencieswithout explicit reference to the possibleinter-actions among amplitudes at different frequencies. Whenapplied to the simulation of appearances of images to ob-servers with normal3 or abnormal2 8 vision, this linear processignores the highly nonlinear characteristics of the visualsystem. Despite large differences in contrast sensitivitythresholds for different frequencies at different eccentrici-ties, appearances of superthreshold images are constant oralmost constant.2 9 3 0 Hess et al. 1 included this nonlinear

Fig. 5. Simulation of the appearance of a face image (spanning 4 degof visualangle) to a low-visionpatient whose contrastsensitivityfunctionis illustrated in Fig. 6. Top left, the originalimage; top right, the simulated appearance of the same image to the patient. The three rows offour images representprocessing at differentspatial frequencieson the pyramid. The far-left-hand image in each rowis the bandpass-filteredimage obtained from the original image. The second column shows the correspondinglow-pass-filtered version for the same scale, i.e., all theenergy below the band represented in the first column, or the local luminance mean. The third column represents the contrast images.Contrast arrays are bipolar, and a DC level of 128 has been added arbitrarily to presentthose arrays as images. Images in the fourth column on

the far-right-handside represent the thresholded,bandpass-filtered images. For each image in the third column, eachpoint was tested againstthe thresholdvalue illustrated in Fig.6 for the correspondingspatial frequency. If the contrast of the image at that point is above threshold,the correspondingpoint from the far-leftimage is reproduced in the far-right column. If the contrast at a certain point is below threshold,thecorrespondingpoint is set to zero (gray) in the far-right image. The simulated appearance image (top right) is generated by summingall theimages in the far-right column. Actual processingincluded two more rows at 2 and 32 cycles per picture (not shown).

Eli Peli


6/9

Vol. 7, No. 10/October 1990/J. Opt. Soc. Am. A 2037

1--

0.1-

A

0.01

0.1

0.4

1 10

Spatial Frequency (cyc/deg)

Spatial Frequency (cyc/face)

4 40

Fig. 6. Contrastdetection thresholds(dotted curve) ofa low-visionpatient with centralscotoma owing to age-relatedmaculopathyusedin the simulation of Fig. 5. Contrast detectionthresholds of 15normal observers areillustratedby the thickcurve. The thin curverepresentsmean, radiallyaveraged contrast spectra of five differentfaces.

characteristicin their simulation of vision in amplyopes byapplyingthe threshold in the Fourierdomain. Such globalprocessing is insufficient, as it does not address the localvariability of contrast across the image. To improve theirsimulation,they have also applied the same process to sub-images.

The pyramidal image contrast structure described in Ap-pendix A enables us to use nonlinear processing to simulatethe appearanceof imagesfor normal- andlow-visionobserv-ers point by point and for every spatial frequency in theimage. An example of this process is illustrated in Fig. 5.The contrast sensitivity functionof a patient with a centralscotoma due to macular disease was measured, using 1-oc-tave-bandwidth sinusoidal patchesof grating in a two-di-mensional Gaussianenvelope.31 The patient's contrast de-tection thresholds used in the processing of Fig. 5 are illus-trated, together with the mean response of 15 normalobservers,in Fig. 6. Thus the final image inFig. 5, top right,represents the appearance of the original image to this pa-tient. The originalimage wasprocessedwiththe stipulationthat the face span 4 deg of visual angle. On this scale, thispatient's visual loss had little effect on information at 4cycles per picture (top row of four images), aminimal effecton information at 8 cycles per picture (middle row), and asubstantial effect on information at 16 cycles per picture(bottom row). Full processing includedalso the bands of 2and 32 cyclesper picture (both not shown). This simulationdiffers from previoussuch simulations3 2 8 because supra-threshold contrast features retain their contrast and are notwashed out by the processing as with other techniques.Thus the simulated image maintains the full contrast ap-pearance reported by patients with central visual loss andclear media and is not faded or washed away, as the appear-ance of images seenthrough cataracts may be.26

The same pyramidalimage contrast structure alsoenablesus to simulate the appearanceof images with a nonuniformretina. Using data on the contrast threshold at differentspatial frequencies at different eccentricitieson the retina,2 9

we can simulate the appearance of images to the nonhomo-geneous visual system by selectinga center of fixation repre-senting thefovealposition on the image and then comparingthe local threshold at each spatial frequencyand each eccen-

Fig. 7. Simulation of the appearance of an image to a normal observer including the nonuniform characteristic of the visual system.Simulationis carried out with the assumptionof fixation at the center of the image. The technique appliedis similar tothe one used for Fig.5,

except that for every point in the contrast image the distance from the center of fixation in degreesof visual angle was calculated, and the con-trast detection thresholdcorrespondingto spatialfrequency andretinaleccentricitywas used in thresholdingthe images. The image at the leftrepresents processing when the scene was considered to span 32 deg of visual angle. The image at the right represents the same imageprocessed as if it spanned only 2deg of visual angle. The most strikingeffect is the small variabilityacross the visual field inboth cases. Notethat more heterogeneity is expressed over the image at the right (2 deg of visual angle).

Eli Peli


7/9


tricity with the measured value. Images shown in Fig. 7illustrate the appearance of the same image when it spans 2and 32 deg of visualangle, respectively. The relatively smalleffect of the nonuniform retina in the appearance of bothimages is striking. The effect is much smaller than theeffect previously simulated by Schwartz and colleagues,us-ing cortical surface data32 33 or an arbitrarily selected non-uniform function.3 4 The same simulationmay be expandedto represent the fullvisual field, as data for the lower spatialfrequencies and the higher eccentricitieswere recentlypub-lished by Pointer and Hess.35

DISCUSSION

The basic assumption of this study was that image contrastsshould be expressed as the dimensionless ratio of the localamplitude and the local average luminancesimilarly to thatexpressed in the definition of Michelson contrast or Weberfraction. The use of such a ratio implies that the humansensitivity to amplitude of change in luminance varies withthe adaptation level associated with the local average lumi-nance.36 This is known to be the case for threshold contrastsensitivityat all spatial frequenciesat high luminancelevels.For low frequencies (


8/9

Vol. 7, No. 10/October 1990/J. Opt. Soc. Am. A 2039

APPENDIX A: PYRAMIDAL STRUCTUREUSED IN ANALYSIS AND SIMULATIONS

A pyramidalimage transform was calculated in the frequen-cy domain.47 For digital processing of images, it is conve-nient to select center frequencies (in cycles per picture) thatare a power of 2 for each segment. Thus the image in thefrequency domain may be representedas

n-1

F(u, v F(r, 0 Lo(r, 0) + , Ai(r, 0 Hn(r, 0 , (Al)i=1

where Lo and Hn represent the low and high residuals, re-spectively. They contain the energy in the low and highfrequencies after the various bandpass layers, Ai, have beensubtracted from the image. The low residual is essentialinour applicationand therefore is maintained. The high re-sidual has little information,and in most applicationsit maybe discardedwithout any perceptualchange in the image.4 8

Although the use ofa Gaussian filter is attractive because

of the mathematical convenience in transformation from thefrequencyto the spatial domain, this filter has several short-comings. 9 48 To obtain an approximationto the shape of aGaussianand at the same time to satisfythe requirement ofsymmetricalshape on a log frequencyaxis, togetherwith therequirement that the image must be able to be reconstructedfrom the various segments by simple addition,4 8 we haveused cosine log filters (Fig. 8). A cosine log filter of (1-

1.2

1.0

0.8

0.6

0.4

0.2

0.0 0 00

Spatial Frequency [cycles picture]

(a)

2

Center Freq.1.0

0.84

0.6 6sum

0.4

0.2

0.01 ~~~~1 00

frequency

(b)

Fig. 8. Comparison of Gaussian (Gabor filters) with the cosine logfilters used here. (a) Filter bank of 1-octave-wide Gaussian filtersand the sum of all filters. (b) Filter bank of l-octave-widecosine log

filters. Here the summation of all the filters adds to the unity.Note also the symmetry of the cosine log filters on a logarithmicscale.

octave) bandwidth centered at frequency2i cycles/picture isexpressedas

Gi(r) = 1/211 + cos(7r log2 r ri ]. (A2)

The small difference between these functionsand the com-monly used Gabor filters or derivatives of Gaussians is oflittle consequence for the concept described here and itspotential applications.

Thus Ai is obtained by multiplyingthe Fourier transformof the image with a torus-shaped dome filter describedin Eq.(A2). The filtered image is transformed back to the spacedomain,where it can be represented as

n-1

f(x, y) = lo x, y) + ai(x, y) + hn(X, y)i=1

(A3)

The residual lo is calculated simply to maintain the ease ofreconstruction with simple addition, but hn is not used in ourmodel. For every ai(x, y), the correspondingli(x, y) is

i-ll(x, Y) = lo(x, y) + E aj(x, y),

j=i

and ci(x, y) is calculated as in Eq. (9):

ai(x, y)1i(XY)A=-

(A4)

(A5)

ACKNOWLEDGMENTSThis study is supported in part by grant EY05957 from theNational Institutes of Health and by a grant from the JamesH. and Alice Teubert Charitable Trust. I thank SteveBurns for valuable discussions and Robert Goldstein forimportant programminghelp.

The author is also with the Department of Ophthalmolo-gy, Harvard Medical School.

REFERENCES AND NOTES1. A. A. Michelson,Studies in Optics (U. Chicago Press,Chicago,

Ill., 1927).2. G. Westheimer, The oscilloscopic view: retinal illuminance

and contrast of point and line targets, Vision Res. 25, 1097-1103 1985).

3. A.P. Ginsburg, Visual informationprocessingbased on spatial

filters constrainedby biologicaldata, Ph.D.dissertation,Aero-

space Medical Research Laboratory Rep. AMRL-TR-78-129(Universityof Cambridge,Cambridge, 1978).

4. C. Owsley, R. Sekuler, and C. Boldt, Aging and low-contrastvision: face perception, Invest.Ophthalmol.Vis. Sci. 21, 362-365 1981).

5. R. Sekuler,C. Owsley,and L. Hutman, Assessingspatialvisionof older people, Am. J. Optom. Physiol. Opt. 59, 961-968(1982).

6. M. Hubner,I. Rentschler,and W. Encke, Hidden-face recogni-tion: comparing foveal and extrafoveal performance, Hum.Neurobiol.4, 1-7 (1985).

7. T. R. Riedl and G. Sperling, Spatial frequencybands in com-plex visual stimuli: AmericanSign Language, J. Opt.Soc. Am.A 5, 606-616(1988).

8. M. Pavel, G. Sperling, T. Riedl,and A. Vanderbeek, Limitsof

visualcommunication: the effect of signal-to-noiseratioon the

intelligibilityofAmerican SignLanguage, J. Opt.Soc. Am.A4,2355-2365 1987).

Eli Peli

G


9/9


9. G. S. Rubin and K. Siegel, Recognition of low-pass filteredfaces and letters, Invest. Ophthalmol.Vis. Sci. Suppl. 25, 71(1984).

10. D.S. Loshin andT. A.Banton, Local contrastrequirementsfo rFacial recognitionin patients with central field defects, Invest.Ophthalmol. Vis. Sci. Suppl. 29,43(1988).

11. R. F. Hess, A. Bradley, and L. Piotrowski, Contrast-codinginamblyopia. I. Differences in the neural basis of human am-blyopia, Proc. R. Soc. London Ser. B 217, 309-330 (1983).

12. J. D. Briers and A. F. Fercher, Retinal blood-flowvisualizationby means of laser speckle photography, Invest. Ophthalmol.Vis. Sci. 22, 255-259 (1982).

13. A. B. Watson, H. B. Barlow, and J. G. Robson, What does theeye see best? Nature (London) 302, 419-422 (1983).

14. D. R. Badcock, Spatial phase or luminance profile discrimina-tion? Vision Res. 24, 613-623 (1984).

15. R. F. Hess and J. S. Pointer, Evidence for spatially local com-putations underlyingdiscrimination of periodic patterns in fo-vea and periphery, Vision Res. 27, 1343-1360 (1987).

16. E. Peli and R. B. Goldstein, Contrast in images, in VisualCommunication and Image Processing 88, T. R. Hsing, ed.,Proc. Soc. Photo-Opt.Instrum.Eng. 1001, 521-528 (1988).

17. R. L. De Valois, D. G. Albrecht, and L. G. Thorell, Spatialfrequency selectivity of cells in macaque visual cortex, VisionRes. 22, 545-559 (1982).

18. A. B. Watson, Efficiency of a model human image code, J.Opt. Soc. Am.A 4, 2401-2417 (1987).

19. D. J. Field, Relationsbetween the statisticsof natural imagesand the responsepropertiesofcorticalcells, J. Opt. Soc. Am.A4, 2379-2394 1987).

20. J. P. Thomas, Independent processingof suprathresholdspa-tial gratings as a function oftheir separation in spatialfrequen-cy, J. Opt. Soc. Am.A 6, 1102-1111 (1989).

21. A. Fiorentini, L. Maffei, and G. Sandini, The role of highspatial frequencies in face perception, Perception 12, 195-201(1983).

22. W. K. Pratt, Digital Image Processing, (Wiley, New York,1978), pp. 307-344.

23. G. E. Legge, G. S. Rubin, D. G. Pelli, and M. M. Schleske, Psychophysics of reading. II. Low vision, Vision Res.25 ,253-266 (1985).

24. G. S. Rubin and G. E. Legge, Psychophysics of reading. VI.The role of contrastin lowvision, Vision Res.29,79-91 (1989).

25. D. G. Pelli, Reading and contrast adaptation, in Digest ofTopical Meeting on Applied Vision (OpticalSocietyof Ameri-ca, Washington, D.C., 1989), pp. 102-103.

26. E. Peli and T. Peli, Image enhancementfor the visually im-paired, Opt.Eng. 23, 47-51 (1984).

27. T. B. Lawton, Improved word recognition for observerswithage-related maculopathies using compensation filters, Clin.Vision Sci. 3, 125-135 (1988).

28. B. L. Lundh, G. Derefeldt, S. Nyberg, and G. Lennerstrand, Picture simulation of contrast sensitivityin organic and func-tional amblyopia, Acta Ophthalmol.59, 774-783 (1981).

29. M. W. Cannon, Jr., Perceived contrast in the fovea and peri-phery, J. Opt. Soc. Am.A2, 1760-1768 (1985).

30. M. W. Cannon, Jr., and S. C. Fullenkamp, Perceived contrastand stimulussize: experiment andsimulation, Vision Res. 28,695-709 (1988).

31. E. Peli, R. Goldstein,G. Young, and L. Arend, Contrast sensi-tivity functions for analysis and simulation of visual percep-tion, in Digest of the Topical Meeting on Noninvasive Assess-ment of the Visual System (Optical Society of America,Wash-ington, D.C., 1990).

32. E. L. Schwartz,B. Merker, E. Wolfson, and A. Shaw, Applica-

tions of computer graphics and image processingto 2D and 3Dmodeling of the functional architecture of visual cortex, inDigest of Meeting on Computer Graphics and Applications(Institute of Electrical and Electronics Engineers, New York,1988), pp. 12-23.

33. E. L. Schwartzand B. Merker, Computer-aided neuroanatomydifferentialgeometry of cortical surfaces and on optimal flat-teningalgorithm, in Digest of Meeting on Computer Graphicsand Applications (Institute of Electrical and ElectronicsEngi-neers, New York, 1986), pp. 36-49.

34. Y. Y. Zeevi,N. Peterfreund,and E. Shlomot, Pyramidalimagerepresentation in nonuniformsystems, in Visual Communica-tions and Image Processing, 88, T. R. Hsing, ed., Proc. Soc.Photo-Opt.Instrum. Eng. 1001, 563-571 (1988).

35. J. S. Pointer and R. F. Hess, The contrast sensitivitygradientacross the human visual field with emphasis on the low spatialfrequency range, Vision Res. 29, 1133-1151 (1989).

36. J. G. Robson, Linear and non-linear operations in the visualsystem, Invest. Ophthalmol.Vis. Sci. 29, 117(1988).

37. D. H. Kelly, Visual contrastsensitivity, Opt. Acta24,107-129(1977).

38. M. A. Georgeson and G. D. Sullivan, Contrast constancy: de-blurring in human vision by spatial frequency channels, J.Physiol. (London)252, 627-656 (1975).

39. A. Toet, L. G. van Ruyven,and J. M. Valeton, Merging thermaland visual images by contrastpyramid, Opt. Eng.28, 789-792(1989).

40. P. S. Schenker,D. R. Urangst, T. F. Knaak,D. T. Huntley,andW. R. Patterson III, Pyramidal normalization filter: visualmodel with applicationto image understanding, in Real TimeSignal Processing V, J. Trimble, ed., Proc. Soc. Photo-Opt.Instrum. Eng. 341, 99-108 (1982).

41. R. Shapley and C. Enroth-Cugell, Visual adaptation and reti-nal gain controls, in Progress in Retinal Research, N. N. Os-borne, ed. (Pergamon,Oxford, 1984), Vol. 3, pp. 263-343.

42. R. W. Bowen, J. Pokorny, andV. C. Smith, Sawtoothcontrastsensitivity: decrements have the edge, Vision Res. 298, 1501-1509 (1989).

43. 0. A. Hilsenrath and Y. Y. Zeevi, Adaptive two-dimensionalneighborhood sensitivity control by a one-dimensional pro-cess, in Visual Communication and Image Processing 88, T.R. Hsing, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1001, 717-723 (1988).

44. C. F. Stromeyer III and S. Klein, Evidence against narrow-band spatial frequency channelsin human vision: the detect-ability of frequency modulatedgratings, Vision Res.15, 899-910 (1975).

45. M. C. Morrone and D. C. Burr, Feature detection in humanvision: a phase-dependent energy model, Proc. R. Soc. Lon-don Ser.B 235, 221-245 (1988).

46. E. Peli, Hilbert transform pairs mechanisms, Invest. Oph-thalmol.Vis. Sci. 30, 110 (1989).

47. The pyramidal image transform used here is conceptually iden-tical to any of the commonly used pyramids of bandpass-fil-tered images. Since for our applicationimagesof equal size areused at allbands, we avoidedthe commonapproachof subsam-pling the imagesrecursively,filtering,and then unsamplingthereduced size images, instead; all filtering was done in the fre-quency domain. Thus the content of our final images in thepyramid of image scales wasidentical to the images that wouldbe calculated by upsampling images obtained on a pyramid ofimage resolution.

48. A. B. Watson, The cortex transform, rapid computation ofsimulated neuro images, Comput.Vision Graphics Image Pro-cess. 39, 311-327 (1987).

Eli Peli

Download - [1990] Contrast in Complex Images

Top Related