dental radiology Editor.
JOHN W. PREECE, D.D.S. American Academy of Dental Radiology Department of Dental Diagnostic Sciences School of Dentistry, The University of Texas Health Science Center at San Antonio 7703 Floyd Curl Dr. San Antonio, Texas 78284
Toward a better understanding of radiographic contrast R. L. Webber, D.D.S., Ph.D., Bethesda, Aid. DIAGNOSTIC
Contrast is a familiar term that relates directly to the ability of human observers to detect differences in optical density. It also has been used to describe changes in x-ray fluence determined by attenuation differences in tissues of diagnostic interest. Ambiguous conclusions in the literature can be often traced to a lack of specificity in what is being measured and the validity of the implicit assumptions involved. Particularly troublesome are nonspecific bases for normalization and the assumption that a finite change in fluence can be accurately represented as a differential. These practices also tend to obscure consideration of system nonlinearities which can result in contrast enhancement produced by exposure to fogging radiation. Precisely defined components of contrast are symmetrically determined by the concept of modulation. This concept provides a powerful basis for mathematical description of linear systems. Bases for linearization of radiographic systems are also confusing unless they are explicitly stated. This is particularly true for transfer functions as defined in many radiographic applications. Special functions which account for nonlinearity commonly associated with contrast gain in the detector simplify description and provide a quantitatively meaningful basis for specifying system performance in terms of information theory.
ontrast is generally considered to be a fundamental measure of image quality which relates directly to the ability of observers to detect small changes of diagnostic interest. This relationship is easily demonstrated psychophysically for simple stimuli (Weber’s law),’ but its implications for more complex images such as radiographs are not so easily appreciated. Much of the problem stems from the lack of a uniform definition of contrast when it is considered in a variety of contexts. The resulting ambiguity is reflected in the diversity of expressions relating to various properties. A brief review of the literature yields references to exposure contrast, brightness contrast, film contrast,2 subject contrast, radiographic contrast,3 image contrast,4 successive contrast, simultaneous contrast,5 meta-contrast,6 border contrast,’ signal-contrast ratio,8 large-area contrast, detail contrast, and noise contrast.’ 466
Much of the confusion associated with these diverse descriptions can be reduced by considering each within the context of its application. Particularly important is the need to distinguish between physical measurementsand perceived responseselicited in one or more human observers. Only the former provides an unequivocal basis for description which is independent of the observer. The multiplicity of human responses to complex visual stimuli assures that spatial and temporal factors as well as previous experience must be considered in addition to changes in intensity before the psychological attributes of contrast can be described unequivocally. Even when consideration is limited to physical stimuli, other sources of ambiguity which relate to quantitative aspects of the description are often encountered. Much of this type of ambiguity can be eliminated by defining contrast in terms of the following mathematical expression:
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No. 1 where C, is the contrast associatedwith any physically measureable quantity X. Definitions of contrast based on physical measurements which do not conform to equation No. 1 are rare and usually can be traced to different basesfor normalization depending on the particular application. With this limitation in mind, contrast may be considered simply as a relative difference in a scalar quantity of interest. This quantity may be x-ray photon fluence, energy fluence, exposure, luminosity, radiance, or any other physical measure of radiologic significance. Although the units cancel when expressed as a ratio, it is important to remember that the magnitude of the result depends on the quantities measured and where in the radiographic chain they are sampled. Appreciation of this fact follows from the realization that differences in tissue attenuation are the only Sourcesof radiographic contrast. All other elements in the system merely modify contrast derived from this source. Modifying influences are cumulative and can involve all functional elements in the radiographic system. Particularly important are intrinsic sources of scatter, the quality of the beam, the characteristics of the detector, and the mode of display. Other basesfor confusion are more subtle because they result from assumptions which are usually expressed only implicitly. Consider again the basic expression for contrast shown in equation No. 1. If contrast is expressed in terms of radiographic exposure, C, is the contrast associated with a change in the amount of radiation to which a radiographic film is exposed and X and AX are, respectively, the magnitude of the reference exposure and its associated change. When AX is assumed to be equal to the differential, dX, equation No. 1 becomes: Cx 0: Alog X.
This follows directly because d(lnX) = $. Misunderstandings can easily arise from a failure to realize that equation No. 2 holds only for very small differences, a condition which may not be met in many radiologic applications. The same limitation also applies to contrast determined from images recorded on film. For example, it is common to
Fig. 1. Luminouscontrastmay be definedas the relative differencebetweentwo luminosities,LT and LB,produced by passinglight, Lo,,through densitiesDT and DB, respectively. In this caseLT is the luminosity associatedwith the areaof interest(target) andLBis the luminosity associated with the referencearea (background).
consider a difference in optical density as being equivalent to contrast measured in terms of luminance obtainable from a viewbox because density is logarithmically related to the intensity of the light reaching the eye under these conditions. It will be shown that, in general, this equivalence doesnot hold for finite differences. This demonstration requires that contrast as expressedin equation No. 1 be defined more explicitly. A common basis for such a definition is illustrated in Fig. 1. Here the uniform luminance of a viewbox, L,, is expressedas two reduced luminances, L, and LB, as determined by the change in the density, DB - DT, over which contrast is to be measured. This particular formulation is commonly used when it is clear that one of the luminances, LT, is associated with a region, of interest (target), while the other, LB, corresponds with a reference area (background).5 Under these conditions contrast may be defined: No. 4 LB
where C, = luminous contrast. Notice that when so defined contrast may be either positive or negative
Oral Surg. October. 1982
depending on the respective magnitudes of LT and L,. To eliminate this ambiguity contrast may be expressedas an absolute value: No. 5
where C,, = absolute luminous contrast. Even with this simplification, the value of this expression dependson the often arbitrary labeling of luminances as target or background, i.e.:
I LT- LBI z I LB- L I LT . LB
This inequality holds whenever a difference exists in luminance. By replacing either L, or L, in the denominator with the arithmetic mean of both, it is possible to modify this expression in a way that eliminates the ambiguity while it assures an unbiased basis for comparison.’
I LT- LBI cR = (I.q + LB)/2
log,, 2 - log,, ; 0 0 = log,o$-
Taking the antilog and subtracting one gives:
Hence, for finite differences in luminosity, contrast is exponentially related to the change in optical density. This finding suggeststhat considering contrast as equivalent to a finite change in density” can lead to a sizeable discrepancy in quantitative determinations. Although this difference posesfew conceptual problems when it is properly identified, it does caution against indiscriminate comparisons of “contrast” from different sources when it is unclear whether or not a distinction has been made between AX and dX. Considering equation No. 9 as influenced by gamma provides additional insight as to the nature of this discrepancy. Because gamma is defined as the slope of the H and D curve, No. 11 AD = yAlog,,X where y = gamma X = exposure. Expressing equation No. 11 in terms of CL in equation No. 10 produces: CL = 1O’rAh X -
= 1orlog2X - 1 XB
where XT = exposure associated with the target x, = exposure associated with the background. From this equation it is apparent that gamma is necessarily a monotonic measure of contrast only so long as the ratio X,/X, remains constant. There are some interesting situations in which this is not the case. For example, consider the effects of fogging radiation reaching the film prior to exposure. Assuming such radiation to be independent of tissuemodulated components, X, and Xg, the radiation reaching the film would be the sum in each case, i.e.: x,, = x, + XF
X BF *This term is used by some investigators to distinguish this function from the more common definition of contrast as noted by equation No. 4.’ Others do not make this distinction because in the limit (AL - dL) they are indistinguishable.
where CR = signal-contrast ratio.* It is informative to explore these implications further vis-a-vis equation No. 1, because contrast defined in this way is a relatively uniform measure of threshold changesin detectability of adjacent stimuli by human observers (Weber’s law). It follows from the definition of optical density, L D = -log,, --1 No. 8 L, where D = optical density L, = the uniform luminance associated with the viewbox L = luminance associatedwith the area of interest on the radiograph.
No. 13 No. 14
where X TF = the total exposure associated with the target region
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Xr,r = the total exposure associated with the background Xr = the fogging exposure It follows that for values of Xr other than zero, y-y
Hence, in the presence of fogging radiation, gamma does not unequivocally determine the contrast produced by a fixed difference in attenuation. An interesting demonstration of this effect occurs when the H and D curve is constrained in such a way that the optical density, expressed as a function of exposure (as opposed to log exposure), has a slope which increases monotonically. Under these conditions C, increases with increasesin fogging exposure. Recently, Oishi and Webber” demonstrated this to be true for a number of screen-film radiographic systems. A similar effect can be produced by controlled exposure to light either before, during, or after radiographic exposure. Indeed, this approach has been recently introduced to increase contrast of photographs made at low light level by incorporating small lamps inside the camera.r2 Another aspect of contrast overlooked by many is the fact that it varies with the size and shape of the target and the background. This is necessarily true for any real system irrespective of whether the visual system is involved or not and follows from the fact that contrast is influenced by the limiting resolution of the system in a way which is determined by the modulation transfer function (MTF) of the system. Thus for most real radiographic systems, contrast tends to be reduced as the distance (space) over which contrast is defined decreases. An intuitively satisfying way to appreciate this fact follows from consideration of the basic inequality No. 6 described earlier. Because contrast (other than zero) defined in relation to the background,
Fig. 2. Arbitrary intensity distribution for which modulation and contrast are determined as a function of spatial frequency in analogy with the modulation transfer function. The dotted curve indicates the underlying hypothetical step function.
contrast characteristics of a complete system. If both components, CLBand CLT,are weighted evenly, then it is easy to show that their reciprocal sum determines the modulation of the system, i.e.: No. 18 where
M EI LT- LBI = modulation. LT
Hence, modulation may be considered an unambiguous measure of system contrast. Note also that signal contrast ratio, C,, as defined in equation No. 7, is just twice the modulation. Because Weber’s law holds only for a limited range of simple stimuli located in close proximity, the perceptual significance of contrast defined in terms of intensity differences separated by space or time is an open question. Indeed most recent psychophysical determinations dealing with the temporal and spatial responsesof the visual system have been
it is necessaryto take both equations Nos. 16 and 17 into account if one is to adequately describe the
rather than in terms of contrast. For this reason and because modulation has been rigorously defined in terms of the MTF for linear systems, it seems
cannot be the same as that defined relative to the target, c
measured in terms of modulation
as defined above5
reasonable to consider the spatial aspectsof contrast in comparable terms. Consider the contrast exhibited by a finite change in intensity produced by the image of an “edge” as shown in Fig. 2. Under these conditions it is obvious that contrast will vary depending on the distance over which the change in intensity is measured and on the convention used to determine target versus background. If one considers the shape of this intensity function to be the result of convolution of a step (shown dotted in Fig. 2) with the line-spread function determined by differentiating the original intensity function, then, by definition, a one-dimensional MTF can be obtained from Fourier transformation of the equivalent line-spread function. An analogous case can be made for two dimensions by substituting point-spread function for line-spread function in the argument above. All that remains is to relate modulation determined in this way to CL, and GT, depending on the convention used to determine target and background via equation No. 18. This method for expressing contrast in terms of the MTF and vice versa holds for linear systems whenever the change in attenuation responsible for the intensity difference is known to be a simple step function. In situations where this is not the case it is still possible to define contrast analogously in terms of modulation expressed as a function of spatial frequency. However, under these conditions the result is unrelated to the MTF of the system, being determined entirely by the localized spatial distribution of intensities in the region of interest. It is also important to recognize that this relationship between modulation and contrast varies with the definition of contrast. In the absenceof scatter, modulation produced by x-rays impinging on tissues having different attenuations may be computed from the following equations: X, = Xoe-(@Or)T No. 20 x, = x e-(rPr) No. 21 X, = eiposure reaching the detector where associated with the target X, = exposure reaching the detector associated with the background X, = incident exposure e = base of natural logarithms P = mass attenuation coefficient p = mass density T = thickness (rp’)T= attenuation factor associated with the target region
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(pp’JB = attenuation factor associated with the background. Expressing these functions in terms of luminance and substituting into No. 19 yields: M=I
BI e-r(uoT)T + e-r(rPT)B
where y is defined by No. 11. If we treat the difference in attenuation between the target and background tissues as deviations, A(pp~),,,, from a mean, we can simplify equation No. 22 by expressing it as a hyperbolic tangent.
From equation No. 23 it is obvious that modulation is influenced uniformly by y and by all the parameters determining the linear attenuation of the tissues of interest. Less apparent is the fact that the hyperbolic tangent may be considered linear for values less than 0.5 with an error of less than 10 percent. This means that the modulation may be considered nearly proportional to A(cL~T),,,and to y when it has a value of 0.5 or less. Unfortunately, in common radiographic systems, modulation (so defined) can vary also with exposure in another way becausey may not be independent of exposure. The resulting lack of linearity in the input-output relationship between exposure and optical density changes the MTF and precludes rigorous direct application of linear theory to radiographic systems.
Some investigators have approached this impasse by defining special transfer functions that, in effect, are derived from linearized input-output relationships.13Others restrict application to domains within which the input-output relationship may be considered linear.14Still others suggest that the system be considered as containing a linear element plus one or more nonlinear components and limit consideration of the MTF to only that element presumed to be linear.14 When such considerations lead to relating output to input modulation of an active system or a system which relates two components which are physically different, it is possible for the output modulation to exceed one as exemplified by the radiographic modulation transfer functions described by Fender.‘) This leads to another basis for semantic confusion because any value greater than one lies outside the possible range of modulations as shown below:
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M>l ifILT-L’I> LT + L,
1 No. 24
the&-&-LT+Lr, which is a contradiction. Hence, in such applications only modulation of the input can be defined using expressions of the type shown in equation No. 19. Another point to remember is that some potential information about the image is always lost by any real operation that changes contrast. This is true even when contrast has been increased by the process.Of course, if such information is manifest at a contrast too small to be reliably appreciated by the human eye or other detector, then the loss of information associated with contrast enhancement may be justified. The relationship between contrast and ultimate detectability of diagnostic information is the subject of a comprehensive paper by Motz and Danos,8 which systematically explains the physical limitations of ideal detectors. Consideration of the relationship between information capacity and contrast that is manifest in real systems is also important. When other factors, such as exposure, geometry, etc., are held constant, the modulation-transfer function determines the maximum amount of radiographic information which can be recorded by the system.15However, when contrast is influenced by changing the amount and/or spatial distribution of modulated radiation, the capacity for recording information also depends largely on the dynamic range of the detector and its ability to detect discrete photon events.14 A final consideration is the fact that the perceptual impact of contrast can be augmented by a variety of schemesto enhance images that trade changes in intensity for other modes of display. Techniques applied in other disciplines include pseudocolor coding, isometric projection, stereoscopic display of differences presented in the third dimension, etc. Because the visual system is profoundly influenced by environmentally familiar spatial patterns, contrast enhancement, per se, should be viewed as only one of many promising techniques for improving the visual interpretability of radiographic images. SUMMARY
Contrast may be defined as a relative change in intensity. When expressed as a perceptual stimulus, contrast is a reasonably uniform measure of detectability by human observers, although other factors render human detection context dependent. In radio-
logic systems, contrast is created by differences in tissue attenuation and modified by other elements in the radiographic chain. When the change in intensity is finite, it is necessary to carefully define the limits of change becauseambiguities result from the use of imprecise basesfor normalization. When normalization is performed in a balanced fashion, contrast may be considered modulation as defined in communication theory. As a result, contrast is influenced by the spatial-frequency characteristics of the system used to create the image. Contrast at any spatial frequency obtainable from a radiographic system can be meaningfully determined by an analysis of the modulation transfer function when the line-spread function is known and constant, and when system gain is independent of exposure. Special transfer functions permit nonlinearities in system response to be taken into account. All elements in the imaging system possessthe potential for either increasing or decreasing contrast in ways which may render the image more interpretable but always at the expenseof some loss of information. Information loss of this type is intuitively obvious when contrast is enhanced by adding photon fog to the image. New modes of display promise to enhance the perceptual impact of complex patterns having a wide range of contrasts. The author is indebted and grateful to Drs. Urs Ruttimann and Hans Grondahl for technical and editorial suggestions which have found their way into the preparation of this paper.
1. Graham, C. H.: Vision and Visual Perception, New York, 1965, John Wiley & Sons, Inc., pp. 6%69,229. 2. Johns. H. E.. and Cunninaham. J. R.: The Phvsics of Radiology, Springfield, Ill., i974, ‘Charles C Thomas, Publisher, pp. 605-614. 3. Ter-Pogossian, M. M.: The Physical Aspects of Diagnostic Radiology, New York, 1967, Harper & Row, Publishers pp. 212-215. 4. Rossman, K.: Image Quality, United States Department of Health, Education, and Welfare Publication No. (FDA) 74-8006, pp. 220-281. 5. Cornsweet, T. N.: Visual Perception, New York, 1970, Academic Press, Inc., pp. 224-418. 6. Ratliff, F.: Mach Bands: Quantitative Studies on Neural Networks in the Retina, San Francisco, 1965, Holden-Day, p. 126. 7. Rosenblith, W. A.: Sensory Communication, New York, 1959, M.I.T. Press, p. 796. 8. Motz, J. W., and Danos, M.: Image Information Content and Patient Exposure, Physics Phys. 5: 8-22, 1978. 9. Wagner, R. F.: Toward a Unified View of Radiological Imaging Systems. Part II. Noisy Images, presented at the Fourth International Conference on Medical Physics, Ottawa, Ontario, Canada, July, 1976. 10. Weyl, C., and Warren, S. R., Jr.: Radiological Physics, Springfield, Ill., 1951, Charles C Thomas, Publisher, p. 392. 11. Oishi, T. T., and Webber, R. L.: Effect of Fog on Contrast in
October, 1982 Dental Radiographs, presented at Annual General Session of the American Association for Dental Research, June 23-26, 1977, Las Vegas, Nev. 12. Wahl. P.: Lights Inside the Camera‘? Pop. Sci. :49-50, July,
1977. 13. Fender, W. D.: Radiographic Image Analysis Through Application of the Radiographic Modulation Transfer Function and System Phase Response, presented at the SPLE Seminar on Quantitative Imaging in the Biomedical Sciences, May 10-12, 1971, Houston, Texas. 14. Dainty, J. E., and Shaw, R.: Image Science, New York, 1974, Academic Press, Inc., pp. 232-237.
15. Gregg, E. C.: Assessment of Radiologic Imaging, Am. J. of Roentgenol. Radium Ther. Nucl. Med. 97: 776-792, 1966. Reprint requests to. Dr. Richard L. Webber Chief, Diagnostic Systems Branch National Institute of Dental Research Building 10, Room 5N-256 9000 Rockville Pike Bethesda, Md. 20205
The September, 1981, issue of the JOURNAL (Duckworth, Webber, Youmans, and Fewell: The Effects of Spectral Distribution on X-ray Image Quality) did not properly acknowledge contributions of various authors and their respective organizations for the effects of spectral distribution on x-ray image quality: J. E. Duckworth, R. L. Webber, H. Youmans, and T. R. Fewell, Bethesda, Maryland, National Institute of Dental Research and Division of Biological Effects, and Division of Electronic Products, Bureau of Radiological Health.