Spie Press BookContrast Sensitivity of the Human Eye and Its Effects on Image Quality
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- 1 Introduction 1 References 5
- 2 Modulation threshold and noise 7
- 2.1 Introduction
- 2.2 Psychometric function 8
- 2.3 Basic properties of image noise 15
- 2.4 Effect of noise on modulation threshold 18
- 2.5 Summary and conclusions 22
- References 22
- 3 Model for the spatial contrast sensitivity of the eye 25
- 3.1 Introduction 25
- 3.2 Outline of the model 25
- 3.3 Optical MTF 27
- 3.4 Photon noise 29
- 3.5 Neural noise 31
- 3.6 Lateral inhibition 32
- 3.7 Monocular versus binocular vision 36
- 3.8 Complete model 36
- 3.9 Comparison with measurements 38
- 3.9.1 Measurements by DePalma and Lowry 38
- 3.9.2 Measurements by Patel 39
- 3.9.3 Measurements by Robson 40
- 3.9.4 Measurements by van Nes and Bouman
- 3.9.5 Measurements by Campbell and Robson 44
- 3.9.6 Measurements by Watanabe et al. 45
- 3.9.7 Measurements by Sachs et al. 46
- 3.9.8 Measurements by van Meeteren and Vos 48
- 3.9.9 Measurements by Howell and Hess 49
- 3.9.10 Measurements by Virsu and Rovamo 50
- 3.9.11 Measurements by Carlson 51
- 3.9.12 Measurements by Rovamo et al. (1992) 52
- 3.9.13 Measurements by Rovamo et al. (1993a) 54
- 3.9.14 Measurements by Rovamo et al. (1993b) 55
- 3.9.15 Survey of the measurements 56
- 3.10 Summary and conclusions 57
- Appendix A. Photon conversion factor 58
- References 62
- 4 Extension of the contrast sensitivity model to extra-foveal vision 65
- 4.1 Introduction 65
- 4.2 Density distribution of cones and ganglion cells 66
- 4.2.1 Geometrical relations 66
- 4.2.2 Cone density distribution 67
- 4.2.3 Ganglion cell density distribution 69
- 4.3 Effect of eccentricity on the different constants used in the model
- 4.3.1 Effect of eccentricity on resolution 72
- 4.3.2 Effect of eccentricity on neural noise 74
- 4.3.3 Effect of eccentricity on lateral inhibition 75
- 4.3.4 Effect of eccentricity on quantum efficiency 76
- 4.3.5 Effect of eccentricity on the maximum integration area 77
- 4.4 Comparison with measurements 78
- 4.4.1 Measurements by Virsu and Rovamo 79
- 4.4.2 Measurements by Robson and Graham 81
- 4.4.3 Measurements by Kelly 83
- 4.4.4 Measurements by Mayer and Tyler 84
- 4.4.5 Measurements by Johnston 85
- 4.4.6 Measurements by Pointer and Hess 86
- 4.4.7 Survey of the measurements 88
- 4.5 Summary and conclusions 89
- References 90
- 5 Extension of the contrast sensitivity model to the temporal domain 91
- 5.1 Introduction 91
- 5.2 Generalization of the spatial contrast sensitivity model 92
- 5.3 Temporal filter functions 93
- 5.4 Spatiotemporal contrast sensitivity measurements 94
- 5.5 Temporal contrast sensitivity measurements 98
- 5.6 Effect of a surrounding field 100
- 5.7 Effect of retinal illuminance and field size on the time constants
- 5.8 Flicker sensitivity: Ferry-Porter law 110
- 5.9 Temporal impulse response 114
- 5.10 Summary and conclusions 116
- References 117
- 6 Effect of nonwhite spatial noise on contrast sensitivity 121
- 6.1 Introduction 121
- 6.2 Model for the masking effect of nonwhite spatial noise 121
- 6.3 Measurements with narrow noise bands by Stromeyer and Julesz 124
- 6.4 Measurements with nonwhite noise by van Meeteren and Valeton 127
- 6.5 Summary and conclusions 129
- References 130
- 7 Contrast discrimination model 131
- 7.1 Introduction 131
- 7.2 Evaluation of the psychometric function 132
- 7.3 Evaluation of the contrast discrimination model 136
- 7.4 Comparison with contrast discrimination measurements 139
- 7.5 Generalized contrast discrimination model 143
- 7.6 Summary and conclusions 147
- References 147
- 8 Image quality measure 149
- 8.1 Introduction 149
- 8.2 Nonlinear effect of modulation 150
- 8.3 Image quality metrics 154
- 8.3.1 Modulation transfer area (MTFA) 155
- 8.3.2 Integrated contrast sensitivity (ICS) 155
- 8.3.3 Subjective quality factor (SQF) 156
- 8.3.4 Discriminable difference diagram (DDD) 156
- 8.3.5 Square-root integral (SQRI) 157
- 8.4 Two-dimensional aspects 158
- 8.5 Functional analysis of image quality metrics 159
- 8.6 Effect of differently shaped MTFs 165
- 8.7 Summary and conclusions 169
- References 169
- 9 Effect of various parameters on image quality 171
- 9.1 Introduction 171
- 9.2 Resolution and image size 172
- 9.3 Luminance and image size 174
- 9.4 Anisotropic resolution 176
- 9.5 Viewing distance, display size, and number of scan lines size 177
- 9.6 Contrast 179
- 9.7 Gamma 181
- 9.8 Noise 185
- 9.9 Pixel density and luminance quantization 190
- 9.10 Summary and conclusions 193
- References 194
- 10 Epilogue 197
- Summary 199
- Samenvatting 203
- Acknowledgement 207
- Curriculum Vitae 209
The eye plays an important role in our life, not only for seeing objects in the surrounding world, but also for reading letters, viewing paintings, photographs, films, etc. The visual acuity of the eye is generally concerned as the most important factor for the ability of the eye for seeing objects. The acuity of the eye is usually measured by acuity tests where single black letters on a white background have to be recognized, or where the minimum visible separation is measured of black rings with a small interrupted part (Landolt rings). These tests are used for decisions about the use of certain types of eye glasses, but give no information about several other factors that also play a role in the properties of the human visual system.
Objects can generally better be distinguished from each other or from their background, if the difference in luminance or color is large. Of these two factors, luminance plays the most important role. This study will, therefore, be concentrated on luminance, and color will be left out of consideration. In practice, it appears that not the absolute difference in luminance is important, but the relative difference. This relative difference can be expressed by the ratio between two luminance values, which is called contrast ratio, or by the difference between two luminance values divided by the sum of them, which is simply called contrast. Both are dimensionless quantities. Objects that have only a small contrast with respect to their background are difficult to observe. The eye is more sensitive for the observation of objects, if the required amount of contrast is lower. The reciprocal of the minimum contrast required for detection is called contrast sensitivity.
For the investigation of the visual properties of the eye, different types of test patterns can be used. Generally sinusoidal test patterns are used for this purpose, as sinusoidal test patterns have an important advantage. According to Fourier analysis, the luminance pattern of an image can be considered as the sum of a number of sinusoidal luminance variations. As far as the visual system can be described by a linear system, the visibility of an image can be predicted with the aid of a Fourier analysis based on the sensitivity of the eye for sinusoidal luminance variations. Although the image forming process in the human eye is not completely linear, Fourier analysis can still be used for the area near the detection threshold, since the response may be assumed to be linear in that area. The use of Fourier analysis for the description of the reproduction capability of an imaging system has been introduced by Schade (1951-1955). He used it first for television systems, where the effect of cameras, signal transport and image tubes on the reproduced image can be described with the aid of Fourier analysis. Later he applied it also on the human eye as the final step in the image forming process (Schade, 1956). In this respect, also the work of Campbell & Robson (1968) may be mentioned, who stimulated the application of Fourier analysis and the use of sinusoidal test patterns for the investigation of the visual sensitivity of the eye.
For a sinusoidal luminance pattern, contrast is defined by the amplitude of the sinusoidal variation divided by the average luminance. This quantity is called modulation depth, or shortly modulation. The minimum modulation required for the detection of this pattern is called the modulation threshold. As the contrast sensitivity is usually measured with sinusoidal luminance variations, the contrast sensitivity of the eye is generally defined as the reciprocal of the modulation threshold. The modulation threshold generally depends on the wavelength of the sinusoidal luminance variation, i.e., the distance between the maxima. The reciprocal of this wavelength is called spatial frequency. The contrast sensitivity is usually expressed as a function of this spatial frequency.
Apart from spatial luminance variations, often also temporal luminance variations occur. The contrast sensitivity of the eye for these variations can be described in the same way as for spatial luminance variations. In this case the spatial frequency has to be replaced by the temporal frequency. For the investigation of the effect of temporal luminance variations, the pioneering work by de Lange (1952, 1954) and by Kelly (1961) may be mentioned, who both applied Fourier analysis at the evaluation of temporal luminance variations.
Contrast sensitivity is sometimes measured with a periodic non-sinusoidal luminance variation. In these cases, contrast is determined by the difference between the maximum and minimum luminance divided by the sum of them. Contrast defined in this way is called Michelson contrast. For a sinusoidal luminance variation, the Michelson contrast is equal to the modulation. For a repeated non-sinusoidal luminance pattern, the equivalent sinusoidal modulation can be found by calculating the fundamental wave of this pattern with the aid of a Fourier analysis. For a square wave pattern, for instance, the modulation of the fundamental wave is 4/( times the Michelson contrast. This has to be taken into account in the evaluation of contrast sensitivity data obtained from this type of measurements.
Knowledge of the contrast sensitivity function is important for the understanding of the visual properties of the eye. Contrary to the calorimetric sensitivity curves of the eye adopted as standard by the CIE (Commission International de l'Eclairage), there exists no such standard for the contrast sensitivity function of the eye. Beyond the spatial or temporal frequency of the luminance pattern, the contrast sensitivity of the eye also depends on other parameters, like luminance and field size. Defining a standard would be difficult because of the strong dependence of the contrast sensitivity on these parameters. A practical expression for the spatial contrast sensitivity function, where also these two parameters were taken into account, has been given some years ago by the author (Barten, 1990). It is an approximation fonntaa based on contrast sensitivity measurements by van Meeteren & Vos (1972) for a large range of luminance levels and on contrast sensitivity measurements by Carlson (1982) for a large range of field sizes. Although in this way a practical solution was found for technical applications, the formula gives no insight in the fundamental basis of the contrast sensitivity of the eye.
The main purpose of this study is to give equations for various aspects of contrast sensitivity based on fundamental assumptions about the functioning of the human eye. From these assumptions, models for the contrast sensitivity will be derived that give not only a qualitative description of contrast sensitivity but also a quantitative description. The models will be given in the form of mathematical expressions that can easily be used for practical applications. The so obtained models will extensively be compared with published measurements. The central idea of these models is the assumption that contrast sensitivity is determined by internal noise in the visual system. A part of these models was already shortly mentioned by the author in earlier publications (Barten, 1992, 1993, 1995). For practical reasons the use of the models is restricted to photopic luminance conditions. In practice, most spatial contrast sensitivity measurements are made with sinusoidal patterns in horizontal or vertical direction. In these directions, the contrast sensitivity appears to be equal. Although the contrast sensitivity of the eye can be slightly different in intermediate directions, the effect of an orientation different from the horizontal or vertical direction will be omitted, as this effect is generally very small.
In Chapter 2 first an insight will be given in the psychometric function with which the modulation threshold can be determined in a well-defined way. Based on the assumption that the contrast sensitivity is caused by internal noise, a formula will be given for the calculation of the modulation threshold from the noise. Furthermore, expressions will be given for the basic properties of image noise and for the limits of the visual system at the processing of the noise. These expressions will be used in the following chapters.
In Chapter 3 a model will be given for the spatial contrast sensitivity of the eye based on internal noise in the visual system. For this model additional assumptions will be made for the optical modulation transfer by the eye and the neural process of lateral inhibition. The model given in this chapter forms the basis of the models used in the other chapters.
The model given in Chapter 3 is restricted to the normal condition of foveal vision where the center of the object is imaged on the center of the retina. Sometimes extra-foveal vision is used to observe objects that are outside the area which the eye is concentrated. At extra-foveal vision, contrast sensitivity is reduced because of the non-homogeneity of the retina that has its optimum efficiency in the center. In Chapter 4, the model for foveal vision given in Chapter 3 will be extended to extra-foveal vision by making some assumptions about the variation of the numerical constants used in the model with increasing eccentricity.
In Chapter 5, the model given in Chapter 3 for the spatial contrast sensitivity will be extended to the temporal domain by using some additional assumptions about the temporal behavior of the neural elements that play a role in the transport of information. In this way a combined spatiotemporal contrast sensitivity model is obtained. With this model also flicker effects occurring at the display of television and computer images can be explained.
The contrast sensitivity can also be influenced by the presence of noise in a displayed image. Although the most common type of noise is white noise, also nonwhite noise can also sometimes influence the contrast sensitivity. In Chapter 6 a generalization will be made of the expressions for white noise given in Chapter 2. This generation is based on the assumption of a distribution function that describes the masking of one spatial frequency by the presence of another spatial frequency.
Besides experiments with contrast detection, where a distinction has to be made between the object and a uniformly illuminated background, sometimes also experiments are made with contrast discrimination, where a distinction has to be made between two sinusoidal signals with a small difference in modulation. In Chapter 7, a model will be given for contrast discrimination. The model is based on the assumption that contrast discrimination can be considered as a special form of masking by nonwhite noise. With this model, the typical dipper shaped curves of the measurement results can be explained.
Visual aspects play an important role in the judgment of image quality. In Chapter 8 a measure will be given for the perceived quality of an image. As images largely contain modulations at suprathreshold level, not only the contrast sensitivity of the eye at threshold level is important, but also the sensitivity of the eye at higher modulation levels. Although the contrast sensitivity is defined at threshold level, it is also related to the sensitivity of the eye at higher modulation levels. In this chapter a model will be given for the nonlinear behavior of the eye at suprathreshold levels of modulation. For this model use is made of the linear relation between perceived image quality and the number of just-noticeable differences that can be derived from the contrast discrimination model given in the previous chapter. An image quality measure will be given that is based on this model. This measure is called square-root integral or SQRI. This measure was already published by the author some years ago (Barten, 1990). It was only based on practical experience mathout the more basic information that AiU be given here. In this chapter also an analysis will be given of the functional suitability of various image quality measures for the description of perceived image quality.
In Chapter 9 an analysis will be given of the effect of various parameters on image quality with the aid of the image quality measure given in the previous chapter. The results will be comparted with published measurements of perceived image quality.
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