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23 2 PSYCHOPHYSICAL VISION PROPERTIES For efficient design of imaging systems for which the output is a photograph or dis- play to be viewed by a human observer, it is obviously beneficial to have an under- standing of the mechanism of human vision. Such knowledge can be utilized to develop conceptual models of the human visual process. These models are vital in the design of image processing systems and in the construction of measures of image fidelity and intelligibility. 2.1. LIGHT PERCEPTION Light, according to Webster's Dictionary (1), is “radiant energy which, by its action on the organs of vision, enables them to perform their function of sight.” Much is known about the physical properties of light, but the mechanisms by which light interacts with the organs of vision is not as well understood. Light is known to be a form of electromagnetic radiation lying in a relatively narrow region of the electro- magnetic spectrum over a wavelength band of about 350 to 780 nanometers (nm). A physical light source may be characterized by the rate of radiant energy (radiant intensity) that it emits at a particular spectral wavelength. Light entering the human visual system originates either from a self-luminous source or from light reflected from some object or from light transmitted through some translucent object. Let represent the spectral energy distribution of light emitted from some primary light source, and also let and denote the wavelength-dependent transmis- sivity and reflectivity, respectively, of an object. Then, for a transmissive object, the observed light spectral energy distribution is (2.1-1) E λ() t λ() r λ() C λ() t λ()E λ()= Digital Image Processing: PIKS Inside, Third Edition. William K. Pratt Copyright © 2001 John Wiley & Sons, Inc. ISBNs: 0-471-37407-5 (Hardback); 0-471-22132-5 (Electronic) 24 PSYCHOPHYSICAL VISION PROPERTIES and for a reflective object (2.1-2) Figure 2.1-1 shows plots of the spectral energy distribution of several common sources of light encountered in imaging systems: sunlight, a tungsten lamp, a FIGURE 2.1-1. Spectral energy distributions of common physical light sources. C λ() r λ()E λ()= LIGHT PERCEPTION 25 light-emitting diode, a mercury arc lamp, and a helium–neon laser (2). A human being viewing each of the light sources will perceive the sources differently. Sun- light appears as an extremely bright yellowish-white light, while the tungsten light bulb appears less bright and somewhat yellowish. The light-emitting diode appears to be a dim green; the mercury arc light is a highly bright bluish-white light; and the laser produces an extremely bright and pure red beam. These observations provoke many questions. What are the attributes of the light sources that cause them to be perceived differently? Is the spectral energy distribution sufficient to explain the dif- ferences in perception? If not, what are adequate descriptors of visual perception? As will be seen, answers to these questions are only partially available. There are three common perceptual descriptors of a light sensation: brightness, hue, and saturation. The characteristics of these descriptors are considered below. If two light sources with the same spectral shape are observed, the source of greater physical intensity will generally appear to be perceptually brighter. How- ever, there are numerous examples in which an object of uniform intensity appears not to be of uniform brightness. Therefore, intensity is not an adequate quantitative measure of brightness. The attribute of light that distinguishes a red light from a green light or a yellow light, for example, is called the hue of the light. A prism and slit arrangement (Figure 2.1-2) can produce narrowband wavelength light of varying color. However, it is clear that the light wavelength is not an adequate measure of color because some colored lights encountered in nature are not contained in the rainbow of light produced by a prism. For example, purple light is absent. Purple light can be produced by combining equal amounts of red and blue narrowband lights. Other counterexamples exist. If two light sources with the same spectral energy distribu- tion are observed under identical conditions, they will appear to possess the same hue. However, it is possible to have two light sources with different spectral energy distributions that are perceived identically. Such lights are called metameric pairs. The third perceptual descriptor of a colored light is its saturation, the attribute that distinguishes a spectral light from a pastel light of the same hue. In effect, satu- ration describes the whiteness of a light source. Although it is possible to speak of the percentage saturation of a color referenced to a spectral color on a chromaticity diagram of the type shown in Figure 3.3-3, saturation is not usually considered to be a quantitative measure. FIGURE 2.1-2. Refraction of light from a prism. 26 PSYCHOPHYSICAL VISION PROPERTIES As an aid to classifying colors, it is convenient to regard colors as being points in some color solid, as shown in Figure 2.1-3. The Munsell system of color classification actually has a form similar in shape to this figure (3). However, to be quantitatively useful, a color solid should possess metric significance. That is, a unit distance within the color solid should represent a constant perceptual color difference regardless of the particular pair of colors considered. The subject of perceptually significant color solids is considered later. 2.2. EYE PHYSIOLOGY A conceptual technique for the establishment of a model of the human visual system would be to perform a physiological analysis of the eye, the nerve paths to the brain, and those parts of the brain involved in visual perception. Such a task, of course, is presently beyond human abilities because of the large number of infinitesimally small elements in the visual chain. However, much has been learned from physio- logical studies of the eye that is helpful in the development of visual models (4–7). FIGURE 2.1-3. Perceptual representation of light. EYE PHYSIOLOGY 27 Figure 2.2-1 shows the horizontal cross section of a human eyeball. The front of the eye is covered by a transparent surface called the cornea. The remaining outer cover, called the sclera, is composed of a fibrous coat that surrounds the choroid, a layer containing blood capillaries. Inside the choroid is the retina, which is com- posed of two types of receptors: rods and cones. Nerves connecting to the retina leave the eyeball through the optic nerve bundle. Light entering the cornea is focused on the retina surface by a lens that changes shape under muscular control to FIGURE 2.2-1. Eye cross section. FIGURE 2.2-2. Sensitivity of rods and cones based on measurements by Wald. 28 PSYCHOPHYSICAL VISION PROPERTIES perform proper focusing of near and distant objects. An iris acts as a diaphram to control the amount of light entering the eye. The rods in the retina are long slender receptors; the cones are generally shorter and thicker in structure. There are also important operational distinctions. The rods are more sensitive than the cones to light. At low levels of illumination, the rods provide a visual response called scotopic vision. Cones respond to higher levels of illumination; their response is called photopic vision. Figure 2.2-2 illustrates the relative sensitivities of rods and cones as a function of illumination wavelength (7,8). An eye contains about 6.5 million cones and 100 million cones distributed over the retina (4). Figure 2.2-3 shows the distribution of rods and cones over a horizontal line on the retina (4). At a point near the optic nerve called the fovea, the density of cones is greatest. This is the region of sharpest photopic vision. There are no rods or cones in the vicin- ity of the optic nerve, and hence the eye has a blind spot in this region. FIGURE 2.2-3. Distribution of rods and cones on the retina. VISUAL PHENOMENA 29 In recent years, it has been determined experimentally that there are three basic types of cones in the retina (9, 10). These cones have different absorption character- istics as a function of wavelength with peak absorptions in the red, green, and blue regions of the optical spectrum. Figure 2.2-4 shows curves of the measured spectral absorption of pigments in the retina for a particular subject (10). Two major points of note regarding the curves are that the cones, which are primarily responsible for blue light perception, have relatively low sensitivity, and the absorption curves overlap considerably. The existence of the three types of cones provides a physio- logical basis for the trichromatic theory of color vision. When a light stimulus activates a rod or cone, a photochemical transition occurs, producing a nerve impulse. The manner in which nerve impulses propagate through the visual system is presently not well established. It is known that the optic nerve bundle contains on the order of 800,000 nerve fibers. Because there are over 100,000,000 receptors in the retina, it is obvious that in many regions of the retina, the rods and cones must be interconnected to nerve fibers on a many-to-one basis. Because neither the photochemistry of the retina nor the propagation of nerve impulses within the eye is well understood, a deterministic characterization of the visual process is unavailable. One must be satisfied with the establishment of mod- els that characterize, and hopefully predict, human visual response. The following section describes several visual phenomena that should be considered in the model- ing of the human visual process. 2.3. VISUAL PHENOMENA The visual phenomena described below are interrelated, in some cases only mini- mally, but in others, to a very large extent. For simplification in presentation and, in some instances, lack of knowledge, the phenomena are considered disjoint. FIGURE 2.2-4. Typical spectral absorption curves of pigments of the retina. α 30 PSYCHOPHYSICAL VISION PROPERTIES . Contrast Sensitivity. The response of the eye to changes in the intensity of illumina- tion is known to be nonlinear. Consider a patch of light of intensity surrounded by a background of intensity I (Figure 2.3-1a). The just noticeable difference is to be determined as a function of I. Over a wide range of intensities, it is found that the ratio , called the Weber fraction, is nearly constant at a value of about 0.02 (11; 12, p. 62). This result does not hold at very low or very high intensities, as illus- trated by Figure 2.3-1a (13). Furthermore, contrast sensitivity is dependent on the intensity of the surround. Consider the experiment of Figure 2.3-1b, in which two patches of light, one of intensity I and the other of intensity , are sur- rounded by light of intensity . The Weber fraction for this experiment is plotted in Figure 2.3-1b as a function of the intensity of the background. In this situation it is found that the range over which the Weber fraction remains constant is reduced considerably compared to the experiment of Figure 2.3-1a. The envelope of the lower limits of the curves of Figure 2.3-lb is equivalent to the curve of Figure 2.3-1a. However, the range over which is approximately constant for a fixed background intensity is still comparable to the dynamic range of most electronic imaging systems. FIGURE 2.3-1. Contrast sensitivity measurements. ( a ) No background ( b ) With background I ∆I+ ∆I ∆II⁄ I ∆I+ I o ∆II⁄ ∆II⁄ I o VISUAL PHENOMENA 31 FIGURE 2.3-2. Mach band effect. ( a ) Step chart photo ( c ) Ramp chart photo B D ( d ) Ramp chart intensity distribution ( b ) Step chart intensity distribution 32 PSYCHOPHYSICAL VISION PROPERTIES Because the differential of the logarithm of intensity is (2.3-1) equal changes in the logarithm of the intensity of a light can be related to equal just noticeable changes in its intensity over the region of intensities, for which the Weber fraction is constant. For this reason, in many image processing systems, operations are performed on the logarithm of the intensity of an image point rather than the intensity. Mach Band. Consider the set of gray scale strips shown in of Figure 2.3-2a. The reflected light intensity from each strip is uniform over its width and differs from its neighbors by a constant amount; nevertheless, the visual appearance is that each strip is darker at its right side than at its left. This is called the Mach band effect (14). Figure 2.3-2c is a photograph of the Mach band pattern of Figure 2.3-2d. In the pho- tograph, a bright bar appears at position B and a dark bar appears at D. Neither bar would be predicted purely on the basis of the intensity distribution. The apparent Mach band overshoot in brightness is a consequence of the spatial frequency response of the eye. As will be seen shortly, the eye possesses a lower sensitivity to high and low spatial frequencies than to midfrequencies. The implication for the designer of image processing systems is that perfect fidelity of edge contours can be sacrificed to some extent because the eye has imperfect response to high-spatial- frequency brightness transitions. Simultaneous Contrast. The simultaneous contrast phenomenon (7) is illustrated in Figure 2.3-3. Each small square is actually the same intensity, but because of the dif- ferent intensities of the surrounds, the small squares do not appear equally bright. The hue of a patch of light is also dependent on the wavelength composition of sur- rounding light. A white patch on a black background will appear to be yellowish if the surround is a blue light. Chromatic Adaption. The hue of a perceived color depends on the adaption of a viewer (15). For example, the American flag will not immediately appear red, white, and blue if the viewer has been subjected to high-intensity red light before viewing the flag. The colors of the flag will appear to shift in hue toward the red complement, cyan. FIGURE 2.3-3. Simultaneous contrast. dIlog() dI I -----=