Hall, R.: Illumination and Color in Computer Generated Imagery. Springer-Verlag (1989)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of refraction in computer graphics, based on Snell s law, was put forward by Kay [13] Whitted [14] later included refraction in a general recursive ray tracing framework. Other effects such as shadows, reflections, global illumination and texturing have long been implemented in surface graphics [15, 16]. There is a trend towards the acceptance and introduction of these rendering effects in volume graphics, for example in vlib [7, 1, 8, 19] however there are few discussions of refraction in volume graphics literature. Critical to implementing refraction in a discrete ray tracer is the problem ....

R. Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag, New York, (1989).

.... While this model is close to the physiological characteristics of the human retina, it is unable to reproduce the real behavior of physical light and physical colored objects [9, 6] For this reason many authors have proposed to consider spectral color models for accurate color manipulations [19, 14, 20, 11, 21, 12, 16]. Let us brie y recall the basis of spectral color models[25] Given a spectral distribution function E( it is possible to compute the CIE 1931 XYZ representation of the color of E( by using the three CIE sensibility functions x( y( z( E( x( d ; E( y( d ; Z = ....

R.H. Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, 1989.

....all spectra with the same XYZ coordinates should be perceived as the same colour by normal human observers. Such perceptually equivalent spectra are called metamers. A 3 Theta 3 matrix multiplication can convert XYZ colour coordinates to any desired linear trichromatic colour coordinate system [7]. Given the XYZ coordinates of a set of phosphors on a monitor, a matrix M can easily be derived to convert from XYZ coordinates to the monitor s RGB phosphor space, at least for colours within the gamut of the monitor and within the limits of an assumption of linearity [3, 5] The traditional ....

....two spectra can interact by multiplication (reflection and absorption) using a trichromatic representation to compute the interaction of spectra can lead to major colour and illumination errors. In particular, absorption cannot be correctly handled using only trichromatic colour computations [7] due to its nonlinear exp( Gammaff( z) factor. In the case of reflection, elementwise multiplication of colour coordinates is equivalent to spectral multiplication if and only if the basis functions used to reconstruct the spectra are nonoverlapping box functions. For only three colour ....

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Roy Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, 1989.

....matching functions. Then we integrate numerically the product over the visible spectrum: where , are the tristimulus values, are colour matching functions defined by the CIE. The normalizing constant should be chosen such that the resulting BRDF is not brighter or dimmer than before [Hal89] The tristimulus values , still need to be converted to RGB. This is done by the following computation: where is a matrix chosen to match the particular display device [Hal89] The whole computation has to be done for each combination of and when the BRDF is initially sampled. We then ....

....the CIE. The normalizing constant should be chosen such that the resulting BRDF is not brighter or dimmer than before [Hal89] The tristimulus values , still need to be converted to RGB. This is done by the following computation: where is a matrix chosen to match the particular display device [Hal89] The whole computation has to be done for each combination of and when the BRDF is initially sampled. We then create three BRDF maps out of the three data sets (i.e. we run three SVDs) and merge the three BRDF maps into one. This is done in the same way as seen in Equation 4.4, i.e. we scale ....

Roy Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, New York, 1989.

....described in Equation 5 in logarithmic space by minimizing RMS error, we will in fact be minimizing relative RMS error for the solution to the original nonlinear problem. This is perceptually desirable, since the eye seems to be roughly sensitive to ratios of intensity, not absolute intensity [7, 13]. 3.2 Parameterization Despite the potential generality of our approach, in this paper we will limit ourselves (mostly) to a three factor approximate BRDF representation and a very simple parameterization that reuses one of two texture maps: h = norm(#o # i ) 8) p(#o ) q( h) p(# i ) ....

R. Hall. Illumination and Color in Computer Generated Imagery. SpringerVerlag, 1989.

....These simulations are typically long running, CPUintensive computations [38] The Monte Carlo sampling is typically performed by evaluating the light spectrum that enters a virtual camera. Since the computation is done in spectral units, it must be transformed into RGB colors suitable for display [41]. To complicate matters, the resulting RGB colors are not always within the range displayable on a computer monitor. There are a wide variety of methods used to compress the gamut of the image, but they vary in subjective quality from image to image [93] Computational steering is used in the ....

....the program is still executing. ffl PathTracer performs the actual Monte Carlo integration of the rendering equation for a particular scene. Produces an image that contains a sampling of a spectrum at each pixel. ffl SpectrumToXYZ transforms the spectrum at each pixel to the XYZ color space [41]. ffl XYZtoRGB transforms each pixel from the XYZ color space to RGB colors, ready for display. The user interface is used to select the gamut compression algorithm used. In addition to the controls on the color space transformation modules, the user can directly manipulate the sampling density ....

HALL, R. Illumination and Color in Computer Generated Imagery. SpringerVerlag, 1989.

....exactly on the destination device. The process of making the colors fit, which can range from a simple clip to elaborate nonlinear scaling transformations, is termed gamut mapping. The aim is to produce a reasonable visual representation of the original image. Further reading References [COLOR 1] through [COLOR 5] provide more detail about color theory. 15 Appendix: Sample CRC Code The following sample code represents a practical implementation of the CRC (Cyclic Redundancy Check) employed in PNG chunks. See also ISO 3309 [ISO 3309] or ITU T V.42 [ITU V42] for a formal specification. ....

Hall, Roy, Illumination and Color in Computer Generated Imagery. Springer-Verlag, NewYork, 1989. ISBN 0-387-96774-5.

....recent ray tracing project, and to document the results. The objective of the project is to redo Mogensen s experiment [Mogensen 86] with applying partial evaluation to ray tracing, but in another setting. We have implemented the standard recursive ray tracing algorithm [Foley 90] Glassner 89] Hall 89] in C and programmed it for speed. The focus in this project is on using partial evaluation to optimize an already efficient program. Also we want to investigate the problems that occur when partial evaluation is applied to production quality programs. The experiments show that this particular ....

Hall, Roy. Illumination and Color in Computer Generated Imagery. 1989.

.... CIE results to display RGB values end We have not discussed the final step, mapping the computed display luminances and chrominances to appropriate values for the display device (e.g. monitor RGB settings) This is a well studied problem, and we refer the reader to the literature (e.g. [Hall89]) for details. Bear in mind that the mapped image accounts for the black level of the display, which must be subtracted out before applying the appropriate gamma and color corrections. Although we state that the above steps must be carried out in this order, a few of the steps may be moved around, ....

R. Hall, Illumination and Color in Computer Generated Imagery, SpringerVerlag, New York, 1989.

....a computer graphics problem. These images can be synthesized using the shape of the object (usually represented as surface normals) the reflectance properties of the object s surface, and the distribution of the light sources. Using this information, one can employ techniques such as ray tracing [8, 15] to create realistic looking images. If we assume a single point light source and Lambertian reflectance, the relationship between image intensity and object shape is [19] E(x; y) n(x; y) Delta s: 2:1) This is interpreted to mean that the image intensity, E(x; y) is equal to the angle ....

....plane as well as the viewing direction vector. The points on the rotated image plane are then projected along the new direction vector (using orthographic projection) and the superquadrics functions are queried to determine where an intersection occurs. This type of raytracing is described in [8, 15]. A sample of these rotated superquadrics is given in Figure 6.1 6.2 Surfaces of Revolution The superquadric equations can model surfaces with properties that are representative of commonly seen objects. However, the standard superquadrics are symmetrical in three dimensions. A wide variety of ....

R. Hall. Illumination and Color in Computer Generated Imagery, chapter 4.2. Springer-Verlag, New York, 1989.

....an effective objective measure of the validity of an imposter will be difficult to derive. Modification schemes similar to luminaire imposters are widely used in image synthesis, 51 for example objects with simplified reflectance functions and objects stored at multiple levels of resolution [21, 27, 80]. Another typical imposter example is to change the physical behavior. For example, non emitting objects in zonal methods can emit the same amount of light as they would reflect [25, 63, 29] 3.3.2 Imposters with Extra Information In a daytime indoor scene, the dominant luminaire would be the sun ....

Roy Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, New York, N.Y., 1988.

....allow us to experiment with biased weighting of the chromatic and achromatic color components, just as the human visual system performs certain scene understanding tasks with segregated achromatic and chromatic color information. Color space conversions were performed using the methods of Hall [4]. Because precise speci cations of the color primaries of the image data were not directly available, we approximated them by the NTSC standard primaries. Although deviations of actual primaries from these are expected to be modest, this approximation does not guarantee the correct absolute CIE ....

Roy Hall. Illumination and Color in Computer Generated Imagery. SpringerVerlag, 1989.

....destination device. The process of making the colors fit, which can range from a simple clip to elaborate nonlinear scaling transformations, is termed gamut mapping. The aim is to produce a reasonable visual representation of the original image. Further reading 14.11 Further reading References [COLOR 1] through [COLOR 5] provide more detail about color theory. 15 Appendix: Sample CRC Code The following sample code represents a practical implementation of the CRC (Cyclic Redundancy Check) employed in PNG chunks. See also ISO 3309 [ISO 3309] or ITU T V.42 [ITU T V42] for a formal specification. ....

Hall, Roy, Illumination and Color in Computer Generated Imagery. Springer-Verlag, New York, 1989. ISBN 0-387-96774-5.

....eye has three types of cones that are used to perceive colour. Roughly speaking one type of cone is especially responsive to red light, one is responsive to green light, and one is responsive to blue light. The colour sensation perceived depends on the output signal generated by these sensors [20]. To get a specific colour sensation, we have to create the receptor response that is specific for this sensation. Thus each colour sensation can be described by three values that are in some form related to the output of the three types of cones. Since the visible light is a continuous spectrum, ....

Roy Hall. Illumination and Color in Computer Generated Imagery. Monographs in Visual Computing. Springer-Verlag, 1988.

....# Luminous flux density(in terms of illuminance) E v = Km Z # Z# L e #x; ##V ### cos #d d# # Luminous intensity I v = Km Z # Z x2A L e #x; ##V ### dA d# # Luminance L v = Km Z # L e #x; ##V ### d# A. 4 IES Luminaires and Spectral Radiance The IES photometric data file format [8] defines the three dimensional distribution of light emitted by a luminaire. The distribution is defined for a point light source even though most luminaires are clearly not point sources. The file format specifies luminous intensities I v for a set of vertical and horizontal directions, thus ....

....Computer Graphics, 20(4) 143 150, August 1986. ACM Siggraph 86 Conference Proceedings. 7] Eric P. Lafortune and Yves D. Willems. The ambient term as a variance reducing technique for Monte Carlo ray tracing. In Proceedings of the Fifth Eurographics Workshop on Rendering, pages 163 172, 1995. [8] Illumination Engineering Society of North America. Ies standard file format for electronic transfer of photometric data and related information. IES Lighting Measurement Series, 1991. IES LM 63 1991. 9] Mark S. Rea, editor. The Illumination Engineering Society Lighting Handbook. Illumination ....

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R. Hall. Illumination and Color in Computer Generated Imagery. Springer- Verlag, New York 1989.

....the rendering process for both importing models and for texture mapping. 1 Introduction The desire for accuracy and realism in images requires a physically based rendering system. Often this can mean using a full spectral representation, as RGB representations have limitations in some situations[4]. The spectral representation does come at some cost, not the least of which is that most available models and model formats specify materials and lights in terms of RGB triples. Using these models conveniently requires the conversion of RGB values into spectra [2] The conversion process should ....

HALL, R. Illumination and Color in Computer Generated Imagery. SpringerVerlag, New York, 1989. includes C code for radiosity algorithms.

....= I 0 e (t) dt 0 s where I 0 is the amount of energy entering the cloud at s=0. We define the transparency at s as: T (s) e (t)dt 0 s . 1 Energy and intensity in general are different, but related. This thesis uses the terms interchangeably. See Cohen and Wallace [15] or Hall [31] for a more detailed description of the differences. 11 s Figure 3 1. s1 s2 For constant attenuation, s we get T (s) e s . Max, et al. 66] show that for linearly varying attenuation, s) as b , the transparency T ( s) e s 2 ( s 1 ) s 2 ) where (s 1 ) and (s 2 ) ....

Hall, R., Illumination and Color in Computer Generated Imagery. Monographs in Visual Computing, ed. D.F. Rogers. 1989, New York: Springer-Verlag. 282.

....1947) and (Ostwald, 1931) In the following sections, several models will be described. For a more complete history of colour models, see (Norman, 1990) or (Gerritsen, 1988) For a more in depth discussion of the colour models described below, see one of (Foley et al. 1990; Rogers, 1985; Hall, 1988; Boynton, 1979) In addition, many of the concepts discussed in this section are treated at an introductory level in (Hope and Walch, 1990) 2.2.1 Colour Mixing From the psychophysical point of view, colour can be defined as (Wyszecki and Stiles, 1982) that characteristic of a visible [colour ....

....independent model such as the XYZ model. 16 Chapter 2. Background Green = 0,1,0) Yellow = 1,1,0) Red = 1,0,0) Magenta = 1,0,1) Blue = 0,0,1) Cyan = 0,1,1) Black = 0,0,0) White = 1,1,1) Figure 2. 7: The RGB Colour Model The conversion between RGB and XYZ can be expressed as follows (Hall, 1988, Eq 3.2) red phosphor: r x ; r y ; r z = 1 Gamma r x Gamma r y green phosphor: g x ; g y ; g z = 1 Gamma g x Gamma g y blue phosphor: b x ; b y ; b z = 1 Gamma b x Gamma b y white point: w x ; w y ; w z = 1 Gamma w x Gamma w y 2 4 X Y Z 3 5 = 2 4 S r (r x ) S g (g x ) S b (b ....

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Hall, R. (1988). Illumination and Color in Computer Generated Imagery. Springer-Verlag, New York.

....and one (Section 3.2) Finally, we break the materials into several classes to compute only non zero coefficients for efficiency. One well known problem with Equation 1 is that the specular terms do not change with incident angle. This is different from the behavior of materials in the real world [14]. In a conventional ray tracer the values of kd , ks and k t can be hand tuned to depend on viewpoint but in an interactive setting this does not work well. Instead, we first break down materials into a few distinct subjective categories suggested in [31] diffuse, dielectric, metal, and polished. ....

Roy Hall. Illumination and Color in Computer Generated Imagery. SpringerVerlag, New York, N.Y., 1988.

....as one unit of a rendering system [28, 44, 21] We treat light material interaction as a component, where the reflection behavior is determined strictly from a set of material parameters. Traditionally this might be accomplished with one shading model with parameters including ks, kt, and kd [19]. One problem with such an approach is that physically implausible parameter combinations can be chosen by the user (e.g. kd = ks = 0, kt = 1) Implausible combinations may be useful for many applications, but if realism is desired, it is better to limit the user s 4 All objects in a zonal scene ....

Roy Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, New York, N.Y., 1988.

....a factor of 30000 is sometimes reached with special illumination cases (Chiu et al. 1993) Therefore traditional 24 bit picture representations with a dynamic range of 256 are inadequate. Moreover, when applying gamma correction, even pure 24 bit pictures can create color bandings for low values (Hall 1989) showing that a greater dynamic range is needed. Ward has proposed a technique (Ward 1991) in which pixels values are coded with a floating point format. Four bytes per pixel are used (one byte for a common exponent and one byte for the mantissa of each primary color) which provides a huge dynamic ....

R. Hall. Illumination and color in computer generated imagery. Springer Verlag, 1989.

....colours, but never the less be an improvement. ffl The addition of a suitable colour deviation is desirable. ffl Alternative colour representations which make considerations for colour difference based on human perception would probably be more suitable. The standard CIE L u v colour space [20][25] has been designed to have this property. This colour space provides a decent measurement between colours but may be inappropriate for finding a measurement of colour average and variance. It also relies on choosing reference colours which are based on the process of acquiring images and image ....

R. Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, 1989.

....a reflectance model is the heart of every rendering method because it provides the illumination of objects in the scene, and therefore the color of pixels in the image. Reflectance models currently in use can be divided in two main families : empirical models and theorical ones. Empirical models [12, 3, 6] are computationally efficient but are lacking of physical validity (energy conservation law, for instance) and thus do not provide plausible values of energy or intensity. In fact, they are generally only used to create bright spots on surfaces in order to add some tridimensional information ....

....: every term that is function of the wavelength will be subscripted by . Such a term has to be defined and or computed, theoretically for every wavelength of the visible spectrum, and practically for a given number of samples (three in trichromatic models, up to twenty in spectral models [6]) The BRDF has got two important properties that result directly from physics of light [2] First, due to the Helmholtz Reciprocity Rule, R is symmetric relative to V and V 0 : 8 V 2 V 8 V 0 2 V R (P; V; V 0 ) R (P; V 0 ; V ) 2) Second, due to the Energy Conservation Law, R has to ....

R.Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag, 1989

....bottom 6 spectra detail a fairer scheme where each initial ray spawns only 1 refracted ray, the wavelength of which is determined stochastically. All computations are performed with respect to these 7 sample points. For final image display however, we must convert to RGB space. This is achieved [Hall89][Peercy93] by multiplying the reconstructed spectrum by the CIEXYZ tristimulus matching curves, using Riemann summation to evaluate the integral, and finally converting the XYZ colour to RGB space using chromaticity data for the monitor phosphors. 4.2 Light Source Data Clearly to model the ....

Hall R., Illumination and Color in Computer Generated Imagery, Monographs In Visual Communication, Springer Verlag, pp. 45-62, 1989.

....concentrated on finding numerical representations of colours which are convenient for use in computer graphics and image processing. These representation schemes use a three dimensional colour space (RGB, CMY, YIQ, HSV, HSL, XYZ, L a b , L u v , etc. and quantify colours as points in that space [3,4,6,9]. This provides a means of accurately specifying most colours in terms of a small set of parameters which are suitable for subsequent numeric manipulation. Schwarz, Cowan and Beatty [7] conducted an extensive comparison of human colour matching performance using five standard numerical colour ....

Hall, R., Illumination and Color in Computer Generated Imagery, Springer-Verlag, NY, 1989

....modes to support both quick answer times and high quality rendering. Figure 3: Sample application Molecular Force Microscope. The fastest visualization method uses colored lines for the bonds and circles for the atoms of a three dimensional configuration and orthogonal or perspective projection [5, 6, 7, 8, 9]. The user can rotate, move and zoom the whole configuration. Using the mouse, one can select an atom or a chain to get the coordinates of the respective atom. Additionally, one can switch between visualizations with or without periodic boundary conditions, which is very useful for the exploration ....

....atom. Additionally, one can switch between visualizations with or without periodic boundary conditions, which is very useful for the exploration of polymer chain properties. The second method of visualization uses a surface representation with hidden surface detection and an illumination model [5, 6, 7, 8, 9]. Figure 3 shows bonds represented as cylinders and atoms as spheres. In general, without special graphics hardware this method is quite slow. Therefore we developed fast software rendering techniques for the graphics library of MXPL and a suitable refresh rate can be obtained on todays ....

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R.A. Hall, Illumination and Color in Computer Generated Images, Springer Verlag, Heidelberg, 1989

....a reflectance model is the heart of every rendering method because it provides the illumination of objects in the scene, and therefore the color of pixels in the image. Reflectance models currently in use can be divided in two main families : empirical models and theoretical ones. Empirical models [12, 3, 6] are computationally efficient but are lacking of physical validity (energy conservation law, for instance) and thus do not provide plausible values of energy or intensity. In fact, they are generally only used to create bright spots on surfaces in order to add some tridimensional information ....

....: every term that is function of the wavelength will be subscripted by . Such a term has to be defined and or computed, theoretically for every wavelength of the visible spectrum, and practically for a given number of samples (three in trichromatic models, up to twenty in spectral models [6]) The BRDF has got two important properties that result directly from physics of light [2] First, due to the Helmholtz Reciprocity Rule, R is symmetric relative to V and V 0 : 8 V 2 V 8 V 0 2 V R (P; V; V 0 ) R (P; V 0 ; V ) 2) Second, due to the Energy Conservation Law, R has to ....

R.Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag, 1989

....6 spectra detail a fairer scheme where each initial ray spawns only 1 refracted ray, the wavelength of which is determined stochastically. All computations are performed with respect to these 6 sample points. For final image display however, we must convert to RGB space. This is achieved [Hall89][Peercy93] by multiplying the reconstructed spectrum by the CIEXYZ tristimulus matching curves, using Riemann summation to evaluate the integral, and finally converting the XYZ colour to RGB space using chromaticity data for the monitor phosphors. Higher order quadratures such as Gauss Legendre ....

Hall R., Illumination and Color in Computer Generated Imagery, Monographs In Visual Communication, Springer Verlag, pp. 45-62, 1989.

....coefficient. Figure 3.4 shows the profile of a surface which can be modelled using such a function. The autocorrelation coefficient is a circularly symmetric function of r, C(r) e Gammar 2 t 2 ; 3. 11) where t is the correlation distance which represents the average peak to valley distance [36]. Using such a representation, surface roughness can be modelled using just two parameters, s z and t. The average slope of the surface facets for this representation is 2s z t [4] 3.3.2 Facet Slope Distribution a normal Mean surface Facet normal Figure 3.5: Facet slope distribution model. A ....

....normalisation constant. Cook [14] proposes using the Beckmann distribution, which has a similar shape but without the arbitrary constant 3 , p(a) 1 4s 2 a cos 4 a e Gamma(tan a=s a ) 2 : 3.13) 3 Cook s original paper [14] omits the 4 in the denominator. This was corrected by Hall [36]. Chapter 3. Surface Reflection 31 This surface representation has advantages in its simplicity and can be used to represent most isotropic surfaces. It can, however, be difficult to visualise the true shape of the surface based on the single parameter s a . There is no direct comparison between ....

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R. Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, 1988.

.... the limitations of the device (limited color gamut, limited dynamic range) in order to display a picture that evokes the same visual sensation as the equivalent real scene [8] Several comprehensive solutions, using work done in color science [13] have been proposed for color gamut limitations [9, 6, 10]. But, except two very recent papers [3, 12] dynamic range limitations have usually been ignored or solved only for specific cases. This paper proposes some fast and simple quantization techniques to display high dynamic range pictures on low dynamic range devices. For simplicity, the algorithms ....

....Range Pictures 9 5 Extension to Color Pictures In this section, we propose to extend our quantization scheme to color pictures. Only images created with a trichromatic model during the rendering step are considered here, but the technique can be straightforwardly adapted to spectral models [6, 9]. The only imperative is to be able to compute the Y coordinate of the CIE XYZ color system. Let s suppose that we have created a color picture using three floating point values per pixel (Val r ; Val g ; Val b ) one for each primary color R,G,B. A naive extension of the quantization scheme could ....

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R.Hall, Illumination and Color in Computer Generated Imagery, Springer Verlag, 1989

....which, if nothing else, is very easy to use and implement. The motivation for utilising such a model seems to arise simply from the need to display computed images on a colour CRT which invariably use a red green blue phosphor set. However, there are much more sophisticated colour models available[2] which have existed for a long time and which have even been specialised for use in generating realistic computer graphics images[8] The CIE colour system[12] is based upon the requirement that any colour which the human eye can see will be represented within this scheme. As such, the CIE system ....

....outside the colour gamut of the monitor. In tests of the software, we found that very few values were out of gamut and of those which were, their magnitudes were 0.05. These instances were treated by setting their value to zero. There are a number of ways to deal with the dynamic range problem[2]. We can adjust the RGB values locally by, for example, clamping the offending value to the required range, or we can adjust the values globally by considering the full range within the entire image and scaling everything at the same time so that no values are out of range. The second method is ....

Hall R, Illumination and Color in Computer Generated Imagery, Springer-Verlag, New York, 1987.

....Key Words and Phrases: brightness, contrast, dynamic range, filter, glare, luminance, radiance, vision. 1 Introduction In recent years much attention has been paid to the chromatic limitations of CRTs and printers, and their resulting shortcomings in accurately reproducing highly saturated colors[5, 14, 17, 4]. This is often referred to as a gamut mapping problem because the gamut (set of distinct colors) in the image we wish to display is not a subset of the CRT gamut. Spatial limitations of CRTs have also been explored, usually in the language of signal processing (e.g. 6, 11, 3] Perhaps the ....

.... set: D = fdjd : P fl 0 ; l 1 ; l 2 ; Delta Delta Delta ; l ngg Though this last step is reasonably straightforward, to get a correctlooking discrete raster image careful attention must still be paid to gamma correction, and dithering (even with twenty four bit color images) is recommended[5]. Of course, the final image on the screen is a member of some subset of F (having the same cardinality as D) because at each pixel a continuous phosphor kernel will be generated, and the overlapping kernels of all pixels form an image continuous in space. The spatial limitations of CRTs is ....

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Roy Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, New York, N.Y., 1988.

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Hall, R.: Illumination and Color in Computer Generated Imagery. Springer-Verlag (1989)

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Roy A. Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag, New York, 1989.

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R. Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, 1988.

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R. Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, 1989.

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Hall R. (1989). Illumination and Color in Computer Generated Imagery. Springer-Verlag, New York.

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Hall, Roy. Illumination and Color in Computer Generated Imagery,Springer-Verlag, 1989. 7

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R.Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag, 1989

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Hall R., Illumination and Color in Computer Generated Images, Springer-Verlag, New-York, 1989.

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Roy Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, New York, NY, 1989. 3, 4

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R. Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, New York, 1989.

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R. Hall. Illumination and Color in Computer Generated Imagery. Springer, New York, 1989.

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R. Hall. Illumination and Color in Computer Generated Imagery. Springer, New York, 1989.

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Hall, Roy. Illumination and Color in Computer Generated Imagery, Springer-Verlag, 1989. f7g

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Hall, R. Illumination and Color in Computer Generated Imagery. SpringerVerlag, New York, 1989.

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Roy Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag, 1988.

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R. Hall, Illumination and Color in Computer-Generated Imagery, Springer, Berlin, 1989.

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Hall89 Roy A. Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag, New York, 1989.

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R. Hall, Illumination and Color in Computer Generated Imagery. Monographs in Visual Computing, SpringerVerlag, (1988).

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