# Patent

## Title
Systems for spectral multiplexing of source images to provide a composite image, for rendering the composite image, and for spectral demultiplexing the composite image to obtain a normalized color image

## Abstract

Methods and apparatus for spectrally-encoding plural source images and for providing the spectrally-encoded plural source images in a composite image, for rendering the composite image in a physical form, or for recovering a normalized version of an encoded source image from the rendered composite image such that the recovered source image is made distinguishable as a normalized color image.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
Cross-reference is made to the following co-pending and commonly-owned applications, the disclosures of which are incorporated herein by reference:
U.S. application Ser. No. 10/268,333, filed Oct. 9, 2002 by Gaurav Sharma et al. and respectively entitled “Systems for spectral multiplexing of source images to provide a composite image, for rendering the composite image, and for spectral demultiplexing of the composite image”.
U.S. application Ser. No. 10/304,171 filed Nov. 25, 2002 by Gaurav Sharma et al. and respectively entitled “Systems for spectral multiplexing of source images to provide a composite image, for rendering the composite image, and for spectral demultiplexing of the composite image by use of an image capture device”.
U.S. application Ser. No. 10/268,394 filed Oct. 9, 2002 by Steven J. Harrington et al. and respectively entitled “Systems for spectral multiplexing of source images to provide a composite image, for rendering the composite image, and for spectral demultiplexing of the composite image to animate recovered source images”.
U.S. application Ser. No. 10/268,295 filed Oct. 9, 2002 by Steven J. Harrington et al. and respectively entitled “Systems for spectral multiplexing of source images including a stereogram source image to provide a composite image, for rendering the composite image, and for spectral demultiplexing of the composite image”.
U.S. application Ser. No. 10/268,505 filed Oct. 9, 2002 by Steven J. Harrington et al. and respectively entitled “Systems for spectral multiplexing of source images including a textured source image to provide a composite image, for rendering the composite image, and for spectral demultiplexing of the composite image”.
U.S. application Ser. No. 10/268,575, filed Oct. 9, 2002 by Gaurav Sharma et al. and respectively entitled “Systems for spectral multiplexing of source images to provide a composite image with gray component replacement, for rendering the composite image, and for spectral demultiplexing of the composite image”.
U.S. application Ser. No. 10/268,246 filed Oct. 9, 2002 by Robert P. Loce et al. and respectively entitled “Systems for spectral multiplexing of a source image and a background image to provide a composite image, for rendering the composite image, and for spectral demultiplexing of the composite images”.
U.S. application Ser. No. 10/268,271 filed Oct. 9, 2002 by Yeqing Zhang et al. and respectively entitled “Systems for spectral multiplexing of source images to provide a composite image, for rendering the composite image, and for spectral demultiplexing the composite image, which achieve increased dynamic range in a recovered source image”.
U.S. application Ser. No. 10/268,241 filed Oct. 9, 2002 by Yeqing Zhang et al. and respectively entitled “System for spectral multiplexing of source images to provide a composite image with noise encoding to increase image confusion in the composite image, for rendering the composite image, and for spectral demultiplexing of the composite image”.
FIELD OF THE INVENTION
The present invention relates to a system or systems for spectrally multiplexing a plurality of source images so as to provide a composite image, rendering the composite image, and demultiplexing of such a composite image to recover one or more of the source images.
BACKGROUND OF THE INVENTION
Whereas light sources are visible by their own emitted light, objects and materials appear to the eye according to how they modify incident light. The sensation of the color of an object is evoked by the physical stimulation of light-sensitive receptors in the human retina. The stimulation consists of electromagnetic radiation in the visible spectrum comprising wavelengths between about 380 and 780 nanometers.
Perceived color of the object is the result of a combination of factors, such as: (1) the spectral power distribution of an illuminant emitted by a light source that is incident upon the object, (2) the modification of the spectral power distribution of the illuminant by the spectral reflectance or transmission characteristics of the illuminated object, (3) the excitation of light sensitive receptors in the eye by the modified light from the object, and (4) the perception and interpretation by the brain of signals produced by the light sensitive receptors.
The perception of color is attributed to the differing spectral sensitivities of the light sensitive receptors. The trichromacy of color sensation implies that many different spectral distributions can produce the same perceived color. Such equivalent stimuli, which produce the same perception even though they are physically different spectral distributions, are called metamers, and the phenomena metamerism. For example, it is known that the perceived color of an object can change quite markedly when the object is moved from incident daylight into incident artificial light. The spectrum of the illuminating light source is also known to have an effect on the perceived colors of a printed image in spite of the considerable physiological compensation that the eye makes for differences in illumination. Light sources of differing relative spectral power distributions are therefore known to have different color rendering properties: for example, light sources which emit very narrow-band, or almost monochromatic, light are considered to render colors very poorly.
According to the concept of metamerism, the respective colors of two objects may appear to be identical even though typically the spectral power distributions produced from the objects are different. Such power distributions, or stimuli, which are spectrally different but visually identical, are considered as metameric pairs. Because we measure light using only three cone types, the differences in these power distributions are indistinguishable. Two objects with different spectral reflectance functions may be perceived to match in color under one illuminant and not match under a different illuminant.
Certain aspects of perceived color have been employed to disguise images by printing an image in one color and then overprinting the first image with a pattern in a different color having approximately the same apparent brightness. Adjacent zones of equal brightness appear to be visually blended, even though they are of differing colors, thereby confusing the perception of the original image.
It is known to print patterns in different colors such that the patterns may be viewed through one or more filters having certain correlated colors, such that the patterns will change, depending upon the colors involved. It is also known to print characters in different colors in an overlapping relationship such that the overlapped characters, when viewed through one colored filter, will give the appearance of only certain ones of the superimposed characters, and when viewed through a second and differing colored filter, will reveal certain other ones of the superimposed characters. Such approaches are known for encoding (or encrypting) information to prevent recognition of the information content of the pattern until the pattern is decoded and made comprehensible. These approaches have been applied to promotional gaming technology and in document security and document verification applications.
Techniques are known for rendering flat, two-dimensional images that can stimulate an illusion of depth perception, that is, of a three-dimensional object or scene. Devices for performing binocular stereoscopic imaging include binocular viewers, parallax stereograms, lenticular-sheet binocular stereoscopic pictures, and binocular displays using Polaroid glasses or color filters. Devices for performing autostereoscopy include parallax panoramagrams, lenticular-sheet three-dimensional imaging, projection type three-dimensional displays, and integral photography. Anaglyphic stereoscopy is a well-known process, in which left and right nearly-identical images are color-encoded by use of respective complementary color filters (e.g. cyan and red) for subsequent viewing through correspondingly colored lenses to separate the images as necessary for a simulated three-dimensional effect. When viewed through colored spectacles, the images merge to produce a stereoscopic sensation. The encoded image pair is known as an anaglyph, as it is typically rendered as two images of the same object taken from slightly different angles in two complementary colors.
SUMMARY OF THE INVENTION
Spectral multiplexing, as used herein, refers to a process for encoding plural source images in a composite image. Composite image rendering refers to a process for rendering the composite image in a physical form. Spectral demultiplexing refers to a process for recovering at least one of the encoded source images from the rendered composite image, such that the recovered source image is made distinguishable from, or within, the composite image, by subjecting the rendered composite image to at least one illuminant having a defined spectral energy distribution that is selected to reveal the source image.
Accordingly, the present invention is directed to methods and apparatus for spectrally-encoding at least one polychromatic source image and for providing the spectrally-encoded source image in a composite image, for rendering the composite image in a physical form, and for recovering the spectrally-encoded source image from the rendered composite image in the form of a normalized color image derived from the polychromatic source image. The normalized color image is recovered when the rendered composite image is subjected to an illuminant having a predefined spectral power distribution for which the polychromatic source image was encoded, such that the normalized color image exhibits substantial similarity to the polychromatic source image.
A given source image is spectrally encoded by mapping values representative of each source image pixel to a corresponding pixel value in one or more of a plurality of colorant image planes. The composite image may be defined in a spectrally multiplexed (SM) image plane, which may have any number of different patterns of pixels, with a primary characteristic being that the SM image plane is spectrally multiplexed. In general, at each location in the SM image plane, a pixel value representing one or more spectral components may be present, and which spectral component is present depends on the gray level of the corresponding pixel in one of the separation image planes that described the source image. Alternatively, the SM image planes may be spectrally multiplexed in which each pixel includes color values representative of color separation image data from more than one source image plane.
One embodiment of the contemplated encoding may include the conversion of a polychromatic source image to an array of respective monochromatic separation images, each of which is a mapped to a corresponding colorant image plane in the composite image. This plurality of separation images can thereby be mapped to a corresponding plurality of colorant image planes in the composite image. The plural separation images are designed to be combined in the composite image, which in turn will control the amount of one or more selected colorants to be deposited on a substrate so as to form the rendered composite image. For example, each colorant may be assigned to a respective colorant image plane of the composite image, and the colorant values in the respective colorant image planes represent the relative amounts of colorant to be deposited in the rendered composite image. For example, a rendered composite image may be rendered using colorants such as cyan, magenta, yellow, and black that are deposited over a given area on a substrate by a rendering device.
Another embodiment of the contemplated encoding may include the aforementioned conversion of a polychromatic source image to an array of respective separation images, and further includes the conversion of a second source image to a respective monochromatic image, wherein the array of separation images and the monochromatic image are mapped to corresponding ones of the plural colorant image planes in the composite image. The resulting composite image then incorporates spectrally encoded information representing both the first (polychromatic) source image and the monochromatic version of the second source image.
In another embodiment of the contemplated encoding, the mapping of each source image is performed according to determinations described herein for compensating the effect of one or more of the following on the composition, rendering, or demultiplexing of the rendered composite image: (a) the trichromacy of human visual response to colorant/illuminant interaction; (b) the spectral characteristics of the colorants selected for rendering the composite image, such spectral characteristics especially comprehending the interaction of plural colorants when such are combined on the substrate, and (c) the spectral characteristics of the narrow-band illuminant(s) that will be used to illuminate the rendered composite image for recovering the source image(s).
It will no doubt be appreciated that the encoding of source images to the composite image may be accomplished according to the teachings herein with use of either software, hardware or combination software-hardware implementations.
Accordingly, the present invention is directed to a system for spectrally-encoding plural source images and for providing the spectrally-encoded source images in a composite image.
The present invention is also directed to a system for rendering the composite image on a substrate. The composite image may be realized as a single, complex, rendered pattern of deposited colorants, wherein at least one colorant is utilized for its particular spectral reflectance characteristic, and in particular for its narrow band absorption characteristic. A composite image composed of the plural colorant image planes may be stored or transmitted as composite image file. The composite image may be physically realized by delivering the composite image file to a rendering device with instructions for rendering the composite image on a substrate using the identified colorants or an array of colorants. One suitable embodiment of a rendering device therefore includes a digital color electrophotographic printer.
The present invention is also directed to a system for spectral demultiplexing of one or more source images encoded in a rendered composite image. A source image may be recovered when the rendered composite image is subjected to illumination by an complementary illuminant having a selected spectral power distribution for which the source image was encoded.
An embodiment of the present invention includes a system for spectral demultiplexing of one or more source images presented in a rendered composite image, wherein a mode of operation is provided for recovering a normalized color version of at least one encoded source image from the rendered composite image such that a normalized color image is made distinguishable to an observer.
In another embodiment of the present invention, the system for spectral demultiplexing is operable in a first mode wherein the normalized color image is recovered when the rendered composite image is illuminated by a controlled field of illumination of a first illuminant having a selected multiband spectral power distribution.
In another embodiment of the present invention, the system for spectral demultiplexing is operable in a second mode wherein a second source image presented in a rendered composite image is recovered when the rendered composite image is illuminated by a controlled field of illumination of a second illuminant having a predefined narrow band spectral power distribution.
In another embodiment of the present invention, source image data representative of disparate first and second source images are encoded. The first source image is provided in the form of a polychromatic image and is thereby represented in the source image data in a set of at least two monochromatic separation images that are spectrally encoded to form image data representative of a normalized version of the polychromatic image. The second source image may initially be presented in the form of a monochromatic or polychromatic image; however, it is converted to a respective monochromatic image and is spectrally encoded in the composite image. The composite image is rendered on a substrate by use of a plurality of narrowband-absorbing colorants. The normalized color version of the polychromatic image may be recovered when the rendered composite image is subjected to illumination by a multiband illuminant for which the set of at least two separation images was encoded, such that the respective first source image is recovered as the normalized color image, thus being detectable by an observer. Alternatively, the second source image is recovered when the rendered composite image is subjected to illumination by the respective narrowband illuminant for which the monochromatic image was encoded, such that the respective second source image is made detectable by an observer.
An embodiment of the system for spectral demultiplexing of a rendered composite image may include a spectral demultiplexer for subjecting the rendered composite image to an incident light spectrum having a selected spectral power distribution in at least two of three selectable bands of radiant energy. In a typical embodiment such selectable bands are contemplated as corresponding to the long, medium, and short (LMS) wavelength bands of the visible light spectrum. Accordingly, a first mode of operation of the spectral demultiplexing may be employed to subject the rendered composite image to a first illuminant exhibiting a spectral power distribution located in the spectral power distributions of the complementary illuminants for at least first and second respective colorants, such that at least two separation images (representing a first source image) are recovered so as to form a normalized color image. Typically such a first illuminant will have a spectral power distribution in two of the three LMS wavelength bands. A second, optional, mode of operation of the spectral demultiplexing will subject the rendered composite image to a second illuminant exhibiting a spectral power distribution located in the spectral power distribution of the complementary illuminant for a third respective colorant. Typically, such a second illuminant will have a spectral power distribution in the remaining third of the three wavelength bands, such that a second source image is recovered.
A rendered composite image, when subject to a wideband illumination condition such as ambient white light, may exhibit visual confusion, that is, the appearance of the rendered composite image lacks, to a certain extent, perceptible resemblance to one or more of the source images encoded therein.
Typically, with respect to a composite image having encoded therein at least two source images, at least one of the first and second source images is not easily recognized as such while the rendered composite image is subject to a wideband illumination condition such as ambient white light. That is, until the rendered composite image is subjected to the spectral demultiplexing process, the rendered composite image is, to a certain extent, visually confused such that an observer is substantially unable to discern one or more of the source images by unaided viewing of the rendered composite image. Alternatively, one or more of the source images may be encoded so as avoid or reduce visual confusion in the rendered composite image during the wideband illumination condition, and therefore be more visible in the rendered composite image when the rendered composite image is subjected to ambient white light or similar wideband illuminant, and so as to become confused or difficult to detect when the rendered composite image is subjected to a complementary illuminant.
In another embodiment of the invention, a colorant selected for its narrow band absorbing properties may be employed so as to appear dark when subjected to a first illuminant having a spectral power distribution that lies substantially within the spectral absorption band of the particular colorant, and to appear light when subjected to a second, differing illuminant having a spectral power distribution that lies substantially outside of the spectral absorption band of the particular colorant. For example, a cyan colorant may be selected for its absorption of red light, and accordingly the regions of a rendered composite image that are composed of a cyan colorant will exhibit high darkness under red light. The cyan colorant will exhibit low darkness under blue light, and will exhibit intermediate darkness under green light. Likewise, a magenta colorant will exhibit high darkness under green light, low darkness under red light, and an intermediate darkness under blue light. A yellow colorant will exhibit high darkness under blue light, low darkness under red light, and an intermediate darkness under green light.
In another embodiment of the invention, by using cyan, magenta, and yellow colorants and complementary illuminants having respective spectral distributions in the red, green, and blue regions of the visible spectrum, respective source images may be encoded and rendered using each of the respective colorants, and each of the corresponding source images are distinguishable within the rendered composite image when the rendered composite image is subjected to illumination by a complementary illuminant.
An embodiment of the system for spectral multiplexing of plural source images includes a spectral multiplexer for receiving image data representative of a plurality of source images and for processing the image data to encode the plurality of source images into a composite image data signal. One embodiment of the spectral multiplexer may be provided in the form of a computer for receiving image data files representative of a plurality of source images and for encoding the image data files as a composite image data file, and a composite image file storage and/or transmission device connected to the computer.
An embodiment of the spectral multiplexer employs a dynamic range determination so as to provide a maximum usable contrast in a recovered source image. A simple, image-independent technique for dynamic range determination is to permute the allocation of the source images to differing monochromatic separations to enable better matching of the requested images to the achievable gamut. This technique will overlap the light and dark regions of colorants, which strongly interact. The maximum/minimum determination may also be applied in an image-dependent fashion, so as to restrict the gamut of an image only to the extent required by the given image. The gamut mapping is preferably performed on an image-dependent basis so as to offer a greater dynamic range than that typically achieved using image-independent gamut mapping. The image-dependent technique need not depend upon the worst-case assumptions of maximum unwanted absorption of one colorant in highlight areas of the complementary image, and therefore allows increased dynamic range. Image-dependent gamut mappings allow increased dynamic range in a recovered source image and improves the optical masking of one or more residual source images. In another version of the contemplated dynamic range determination, a source image that is selected for spectral multiplexing can be preprocessed so as to be gamut-limited; such pre-processing of the source image is expected to enhance the detectability of the recovered source image. Image masking signals are also employed to increase contrast.
An embodiment of the system for rendering the composite image includes an image recording device which is responsive to the system for spectral multiplexing for receiving the composite image data file and for rendering the corresponding composite image on a substrate. One embodiment of the image recording device may be provided in the form of a printer connected to the composite image file storage and/or transmission device, for printing the composite image on a substrate. An embodiment of the printer may include colorants in the form of cyan, magenta, yellow, and black pigments, inks, or dyes selected for their apparent darkness when exposed to complementary illuminants.
The spectral demultiplexer may include an illuminant source responsive to manual control, or a controller and an illuminant source responsive to control by illuminant source control signals provided by the controller. An embodiment of the illuminant source may include one or more light sources for providing desired spectral power distributions in plural selectable bands of radiant energy. In certain embodiment, three selectable bands of radiant energy are provided which correspond to predefined spectral power distributions in the red, green, and blue regions of the visible spectrum.
An embodiment of the controller may include a computer, operable according to control programs for generating one or more of the illuminant source control signals, and an illuminant source responsive to the illuminant source control signals for generating a defined field of illumination of narrow band illuminant, whereby a rendered composite image on a substrate may be located within the field of illumination and thereby subjected to illumination by one or more illuminants that exhibit the desired spectral power distributions.



BRIEF DESCRIPTION OF THE DRAWINGS
The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.
FIG. 1 represents reflectance spectra for a white paper substrate and for colorants in the form of Cyan, Magenta, Yellow, and Black dyes (at 100% density) operable in a dye sublimation printer.
FIG. 2 represents the relative radiance spectra for the red, green, blue primaries generated by a typical cathode ray tube (CRT).
FIG. 3 is a block diagram of systems for spectral multiplexing and demultiplexing of plural source images, and for rendering a composite image having therein at least one encoded source image, constructed according to the invention.
FIG. 4 is a simplified schematic diagram of methods operable in the system of FIG. 3 for spectrally multiplexing first and second source images in a composite image, rendering the composite image with use of plural colorants, and for demultiplexing the rendered composite image.
FIG. 5 is a schematic simplified representation of the spectral multiplexing system of FIG. 3, in which an image processing unit and associated peripheral devices and subsystems are employed.
FIG. 6 is a simplified schematic representation of the spectral demultiplexing system of FIG. 3, in which a controller and associated peripheral devices and subsystems are employed.
FIG. 7 is a rendered composite image generated according to an embodiment of the present invention.



DETAILED DESCRIPTION OF THE EMBODIMENTS
Definition of Terms
Color—A color can be uniquely described by three main perceptual attributes: hue, denoting whether the color appears to have an attribute according to one of the common color names, such as red, orange, yellow, green, blue, or purple (or some point on a continuum); colorfulness, which denotes the extent to which hue is apparent; and brightness, which denotes the extent to which an area appears to exhibit light. Light sources used to illuminate objects for viewing are typically characterized by their emission spectrum and to a reduced degree by their color temperature, which is primarily relevant for characterization off sources with a spectrum similar to a black body radiator. See, for instance, Hunt, R. W. G., Measuring Colour, Ellis Horwood, 1991, and Billmeyer and Saltzman, Principles of Color Technology, 3rd Ed. (Roy S. Berns), John Wiley & Sons, 2000.
Chroma—Colorfulness of an area judged as a proportion of the brightness of a similarly illuminated area that appears white or transmitting.
Colorant—A dye, pigment, ink, or other agent used to impart a color to a material. Colorants, such as most colored toners, impart color by altering the spectral power distribution of the light they receive from the incident illumination through two primary physical phenomenon: absorption and scattering. Color is produced by spectrally selective absorption and scattering of the incident light, while allowing for transmission of the remaining light. A narrow band (absorbing) colorant exhibits an absorption band that is situated in a substantially narrow region of the visible region of the spectrum. Cyan, magenta and yellow colorants are examples of narrow band colorants that selectively absorb red, green, and blue spectral regions, respectively. Some colorants, such as most colored toners, impart color via a dye operable in transmissive mode. Other suitable colorants may operate in a reflective mode.
Composite Image—An array of values representing an image formed as a composite of plural overlaid (or combined) colorant image planes. Source images may be encoded as described herein and the resulting image planes are combined to form a composite image. When a rendered composite image is subjected to a complementary illuminant having a selected spectral power distribution, the combined density of all colorants in the rendered composite image will reveal at least one source image that is otherwise difficult to distinguish, or the reverse, depending upon the interaction of the specific colorant and its complementary illuminant.
Density (Optical)—The degree of darkness of an image. Higher density values represent greater darkness. Mathematically, optical density is defined as the negative logarithm of the reflectance or transmittance. The spectral density is correspondingly the negative logarithm of the reflectance/transmittance spectrum.
Hue—Attribute of visual sensation according to which an area appears to be similar to one of the perceived colors: red, green, yellow, and blue, or to a combination thereof. An achromatic color is a perceived color devoid of hue and a chromatic color is a perceived color possessing a hue. See, for instance, Fairchild, Mark D., Color Appearance Models, Addison Wesley, 1998.
Gamut—A range of colors; typically, the range of colors that can be produced by a device.
Grayscale—Image data representing one of a series of tones stepped from light to dark.
Gray Component Replacement (GCR)—A technique whereby a replacement colorant is used to replace a portion of common darkness of other component colorants in printing an image.
Image—An image may be described as an array or pattern of pixels that are mapped in a two-dimensional format. The intensity of the image at each pixel is translated into a numerical value which may be stored as an array that represents the image. An array of numerical values representing an image is referred to as an image plane. Monochromatic or black and white (gray scale) images are represented as a two-dimensional array where the location of a pixel value in the array corresponds to the location of the pixel in the image. Multicolor (polychromatic) images are represented by multiple two-dimensional arrays. In a three color arrangement, each array represents one of the primary colors. In the digital processing of color images, the individual color separations are represented as a digital image with a plurality of discrete elements (“pixels”) defined by position and gray value. In such a system, gray value is described as one level in a number of possible states or levels. When more than two different levels are used in the description of an image, the levels are termed “gray” (without regard to the actual color) to indicate that the pixel value is between some maximum and minimum gray level.
Illuminant—Incident luminous energy specified by its relative spectral power distribution; typically provided by a light source having a predefined spectral power distribution. A narrowband illuminant is an illuminant having a spectral power distribution that is substantially limited to a narrow region of the spectrum. The bandwidth of the region may vary from extremely narrow (for a LASER source), to narrow band illuminants such as natural or artificial light transmitted through a band-limited color filter. Examples of red, green and blue narrow light are shown in FIG. 2, which illustrates the spectral power distributions obtained from activated red, green, and blue phosphors in a typical CRT. An illuminant that is designed to particularly interact with a given colorant is said to be complementary, and vice versa. A complementary illuminant typically exhibits a spectral power distribution that substantially corresponds to the spectral absorption band of a particular colorant.
Image plane—A two-dimensional representation of image data. The uppercase letters C, Y, M, K are used herein to indicate two-dimensional arrays of values representing a monochromatic image or a separable component of a polychromatic (multicolor) image. Two-dimensional arrays of values may also be referred to as “planes.” For example, the Y plane refers to a two-dimensional array of values that represent the yellow component at every location (pixel) of an image.
Imaging Device—A device capable of generating, capturing, rendering, or displaying an image; including devices that store, transmit, and process image data. A color imaging device has the capability to utilize color attribute information.
Lightness—The perceptual response to luminance; denoted L*and is defined by the CIE as a modified cube root of luminance. Common notation indicates the lightness or darkness of a color in relation to a neutral grey scale, which extends from absolute black to absolute white.
Monochrome/monochromatic image—For a digital representation, a monochrome or monochromatic image is understood as having only a single channel. A perceived image is generally described as being monochrome/monochromatic if it has no perceived variations of hue. Instances of a monochrome image can be considered to include an achromatic image, or a black and white printed image.
Monochromatic light/illumination—A source of light with a spectral power distribution substantially centered on a single wavelength. A practical monochromatic light source typically exhibits a spectral power distribution that is substantially limited to a narrow region of the spectrum.
Polychrome/polychromatic image—For a digital image representation, a polychrome or polychromatic image is understood as including multiple channels with corresponding color interpretations; for example, RGB. A perceived image is generally described as being polychromatic if it has perceived variations in hue.
Neutral—A quality of a color that describes its lack of a predominant hue. Neutral colorants give rise to the perception of neutral colors when subjected to broadband white illumination. Examples of neutral colors are black, gray and white. Non-neutral refers to a color that exhibits a predominant hue. Non-neutral colorants give rise to the perception of non-neutral colors when subjected to a broadband white illumination. Examples of common non-neutral colorants are cyan, magenta and yellow.
Primary Colors—Colors, usually three, which are combinable to produce a range of other colors within a color mixing model. All non-primary colors are mixtures of two or more primary colors. Red, green, and blue (R, G, B) are the standard additive primary colors. Cyan, magenta, and yellow (C, M, Y, K) are the standard subtractive primary colors. Black (K) colorant absorbs light energy substantially uniformly over the full extent of the visible spectrum and may be added to enhance color and contrast and to improve certain printing characteristics. Cyan, magenta, and yellow are the subtractive complements of red, green, and blue, respectively and they absorb the light energy in the long, middle, and short wavelength regions, respectively, of the visible spectrum, leaving other regions of the visible spectrum unchanged. Ideally, the absorption bands of individual CMY colorants are non-overlapping and completely cover the visible region of the spectrum. Actual CMY colorants do not satisfy these block-dye assumptions; instead, their absorption spectra are smooth and include some unwanted absorptions in their transmission bands. The reflectance spectra for white paper and cyan, magenta, yellow, and black colorants (100%) from a dye-sublimation printer are shown in FIG. 1. Red, green, and blue are the additive complements of cyan, magenta, and yellow respectively.
Saturation—Colorfulness of an area judged in proportion to its brightness. Saturation is judged for an area relative to its own brightness whereas chroma is judged relative to a similarly illuminated area that appears white.
Subtractive Color Model The production of color wherein light is subtracted through a process such as absorption; a color model in which colors may be produced by combining various percentages of the subtractive primaries (cyan, magenta, and yellow).
Introduction to a General Theory of the Invention
Two predominant modes for producing color are: Additive color, whereby color is produced by the addition of spectrally selective lights to a dark background that is otherwise substantially devoid of light; and subtractive color, whereby color is produced by spectrally selective subtraction of light energy from the light emitted by a source. Red, green and blue lights are typically used as the primaries that are mixed together in an additive system. In a subtractive system, colorants are typically used as the subtractive primaries. These colorants selectively absorb, or subtract, a portion of the visible spectrum of incident light while transmitting the remainder. Cyan, magenta, and yellow colorants are typically used.
Color in printed images results from the combination of a limited set of colorants deposited on a substrate over a small area in densities selected to integrate the desired color response. This is accomplished in many printing devices by reproducing so called “separations” of the image, where each separation provides varying gray values of a single primary color. When the separations are combined together, the result is a full color image.
Colorants that are deposited on a reflective substrate, such as a paper sheet, will selectively transmit incident light in a first pass to the surface of the substrate whereupon the transmitted light is then reflected by the substrate and is again filtered by the colorants in a second pass, thus encountering additional selective absorption before being perceptible as a particular color by an observer. It is also common for colorants to possess a degree of scattering, and the color appearance of a colorant on a printed substrate is determined by the amount and types of the colorants present, and the combination of their absorption and scattering properties.
In one or more embodiments of the invention, most colors in a subtractive color setting may be reproduced in an image by use of different proportions of cyan, magenta, and yellow colorants. Each of these colorants is characterized primarily by its absorption characteristics. An idealized cyan colorant, for instance, may be defined as having absorption band covering the wavelength interval 600-700 nm, commonly referred to as the red region of the spectrum. Likewise, an idealized magenta colorant has an absorption band covering the interval 500-600 nm, commonly referred to as the green region of the spectrum; and an idealized yellow colorant has an absorption band covering the interval 400-500 nm, commonly referred to as the blue region of the spectrum.
Thus, cyan, magenta, and yellow colorants absorb red, green and blue light, respectively. The idealized absorption bands for the cyan, magenta, and yellow colorants are referred to as the block-dye assumption. In reality, colorants exhibit significant deviations from this idealized behavior, including variations of absorption within the absorption band, extension of the absorption band beyond the idealized limits, and scattering in the colorants. In particular, the absorption of light in a spectral region outside the main absorption band of a colorant (as, for example, demonstrated by absorption in the blue and red regions of the spectrum by a magenta colorant), is considered unwanted absorption. Among typical colorants used for CMYK printing, magenta demonstrates the most unwanted absorptions and yellow the least. The black colorant absorbs uniformly through the visible region of the spectrum and can be used as a replacement for combined CMY for reasons of economy and improved rendition of dark regions.
Thus, according to the subtractive principle, a surface layer of a substrate such as a sheet of white paper, on which one can vary the concentrations of a cyan, a magenta, and a yellow colorant, thereby offers a way of varying the intensities of the reddish, greenish, and bluish parts of the white light reflected from the paper. To produce a subtractive color image reproduction, one can control the concentrations of the three colorants independently at localized areas on the paper substrate.
All surfaces, whether of a colorant or substrate, reflect from their topmost layer a certain proportion of the incident light which is added to that reflected from the body of the surface. This light reflected from the topmost layer is the same color as the illuminant, and therefore when a color surface is viewed in white light, some of the white light is added to the colored light reflected from the body of the surface and the colorfulness is therefore reduced. Most surfaces also exhibit some degree of gloss, and this means that, if the lighting is directional, the white light reflected from the topmost layer of the surface will be confined chiefly to a single direction, thus altering the appearance of the image to some extent depending on the angles of viewing and illumination.
Under normal viewing illumination, the eye adapts to the white-point, which usually corresponds to blank paper with the highest reflectance and different colors can be seen by the eye for prints made with different colorant combinations. However, under relatively narrow band illumination, such as that obtained from a phosphor excited by a single gun of a CRT monitor, the eye is unable to distinguish color. Images viewed under narrow band illumination therefore appear to have only varying levels of gray and little or no chroma. Since the absorption characteristics of each of a plurality of colorants will differ in different spectral bands, the respective reflectance (or density) of each colorant when subjected to a series of differing narrow band illuminants will also appear to have varying levels of gray.
Embodiments of the present invention accordingly exploit the interaction between certain narrow band illuminants and their corresponding (complementary) colorants (especially the colorants typically used for printing), and the manner in which the eye detects images illuminated with illuminants having narrow band spectral power distributions. The methodology described herein may be generalized to apply to an arbitrary number of illuminants and colorants, and for the purpose of simplicity the invention is described with reference to the cyan, magenta, yellow, and black colorants commonly used in color printing applications, and to the narrow-band red, green, and blue illuminants commonly generated by CRT-based light sources. This description thus makes reference to the handling of monochromatic and polychromatic source images encoded according to an array of colorants such as the CMYK color primaries. However, it will be apparent to one of ordinary skill in the art that there are alternative spectral schemes to be employed in the spectral multiplexing of the invention. An alternative would include a color system that employs primary colorants other than CMYK for color representations, such as systems that use RGB primaries or high-fidelity colorants such as orange and green.
The general theory of the invention may be understood with reference to a rendering device in the form of a color hardcopy output device, such as a printer, and to a mathematical framework that employs nomenclature similar to that used in conventional color imaging. Consider a color hardcopy output device with M colorants. Prints from this device are to be viewed under N different illuminants, {Li}i=1N. The luminance characterization of the printer under the K viewing lamps is given by the relation between the control values {Aj}j=1M used for each of the M colorants at a given pixel location and the luminance produced at the given pixel location under each of the N illuminants. This can be denoted as the set of N functions, where I=1, 2, . . . N:

ƒi(A1, A2, . . . AM)=luminance of region with colorant control values A1, A2, . . . AM under ith illumination Li

In the following description, we assume that a control value of 0 for a given colorant represents no printing of that colorant. This convention is not a requirement for the invention and is only adopted for notational simplicity. The following description is limited to the case of luminance characterization alone, because under narrow band illumination the eye primarily sees differences of luminance and is unable to distinguish most color differences. Note that luminance as described here agrees in concept with its standard usage, i.e., as a measure of the perceived light energy; however, it's definition is not limited to the conventional usage and is expanded to comprehend the special viewing situations also described herein. In particular, under narrow band illumination, specific visual effects may influence the perception of a source image. A specific instance of this is the Purkinje effect that causes increased sensitivity in the blue region of the spectrum at low light levels, which may be of particular relevance for viewing under blue light and CRT illumination in general. Some of the advanced concepts from photometry and colorimetry that are required in such situations are described for instance in G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Edition, John Wiley and Sons (1982).
The methods of the present invention are directed to the multiplexing, rendering, and recovery via demultiplexing of one or more source images encoded in a composite image. We assume that the one or more source images to be recovered are described by the spatial luminance distributions desired under each of the illuminants (although, in the alternative, any other equivalent specification that can be transformed to luminance/density may be used.) Thus, there are N images specified, with Yi(x, y) being the desired luminance values that we wish to produce under the ith illuminant Li where x, y denote the two spatial coordinates. For the purposes of simplifying the notation in the following discussion, the spatial dependence is sometimes dropped in the following description with the understanding that the discussion applies to each pixel location independently.
To examine the basic methodology symbolically, consider a simplified example of a composite image rendered in cyan and yellow colorants. In the simplified example below, additivity of “RGB” densities is assumed. This is for the purposes of simple illustration of the principles only and not intended to restrict the invention; in those situations where this approximation is invalid, more precise assumptions can be made. In this example: C, M, Y, K and R, G, B will respectively denote the colorants and illuminants; a superscript will denote illuminant; and a subscript will denote a colorant. Let:

    
    
        dR=density of the image perceived under R illumination,
        dB=density of the image under B,
        dCR=density C separation under R,
        dCB=density C separation under B,
        dYR=density Y separation under R,
        dYB=density Y separation under B.
    
    


When illuminated with a R or B illuminant, the total density perceived can be approximated as,

dR(x, y)=dCR(x, y)+dYR(x, y)≈dCR(x, y)

dB(x, y)=dCB(x, y)+dYB(x, y)≈dYB(x, y)

Accordingly, this methodology exploits the characteristically low density of a colorant when subjected to a first illuminant having a predefined spectral power distribution and the characteristically high density exhibited by the same colorant when subjected to a second illuminant having a differing spectral power distribution. Thus, at least one perceptibly distinct source image (that is encoded in the rendered composite image by use of the particular colorant), can be imperceptible (or nearly so) to an observer when subjected to the first illuminant, but perceptibly distinguishable to the observer when illuminated by the second illuminant. Upon perception of the source image by an observer, the source image may be comprehended and the information embedded in the composite image, or the composite image itself, is thereby readily comprehended.
Determinations of Gamut Mapping, Dynamic Range, and Colorant Interaction
The example presented above assumed that colorant interactions can be entirely ignored. This assumption is not true with most practical colorants and additional considerations are therefore required.
Consider the case of a rendered composite image that is produced by using C and M colorants for subsequent illumination under red and green illuminants. For simplicity, in our illustration below we assume additivity for the red, green, blue band densities, as the general case for situations where this approximation does not hold is described subsequently. A first source image may be recovered primarily from the cyan component of a composite image, and a second source image may be recovered primarily from the magenta component; however, unwanted absorption by these colorants are preferably compensated to avoid artifacts discernible by an observer. The total density under red illumination at pixel location (x,y) can be approximated as

dR(x,y)=dCR(x,y)+dMR(x,y)

and the total density under green illumination is

dG(x,y)=dMG(x,y)+dCG(x,y)

where dUV(x,y) represents the visual density under illuminant V due to colorant U at pixel location (x,y).
The terms dMR(x,y) and dCG(x,y) represent the unwanted absorption. In the simplest case, it can be assumed that a colorant's absorption under its complementary illuminant is used for two purposes: 1) to recover the desired image and 2) to compensate for unwanted absorption by the other colorant(s) present in the composite image. So a magenta colorant may be used to produce the desired image to be seen under green illumination and to compensate for the unwanted absorption of the cyan colorant; a cyan colorant may be used to produce the desired image under red illumination and to compensate for unwanted absorption of magenta under red illumination.
The portion that is used to compensate for the unwanted absorption should combine with the unwanted absorption to result in a constant spatial density so as to make the unwanted absorption imperceptible, or nearly so. Let d1CR(x,y) represent the portion of Cyan density that is used to compensate for the unwanted absorption of Magenta under red, which is determined by:

d1CR(x,y)+dMR(x,y)=constant=qR

The remaining density contribution of cyan under red illumination is d2CR(x,y)=dCR(x,y)−d1CR(x,y). Note that the total density can be written in terms of these components as




  
    
      
        
          
            d
            R
          
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        =
        
          
            
              d
              C
              R
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
          +
          
            
              d
              M
              R
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
        
      
    
  
  
    
      
        =
        
          
            
              d2
              C
              R
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
          +
          
            (
            
              
                
                  d1
                  C
                  R
                
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
              +
              
                
                  d
                  M
                  R
                
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
            
            )
          
        
      
    
  
  
    
      
        =
        
          
            
              d2
              C
              R
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
          +
          
            q
            R
          
        
      
    
  




Therefore the overall visual density under red illumination corresponds a constant background density of qR with the spatially varying density pattern of d2CR(x,y) superimposed. This spatially varying pattern is the one that is seen under red illumination and should therefore represent the first multiplexed image that is to be seen under red illumination.
In a similar manner the density contribution of magenta under green illumination can be decomposed into a component d1MG(x,y) that is used to compensate for the unwanted absorption of cyan under green illumination, given by

d1MG(x,y)+dCG(x,y)=constant=qG

and the remaining component

d2MG(x,y)=dMG(x,y)−d1MG(x,y)

which satisfies




  
    
      
        
          
            d
            G
          
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        =
        
          
            
              d
              M
              G
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
          +
          
            
              d
              C
              G
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
        
      
    
  
  
    
      
        =
        
          
            
              d2
              M
              G
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
          +
          
            
              d1
              M
              G
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
          +
          
            
              d
              C
              G
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
        
      
    
  
  
    
      
        =
        
          
            
              d2
              M
              G
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
          +
          
            q
            G
          
        
      
    
  




Therefore the overall visual density under green illumination corresponds to a constant background density of KG with the spatially varying density pattern of d2CR(x,y) superimposed. This spatially varying pattern is the one that is seen under red illumination and should therefore represent the second multiplexed image that is to be seen under green illumination.
Since the terms d2CR(x,y) and d2MG(x,y) represent the visual variations in density corresponding to the two multiplexed images, we would like to maximize their dynamic range. Since colorants can only add positive density, this requirement translates to minimizing the terms qR and qG subject to meeting the required equations and the physical constraint that colorants can only add positive density. We would therefore like to determine the smallest feasible values of qR and qG for which the above equations are feasible.
For the purpose of further illustration we use a first order approximation, that the amount of colorant added to compensate for unwanted absorption of the other colorant, itself only contributes a negligible amount of unwanted absorption (because of its small value). This assumption implies that the component of Magenta used to offset unwanted absorption of Cyan contributes negligibly to unwanted absorption under green and the component of Cyan used to offset unwanted absorption of Magenta contributes negligibly to unwanted absorption under blue. This assumption is used for illustration only, in practice, one can iteratively determine the appropriate amounts to account for higher-order effects or use an appropriate model or look-up table (LUT). With this simplifying assumption, the range achievable for the desired spatially varying pattern d2CR(x,y) under red illumination is between qR and dCR(x,y) with a total density variation or dynamic range of dCR(x,y)−qR. Likewise the total density range available under green illumination is dMG(x,y)−qG.
One set of feasible values for the terms qR and qG can be determined as:

qR=max (dMR(x,y))=dMR(255)=max density for Magenta under red illuminant

qG=max (dCG(x,y))=dCG(255)=max density for Cyan under green illuminant

This can be thought of as follows: the background density under red light qR is equal to the maximum unwanted density that one can have from Magenta. The Cyan density component d1CR(x,y) is designed carefully so that the combination of Cyan and Magenta at each pixel has a density qR, this can be achieved by putting no Cyan where Magenta is 100% (255 digital count) and appropriate amounts of Cyan to make up the density to qR at pixels which have less than 100% Magenta. A similar argument applies to the Magenta density component d1MG(x,y) that compensates for the unwanted absorption of Cyan under red illumination.
With the notation and terminology defined earlier, the general multi-illuminant imaging problem reduces to the following mathematical problem:
Given N luminance values {Yi}i=1N corresponding to the desired luminance values under the N different illuminants, determine a set of control values for the M colorants {Bj}j=1M to be used in printing a pixel, such that for all I=1, 2 . . . N:

ƒi(B1, B2, . . . BM)=luminance of pixel under ith illumination Li=Yi  (1)

Typically, for N>M (number of image specifications > number of colorants) the system is over-determined and has a solution only under severe constraints on the {Yi}i=1K luminance values limiting its utility in illuminant multiplexed imaging. Even if N≦M (number of image specifications ≦ number of colorants), the system of N equations presented in (1) above has a solution (corresponding to realizable device control values {Bj}j=1M) only in a limited region of luminance values, which we refer to as the gamut for the spectrally multiplexed imaging problem:




  
    
      
        G
        =
        
          
            gamut
            ⁢
            
              
            
            ⁢
            achievable
            ⁢
            
              
            
            ⁢
            for
            ⁢
            
              
            
            ⁢
            illuminant
            ⁢
            
              
            
            ⁢
            multiplexed
            ⁢
            
              
            
            ⁢
            imaging
          
          ⁢
          
            

          
          ⁢
          
            
          
          =
          
            {
            
              Y
              ∈
              
                
                  R
                  +
                  K
                
                ⁢
                
                  
                    
                  
                  ⁢
                  
                    
                  
                
                ⁢
                such
                ⁢
                
                  
                
                ⁢
                that
                ⁢
                
                  
                
                ⁢
                system
                ⁢
                
                  
                
                ⁢
                
                  (
                  1
                  )
                
                ⁢
                
                  
                
                ⁢
                has
                ⁢
                
                  
                
                ⁢
                a
                ⁢
                
                  
                
                ⁢
                realizable
                ⁢
                
                  
                
                ⁢
                solution
              
            
            ⁢
            
              
            
            }
          
        
      
    
    
      
        (
        2
        )
      
    
  




where Y=[Y1, Y2, . . . YN], denotes the vector of luminance values under the N illuminants, and R+ is the set of nonnegative real numbers. For specified N-tuples of luminance values within the gamut G, there is a set of realizable control values such that a pixel printed with the control values produces the required luminance values under the given illuminants. Vice versa, N-tuples of luminance values outside the gamut G cannot be created using any realizable control values. The situation is analogous to the limited color gamut encountered in color reproduction. It is necessary to include a gamut mapping step in the spectral multiplexing described herein to ensure that the source images are limited to the gamut of the system before attempting to reproduce them. The gamut mapping may be image independent or image dependent, where the term image is used to imply the set of desired source images recoverable under the different illuminants. In addition, the set of images to be multiplexed may be designed to take into account the gamut limitations and produce the best results with those gamut limitations.
Once the source images to be multiplexed have been mapped to the achievable gamut G, the problem of reproduction reduces to the determination of the control values for each of the M colorants for each pixel. This corresponds to an inversion of the system of equations in (1) and in a manner similar to color calibration, the inverse could be pre-computed and stored in N-dimensional look-up tables (LUTs), with one LUT one per colorant (or alternately, a single N-dimensional LUT with M outputs).
In practice, the function in (1) itself needs to be determined through measurements of the device response by printing a number of patches with different M-tuples of control values and measuring them suitably to obtain the luminance under the different illuminants. The full spectrum of the patches may be measured for instance on a spectrophotometer from which the luminances may be computed using the spectral power distribution of the different illuminants and the visual luminance sensitivity function. The visual luminance sensitivity function might incorporate adjustments for the appropriate light level that account for visual phenomena such as the Purkinje effect. See for instance, G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Ed., 1982, John Wiley and Sons, Inc., New York, N.Y., in particular pages 406-409.
Simplification According to a One Illuminant/One Colorant Interaction Assumption
Several simplifications can be incorporated into the general framework above. Suppose first, that N=M and the colorants and lights are such that colorant i absorbs only illuminant Li and is completely transparent to all other colorants, then we have




  
    
      
        
          
            
              
                
                  f
                  i
                
                ⁡
                
                  (
                  
                    
                      A
                      1
                    
                    ,
                    
                      A
                      2
                    
                    ,
                    
                      ...
                      ⁢
                      
                        
                      
                      ⁢
                      
                        A
                        M
                      
                    
                  
                  )
                
              
              =
              
              ⁢
              
                function
                ⁢
                
                  
                
                ⁢
                of
                ⁢
                
                  
                
                ⁢
                
                  A
                  i
                
                ⁢
                
                  
                
                ⁢
                alone
              
            
          
          
             
          
        
        
          
            
              =
              
              ⁢
              
                
                  f
                  i
                
                ⁡
                
                  (
                  
                    0
                    ,
                    0
                    ,
                    ...
                    ,
                    
                      
                    
                    ⁢
                    0
                    ,
                    
                      A
                      i
                    
                    ,
                    0
                    ,
                    
                      ...
                      ⁢
                      
                        
                      
                      ⁢
                      0
                    
                  
                  )
                
              
            
          
          
            
              
              ⁢
              
                
                  i
                  =
                  1
                
                ,
                2
                ,
                
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  N
                
              
            
          
        
        
          
            
              ≡
              
              ⁢
              
                
                  g
                  i
                
                ⁡
                
                  (
                  
                    A
                    i
                  
                  )
                
              
            
          
          
             
          
        
      
    
    
      
        (
        3
        )
      
    
  




The system of equations in (1) then reduces to M independent nonlinear equations one for each colorant under the corresponding illumination:

gi(Bi)=Yi i=1, 2, . . . N  (4)

The achievable gamut can be defined as follows. Let:




  
    
      
        
          
            
              
                g
                i
                min
              
              =
              
                
                  min
                  
                    A
                    i
                  
                
                ⁢
                
                  
                    g
                    i
                  
                  ⁡
                  
                    (
                    
                      A
                      i
                    
                    )
                  
                
              
            
            ⁢
            
              

            
            ⁢
            
              
                g
                i
                max
              
              =
              
                
                  max
                  
                    A
                    i
                  
                
                ⁢
                
                  
                    g
                    i
                  
                  ⁡
                  
                    (
                    
                      A
                      i
                    
                    )
                  
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            
              
                
                  
                    h
                    i
                  
                  =
                  
                  ⁢
                  
                    [
                    
                      
                        g
                        i
                        min
                      
                      ,
                      
                        g
                        i
                        max
                      
                    
                    ]
                  
                
              
            
            
              
                
                  =
                  
                  ⁢
                  
                    the
                    ⁢
                    
                      
                    
                    ⁢
                    interval
                    ⁢
                    
                      
                    
                    ⁢
                    of
                    ⁢
                    
                      
                    
                    ⁢
                    luminances
                    ⁢
                    
                      
                    
                    ⁢
                    from
                    ⁢
                    
                      
                    
                    ⁢
                    
                      g
                      i
                      min
                    
                    ⁢
                    
                      
                    
                    ⁢
                    to
                    ⁢
                    
                      
                    
                    ⁢
                    
                      g
                      i
                      max
                    
                  
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            
              
                where
                ⁢
                
                  
                    
                  
                  ⁢
                  
                    
                  
                
                ⁢
                i
              
              =
              1
            
            ,
            2
            ,
            
              ...
              ⁢
              
                
              
              ⁢
              N
            
          
        
        ⁢
        
          
            
          
          ⁢
          
            
          
        
      
    
    
      
        (
        5
        )
      
    
  




G1=achievable gamut under assumption of one illuminant interacting with only one colorant=h1×h2× . . . ×hN  (6)

In other words, the achievable gamut is the product set of these individual luminance intervals. Note that the assumption in Eq. (6) is that the complete interval between the max and min limits can be realized without any “gaps” which would typically be expected with physical colorants. (For a definition of a product set, see for instance, Friedman, The Foundations of Modern Analysis, Dover, 1982, New York, N.Y.)
Under the assumption of one illuminant interacting with only one colorant, the multi-illuminant imaging characterization problem reduces significantly. Instead of requiring N-dimensional LUTs only one-dimensional LUTs—one per colorant are needed. The value of each colorant may be determined by the luminance under the corresponding illumination alone.
Alternative Simplifications
In practice, the assumption of one illuminant interacting with only one colorant does not hold for typical colorants. However, if the strongest interactions are between the ith illuminant and the ith colorant with other interactions having a smaller magnitude, the achievable gamut is a reduced N-dimensional region that is contained in G1. Note that the situation of using cyan, magenta, and yellow colorants with red, green, and blue lights for illumination corresponds to this case, where the cyan interacts most with red, magenta with green, and yellow with blue. Note also that the use of a black colorant that (typically) absorbs all illuminants almost equally, does not satisfy the requirement of strong interaction with only one illuminant. In practice this implies that a black colorant should be viewed as an additional colorant, i.e., if one colorant is black we should have:

N=number of illuminants=number of images≦number of colorants−1=M−1

Black may, however, be used with other colorants in special situations (as is described in the examples below) and can help improve achievable gamut (i.e., improve dynamic range), simplify computation, and reduce cost.
Simplifications Based on Additive Density Models
The general technique described earlier requires a measurement of the device response in the M-dimensional input space of device control values, and the final characterization may be embodied in the form of multi-dimensional LUTs with N-dimensional inputs. In several cases, the measurement and storage/computation requirements for multi-illuminant color imaging can be significantly reduced by using simple models of the output processes. One useful model is to assume that the visual densities follow an additive model, i.e.,




  
    
      
        
          d
          i
        
        ⁢
        
          
            
              
                
                  (
                  
                    
                      A
                      1
                    
                    ,
                    
                      A
                      2
                    
                    ,
                    
                      ...
                      ⁢
                      
                        
                      
                      ⁢
                      
                        A
                        M
                      
                    
                  
                  )
                
                ≡
                
                ⁢
                
                  -
                  
                    log
                    ⁡
                    
                      (
                      
                        
                          
                            f
                            i
                          
                          ⁡
                          
                            (
                            
                              
                                A
                                1
                              
                              ,
                              
                                A
                                2
                              
                              ,
                              
                                ...
                                ⁢
                                
                                  
                                
                                ⁢
                                
                                  A
                                  M
                                
                              
                            
                            )
                          
                        
                        
                          
                            f
                            i
                          
                          ⁡
                          
                            (
                            
                              0
                              ,
                              0
                              ,
                              
                                ...
                                ⁢
                                
                                  
                                
                                ⁢
                                0
                              
                            
                            )
                          
                        
                      
                      )
                    
                  
                
              
            
          
          
            
              
                =
                
                ⁢
                
                  -
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                    
                    ⁢
                    
                      log
                      ⁡
                      
                        (
                        
                          
                            
                              f
                              i
                            
                            ⁡
                            
                              (
                              
                                0
                                ,
                                0
                                ,
                                ...
                                ⁢
                                
                                  
                                
                                ,
                                
                                  
                                
                                ⁢
                                
                                  A
                                  j
                                
                                ,
                                
                                  ...
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  0
                                
                              
                              )
                            
                          
                          
                            
                              f
                              i
                            
                            ⁡
                            
                              (
                              
                                0
                                ,
                                0
                                ,
                                
                                  ...
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  0
                                
                              
                              )
                            
                          
                        
                        )
                      
                    
                  
                
              
            
          
          
            
              
                =
                
                ⁢
                
                  -
                  
                    
                      ∑
                      
                        j
                        =
                        1
                      
                      M
                    
                    ⁢
                    
                      
                        d
                        i
                      
                      ⁡
                      
                        (
                        
                          A
                          j
                        
                        )
                      
                    
                  
                
              
            
          
        
      
    
    
      
        (
        7
        )
      
    
  
  
    
      
        
          where
          ⁢
          
            
          
          ⁢
          
            
              d
              i
            
            ⁡
            
              (
              
                A
                j
              
              )
            
          
        
        ≡
        
          -
          
            log
            ⁡
            
              (
              
                
                  
                    f
                    i
                  
                  ⁡
                  
                    (
                    
                      0
                      ,
                      0
                      ,
                      ...
                      ⁢
                      
                        
                      
                      ,
                      
                        
                      
                      ⁢
                      
                        A
                        j
                      
                      ,
                      
                        ...
                        ⁢
                        
                          
                        
                        ⁢
                        0
                      
                    
                    )
                  
                
                
                  
                    f
                    i
                  
                  ⁡
                  
                    (
                    
                      0
                      ,
                      0
                      ,
                      
                        ...
                        ⁢
                        
                          
                        
                        ⁢
                        0
                      
                    
                    )
                  
                
              
              )
            
          
        
      
    
    
      
        (
        8
        )
      
    
  




(Traditionally, densities are defined as logarithms to the base 10, any other base can also be used in practice as it changes the densities only by a scale factor and does not impact any of the other mathematical development.) Note as per our convention, the control values {0,0, . . . ,0} represent an blank paper substrate and therefore ƒi(0,0, . . . 0) represents the luminance of the paper substrate under the ith illuminant, and the logarithmic terms represent paper normalized visual densities. The additive model for visual densities is motivated by the Beer-Bouguer law for transparent colorant materials and the assumption of relatively narrow band illumination, for which the additive nature of spectral density implies the approximation above is a valid one. The model also often provides a reasonable approximation for halftone media where the assumptions do not strictly hold. (For a more detailed background, see: F. Grum and C. J. Bartleson, Ed., Optical Radiation Measurements: Color Measurement, vol. 2, 1983, Academic Press, New York, N.Y. or G. Sharma and H. J. Trussell, “Digital Color Imaging”, IEEE Transactions on Image Processing, vol. 6, No. 7, pp. 901-932, July 1997.) Full computations using a spectral density model might be performed if necessary to improve the model accuracy, this would be potentially advantageous in a situation where the illuminating lights are not strictly narrow band.
The terms




  
    
      d
      i
    
    ⁡
    
      (
      
        A
        j
      
      )
    
  
  ≡
  
    log
    ⁡
    
      (
      
        
          
            f
            i
          
          ⁡
          
            (
            
              0
              ,
              0
              ,
              ...
              ⁢
              
                
              
              ,
              
                
              
              ⁢
              
                A
                j
              
              ,
              
                ...
                ⁢
                
                  
                
                ⁢
                0
              
            
            )
          
        
        
          
            f
            i
          
          ⁡
          
            (
            
              0
              ,
              0
              ,
              
                ...
                ⁢
                
                  
                
                ⁢
                0
              
            
            )
          
        
      
      )
    
  




represent the paper normalized visual density of a patch printed with the jth colorant alone and no other colorants, with the control value for the jth colorant set as Aj. Therefore the additive density model proposed above allows the determination of the visual density of any patch based on the visual density of control patches of individual colorants. This reduces significantly the number of measurements required. Measurements of “step-wedges” of the individual colorants (for which other colorants are not printed) allow one to determine the functions di(Aj) i=1, 2, . . . N, j=1, 2, . . . M, from which the complete device characterization function can be determined using Eq. (8).

Using the above model, the system of equations in (1) reduces to:




  
    
      
        
          
            ∑
            
              j
              =
              1
            
            M
          
          ⁢
          
            
          
          ⁢
          
            
              d
              i
            
            ⁡
            
              (
              
                B
                j
              
              )
            
          
        
        =
        
          
            
              log
              ⁡
              
                (
                
                  
                    Y
                    i
                  
                  /
                  
                    Y
                    i
                    0
                  
                
                )
              
            
            ⁢
            
              
            
            ⁢
            where
            ⁢
            
              
            
            ⁢
            
              Y
              i
              0
            
          
          =
          
            
              f
              i
            
            ⁡
            
              (
              
                0
                ,
                0
                ,
                
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  0
                
              
              )
            
          
        
      
    
    
      
        (
        9
        )
      
    
  




The equations in (9) represent a system of K nonlinear equations in M variables (B1, B2, . . . BM). The functions di(Aj) are available from the measurements of the “step-wedges” and the above equations can be solved for the control values Bj for luminance values within the gamut G, which was defined earlier. For points outside the gamut, the equations may be solved in an approximate sense providing a (less-controlled) form of gamut mapping.
Further simplification of these equations is possible by assuming that the densities in different spectral bands are linearly related, i.e.,

di(C)=αij dj (C) i=1, 2, . . . N  (10)

where αij=di(C)/dj(C) is the proportionality factor relating the visual density for the jth colorant under the ith illuminant to the visual density for the jth colorant under the jth illuminant and is assumed to be independent of the colorant value C, and αjj=1, Thus the convention adopted in Eq. (10) is that the density of the jth colorant under all other illuminants is referenced to its density under the jth illuminant itself, which is not strictly a requirement of our model but is chosen because it results in a simplification of the notation alternate conventions could also be equivalently used. Equation (10) is also motivated by the Beer-Bouguer law for transparent colorant materials and the assumption of relatively narrow band illuminants. (For a more detailed background, refer to: F. Grum and C. J. Bartleson, Ed., Optical Radiation Measurements: Color Measurement, vol. 2, 1983, Academic Press, New York, N.Y. or G. Sharma and H. J. Trussell, “Digital Color Imaging”, IEEE Transactions on Image Processing, vol. 6, No. 7, pp. 901-932, July 1997.) Even though a number of colorants and marking processes do not follow the Beer-Bouguer law exactly, in practice, Eq. (10) often provides a reasonably accurate empirical model for measured data and may be used for the purposes of the current invention. With the simplification of (10) the system of equations in (9) reduces to a linear system of equations:




  
    
      
        
          
            
              ∑
              
                j
                =
                1
              
              M
            
            ⁢
            
              
            
            ⁢
            
              
                α
                i
                j
              
              ⁢
              
                
                  d
                  j
                
                ⁡
                
                  (
                  
                    B
                    j
                  
                  )
                
              
            
          
          =
          
            
              
                log
                ⁡
                
                  (
                  
                    
                      Y
                      i
                    
                    /
                    
                      Y
                      i
                      0
                    
                  
                  )
                
              
              ⁢
              
                
              
              ⁢
              i
            
            =
            1
          
        
        ,
        2
        ,
        
          ...
          ⁢
          
            
          
          ⁢
          N
        
      
    
    
      
        (
        11
        )
      
    
  




which can be written in matrix-vector notation as

A d=t  (12)

where A is the N×M matrix whose ij th element is αij, d is M×1 the vector whose jth component is dj(Bj) and t is the N×1 vector whose ith component is log(Yi/Yi0).
The system of linear equations can be solved to determine a value of d, which provides the desired luminance values under the different illuminants (corresponding to the multiplexed images). The individual components of d, i.e., the dj(Bj) values can then be used with the visual density response for the jth colorant under the jth illuminant to determine the control value corresponding to the jth colorant, i.e., Bj. This process is analogous to inverting a 1-D TRC. Repeating the process for each colorant provides the complete set of colorant control values required by {Bj}j=1M that produce the desired set of luminance values under the different illuminants.
Note that if N=M, the above set of equations has a unique solution provided A is invertable, which is normally the case for typical colorants and illuminants. The solution in this case is obtained simply by inverting the matrix A. Furthermore, if the colorants and illuminants can be ordered in correspondence, i.e., colorant i absorbs illuminant i most and the other illuminants to a lesser extent, then αij≦αjj=1, for all i=1, 2 . . . N, i.e., the matrix A is square with the elements along the diagonal as the largest along each row, which is often desirable from a numerical stability standpoint. If M>N the system of equations will have multiple mathematical solutions, and the choice of a particular solution may be governed by additional criteria. One example of a criterion for choosing among the multiple mathematical solutions is feasibility, a feasible solution being a set of density values that can be realized with the range of colorant control values exercisable.
The model inherent in Eq. (12) can also be used to determine suitable approximations to the achievable gamut G and can be of assistance in performing gamut mapping. Typically, the density curves dj(C) are monotonically increasing functions of the colorant control value C and the achievable range of densities for the jth colorant under the jth illuminant is between djmin=dj(0)=0 and djmax=dj(Cjmax), where Cjmax is the maximum control value for the jth colorant. The achievable gamut assuming the model of Eq. (12) is valid is




  
    
      
        
          
            G
            D
          
          =
          
            
              achievable
              ⁢
              
                
              
              ⁢
              luminance
              ⁢
              
                
              
              ⁢
              gamut
              ⁢
              
                
              
              ⁢
              assuming
              ⁢
              
                
              
              ⁢
              additive
              ⁢
              
                
              
              ⁢
              densities
            
            ⁢
            
              

            
            ⁢
            
              
            
            =
            
              {
              
                
                  
                    
                      
                        y
                        ⁢
                        
                          
                        
                        ⁢
                        such
                        ⁢
                        
                          
                        
                        ⁢
                        that
                        ⁢
                        
                          
                        
                        ⁢
                        there
                        ⁢
                        
                          
                        
                        ⁢
                        exists
                        ⁢
                        
                          
                        
                        ⁢
                        a
                        ⁢
                        
                          
                        
                        ⁢
                        d
                        ⁢
                        
                          
                            
                          
                          ⁢
                          
                            
                          
                        
                        ⁢
                        with
                        ⁢
                        
                          
                            
                          
                          ⁢
                          
                            
                          
                        
                        ⁢
                        Ad
                      
                      =
                      
                        
                          log
                          (
                          
                            y
                            /
                            
                              y
                              0
                            
                          
                          )
                        
                        ⁢
                        
                          
                        
                        ⁢
                        and
                      
                    
                  
                
                
                  
                    
                      0
                      =
                      
                        
                          d
                          min
                        
                        ≤
                        d
                        ≤
                        
                          d
                          max
                        
                      
                    
                  
                
              
              ⁢
              
                
              
              }
            
          
        
        ⁢
        
          
        
      
    
    
      
        (
        13
        )
      
    
  




where dmin is an M×1 vector whose jth component is djmin=0, and dmax is an M×1 vector whose jth component is djmax, y is an N×1 vector whose ith component represents the luminance under the ith illuminant Li, and y0 is a N×1 vector whose ith component represents the paper luminance under the ith illuminant. The inequalities, the division, and the logarithm in the right hand side of Eq. (13) are understood to be applicable on a term-by-term basis for the vectors.
The N images to be produced under the N illuminants provide a N-tuple for each pixel location corresponding to the desired luminance values at that pixel location under the N illuminants. The N-tuples corresponding to all the pixel locations must lie within the gamut G defined earlier in order for the image to be producible using the given colorants and illuminants. If images specified for multiplexing do not satisfy this constraint some form of gamut mapping is necessary.
A simple image-independent gamut mapping scheme may be defined as follows. First, ranges of luminance values under the different illuminants are determined such that all possible values within these ranges lie within the gamut G. This is mathematically equivalent to stating that we determine a set of N-intervals Si=[Yimin, Yimax], i=1, 2, . . . N such that the product set of these intervals is contained within the gamut G, i.e.,

S1×S2×S3× . . . SN⊂G  (14)

The gamut mapping may then be performed on an image independent basis by mapping the set of requested luminance values under the ith illuminant to the interval Si=[Yimax, Yimax] by some (typically monotonous) function. The interval Si determines the luminance dynamic range achieved under the ith illuminant. Since there are typically multiple choices of the sets {Si}i−1N for which Eq. (14) is valid, one method for selecting the intervals may be by using a max min optimization where we maximize the minimum dynamic range achievable. Mathematically, this approach can be described as follows: Select the sets {Si}i=1N such that miniƒ(Si) is maximized, where ƒ(Si) is some suitably chosen function that measures the contrast achieved corresponding to the luminance range Si. Examples of suitable choices of the function ƒ( ) are simple luminance ratio i.e., ƒ(Si)=Yimax/Yimin, or density range ƒ(Si)=log(Yimax/Yimin), or CIE lightness range ƒ(Si)=L*(Yimax)−L*(Yimin), where L*( ) is the CIE lightness function. (See for instance, G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Ed., 1982, John Wiley and Sons, Inc., New York, N.Y.) Note that the choice of the density range as the function in the max-min optimization along with the model of Eq. (13) reduces this to a linear max-min optimization problem with box constraints that can be solved using numerical optimization schemes.
Image-Dependant Mapping for Improved Dynamic Range
The method proposed above is independent of the images to be used in creating a composite image; this method however is based on worst case assumptions and may sacrifice some dynamic range in the recovered image.
Accordingly, the aforementioned methods for encoding and rendering of composite images may also utilize an image-dependent mapping that avoids such a loss in dynamic range. By determining the terms KR and KG in an image-dependent fashion, the dynamic range of the recovered source image can be improved.
In particular, we have found that regions of a particular rendered composite image that are intended to appear dark under plural illuminants will, in most instances, need little or no compensation for unwanted absorptions. Accordingly, a better overlap between the dark regions under plural illuminants can be achieved through suitable design of the source images, or by shifting the images appropriately.
Hence, an improved dynamic range can be obtained by using:

qR=maxover all (x,y)(dMR(iG(x,y)−dCR(iR(x,y)), 0)  (15)

qG=maxover all (x,y)(dCG(iR(x,y))−dMG(iG(x,y)), 0)  (16)

where iR(x,y) represents the digital count for the image desired under red illumination, and iG(x,y) represents the digital count for the image desired under green illumination, and dUV(t) represents the visual density under illuminant V for colorant U at a digital count t.
Note that qR and qG in Eq. (16) are guaranteed to be smaller than the values in Eq. (1) thereby ensuring a higher dynamic range for the desired density variations d2cR(x,y) and d2MG(x,y) corresponding to the rendered composite images, a condition that may be advantageous to image quality to design or shift the rendered composite images to have overlapping dark regions, which can minimize contrast degradation. This spatial effect can be seen in Eq. (16), where a spatial transformation of an image i can yield a reduced constant floor density K. Spatial optimization can be performed either computationally or by design.
The argument developed above can be extended to the case of images using C/M and K. By setting:

qe=min(qR, qG)  (17)

and using a spatial value of K(x,y) such that the density corresponding to K(x,y)

d(K(x,y))=max(qe−dCR(iR(x,y)), qe−dMG(iG(x,y))  (18)

the K takes up part of the responsibility for the unwanted absorptions increasing the dynamic range available for the desirable images.
Such dynamic range determinations relevant to the production of rendered composite images that employ cyan and yellow colorants, and of rendered composite images that employ cyan, yellow, and black colorants, can be developed in a manner similar to the above determinations for the rendered composite images that employ cyan and magenta colorants and rendered composite images that employ cyan, magenta, and black colorants. The determinations for the production of rendered composite images that employ cyan and yellow colorants is made simpler because the unwanted absorptions of yellow can be neglected.
Spectral Encoding of a Polychromatic Source Image and its Recovery as a Normalized Color Image
Embodiments of the present invention can perform encoding of at least two separation images so as to represent a polychromatic source image in a rendered composite image which, when subjected to an illuminant having a spectral power distribution that differs from white light, can be observed to exhibit a normalized version of the original polychromatic image, i.e. exhibit a “normalized color image.” This nomenclature attempts to denote the perception of a rendered composite image which, when subjected to an illuminant having a spectral power distribution that differs from that of a wideband illuminant, nonetheless appears to an observer as a “normalized” polychromatic version of the original polychromatic image, that is, a version having sufficient color fidelity such that the rendered composite image is accordingly perceived by an observer as substantially similar to the original polychromatic image. For example, a rendered composite image generated as described herein can be perceived as having degraded color fidelity when observed in wideband illuminant conditions such as white light, and be perceived as having improved color fidelity when subjected an illuminant having a spectral power distribution that differs from that of the wideband illuminant. We accordingly now describe a conceptual basis for contemplated embodiments of the spectral multiplexing, rendering, and demultiplexing operations for yielding a normalized color image.
Consider an example of a rendered composite image from which one desires to recover first and second source images that were encoded in a rendered composite image, in accordance with first and second respective but differing illumination conditions, whereby recovery of a monochromatic version of the first source image (during the first illumination condition) is desired, and recovery of a normalized color version of the second source image (during the second illumination condition) is also desired. The following discussion will first describe this scenario with reference to three exemplary illuminants having respective spectral power distributions in the red, green, and blue wavelength bands; the following discussion can subsequently the generalized so as to be applicable to other illuminants.
First, one may describe the recovery of such first and second source images using an assumption that the unwanted absorption characteristics, with respect to the colorants used to render the composite image, are negligible. One can presume the encoding of the composite image includes encoding the first disparate image as a blue-viewable source image in a yellow channel, which is described as:

dYB(x,y)

and by encoding the second source image as a red/green-viewable separation images in the cyan and magenta channels, as respectively:

dCB(x,y) and dMG(x,y).  (19)

For example, cyan and magenta separation images may be encoded according to the respective cyan and magenta image planes of source image data representing the second source image.
In a first mode of illumination, when subjecting the rendered composite image to a narrowband blue illuminant, an observer will perceive:

dB(x,y)=dYB(x,y)+dCB(x,y)+dMB(x,y)≈dYB(x,y)  (20)

which is a monochromatic image possessing the desired spatial density distribution.
In a second mode of illumination, when subjecting the rendered composite image to an illuminant that exhibits a spectral power distribution over the red and green wavelength bands, an observer will perceive hue variations in addition to lightness variations. For purposes of this discussion, we will consider only the visual density under the individual illuminants to describe the situation. It is understood that the following discussion is intended primarily for illustration and an iterative adjustment based on psychophysical evaluation may be useful in practice. The visual density under the red and green illuminants respectively is given by:

dR(x,y)=dYR(x,y)+dCR(x,y)+dMR(x,y)≈dCR(x,y)  (21)

and

dG(x,y)=dYG(x,y)+dCG(x,y)+dMG(x,y)≈dMG(x,y)  (22)

Accordingly, a rendered composite image subject to illuminants having spectral power distributions selected according to Eqs. 21 and 22 may be seen to yield separation images which in combination are perceived to form a normalized version of the second source image. Accordingly, in addition to Eqs. (21) and (22) we may write the visual density of the corresponding illumination under the combined illumination as:

dRG(x,y)=dYRG(x,y)+dCRG(x,y)+dMRG(x,y)≈dCRG(x,y)+dMRG(x,y)  (23)

In certain situations it may be feasible to simplify (23) in terms of (21) and (22) using knowledge of how the visual densities are added when under individual illuminants (e.g. dRG(x,y)=0.4dR(x,y)+0.6dG(x,y)). The foregoing example presumed a first illuminant having a spectral power distribution primarily located in the blue wavelength region and a second illuminant having a spectral power distribution primarily located in the red and green wavelength regions. Accordingly, one can employ illuminating devices that exhibit overlapping spectral power distributions so as to provide the second illuminant, much the way that the spectral power distributions of activated red and green phosphors will overlap. The second illuminant could be provided in the form of a smooth monomodal distribution, as can be obtained with use of gelatin filters on a wideband light source, or in the form of co-located fields of illumination provided by simultaneous operation an array of narrowband light emitting devices such as light emitting diodes or lamps containing specialized phosphors or interference filters.
Determinations of Gamut Mapping, Dynamic Range, and Colorant Interaction for Optimized Recovery of the Normalized Color Image
As mentioned earlier, unwanted absorption characteristics of common colorants can affect the perceived quality of the normalized color image. Certain compensation techniques can offer desirable improvements.
Consider the case of a rendered composite image that is produced by using a yellow colorant selected for recovery of a first source image when subjected to light in the blue wavelength band and cyan and magenta colorants for recovery of second and third separation images when subjected to light in the red and green wavelength bands. For simplicity, in our illustration below, we assume additivity for the red, green, and blue wavelength band densities. The first source image is then recovered primarily from the yellow component of the composite image, and the second and third separation images are recovered primarily from the cyan and magenta components. However, unwanted absorption by these colorants can be compensated to avoid artifacts otherwise discernible by an observer. The total density of the rendered composite image at pixel location (x,y) subjected to an illuminant in the blue wavelength band can be approximated as:

dB(x,y)=dYB(x,y)+dCB(x,y)+dMB(x,y)  (24)

and the total density when subjected to an illuminant in the red-green wavelength band is:

dRG(x,y)=dYRG(x,y)+dCRG(x,y)+dMRG(x,y)  (25)

and the corresponding perceived densities under red and green illumination are:

dR(x,y)=dYR(x,y)+dCR(x,y)+dMR(x,y)

and

dG(x,y)=dYG(x,y)+dCG(x,y)+dMG(x,y)  (26)

where dUV(x,y) represents the visual density due to colorant U at pixel location (x,y) when subjected to illuminant V.
The image perceived under the blue illumination is image with no hue variation and therefore only the density variations are seen. The image seen under the mix of red and green illumination on the other hand has a luminance perception that is governed by the term dRG(x,y) and a hue perception that is governed by the relative amplitudes of the densities under individual red and green illuminants dR(x,y) and dG(x,y), respectively. Thus one may generate one image that will be perceptible with no hue variation under yellow illumination (by controlling dB(x,y)) and a normalized color image that will be perceived under the red-green illumination (by controlling the relative proportions of dR(x,y) and dG(x,y).
First, consider the image perceived under the blue illumination. The term dCB(x,y)+dMB(x,y) represents the unwanted absorption when subjected to light in the blue wavelength band and dYRG(x,y) represents the unwanted absorption when subjected to light in the red and green wavelength bands. For simplicity, one can assume that a colorant's absorption under its complementary illuminant is used for two purposes: 1) to recover the desired source image and 2) to compensate for unwanted absorption by the other colorant(s) present in the rendered composite image. So, for example, a yellow colorant may be used to recover a desired image under blue wavelength band and to compensate for the unwanted absorption of the cyan and magenta colorants.
The portion that is used to compensate for the unwanted absorption should combine with the unwanted absorption to result in a constant spatial density. Let d1YB(x,y) represent the portion of yellow density that is used to compensate for the unwanted absorption of cyan and magenta under blue wavelength band, which is determined by

d1YB(x,y)+dCB(x,y)+dMB(x,y)=constant=qB  (27)

The remaining density contribution of yellow under blue illumination is d2YB(x,y)=dYB(x,y)−d1YB(x,y). Note that the total density can be written in terms of these components as




  
    
      
        
          
            
              
                
                  d
                  B
                
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
              =
              
              ⁢
              
                
                  
                    d
                    Y
                    B
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  
                    d
                    C
                    B
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  
                    d
                    M
                    B
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    d2
                    Y
                    B
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  (
                  
                    
                      
                        d1
                        Y
                        B
                      
                      ⁡
                      
                        (
                        
                          x
                          ,
                          y
                        
                        )
                      
                    
                    +
                    
                      
                        d
                        C
                        B
                      
                      ⁡
                      
                        (
                        
                          x
                          ,
                          y
                        
                        )
                      
                    
                    +
                    
                      
                        d
                        M
                        B
                      
                      ⁡
                      
                        (
                        
                          x
                          ,
                          y
                        
                        )
                      
                    
                  
                  )
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    d2
                    Y
                    B
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  q
                  B
                
              
            
          
        
      
    
    
      
        (
        28
        )
      
    
  




Therefore the overall visual density of a rendered composite image when subjected to light in the blue wavelength band will correspond to a constant background density of qB with the spatially varying density pattern of d2YB(x,y) being superimposed. This spatially varying density pattern is desirably seen under blue illumination and should therefore represent the source image that is to be recovered under blue illumination. (Note that some deviation from ideal spatial uniformity of the constant component can be acceptable depending on the image subject matter based on the principles of perceptual masking. For instance, a complex appearing image may have an acceptable appearance with a small amount of nonuniformity, while more uniform subject matter, like a sky scene or large image of a human face, may be significantly degraded with a small amount of nonuniformity.)
In a similar manner the density contribution of cyan and magenta under red and green illumination can be decomposed into respective components:

d1CRG(x,y) and d1MRG(x,y)  (29)

that are used to compensate for the unwanted absorption of yellow under green and red wavelength bands:

d1CRG(x,y)+d1MRG(x,y)+dYRG(x,y)=constant=qRG  (30)

and the remaining component

d2CRG(x,y)+d2MRG(x,y)=dCRG(x,y)+dMRG(x,y)−d1MRG(x,y)  (31)

which satisfies




  
    
      
        
          
            
              
                
                  d
                  RG
                
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
              =
              
              ⁢
              
                
                  
                    d
                    M
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  
                    d
                    C
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  
                    d
                    Y
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    d2
                    M
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  
                    d1
                    M
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  
                    d2
                    C
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    d1
                    C
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  
                    d
                    Y
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    d2
                    M
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  
                    d2
                    C
                    RG
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                +
                
                  q
                  RG
                
              
            
          
        
      
    
    
      
        (
        32
        )
      
    
  




Where it is implied that it is equivalent to write red and green illumination condition as separate R and G equations, or they can be written in combined form, as shown above.
A second condition that should be satisfied is that the color hue and saturation of the components forming d1MRG(x,y)+d1CRG(x,y)+dYRG(x,y) must set so that hue and saturation are spatially constant. Further, it is preferred if the sensed color of these components is a neutral color or nearly neutral, say within 10 delta E units in an L*a*b*color space. Whereas blue illumination produced a monochromatic perceived image with density being the visual sensation, red/green illumination produces a color perceived image where the density, hue and saturation are sensed. Calibration to determine colorant amounts to achieve a particular color is a standard procedure in color printing. For instance, gray balance and color calibration typically determines cyan, magenta, and yellow colorant amounts such that selected values of those colorants produce neutral colors and non neutral colors, respectively of known desired color under a particular illuminant. In those processes, calibration prints with patches of colors possessing a range of colorant amounts are printed and the color is measured. Based on the relationship between requested colorant amount and measured color, a pixel value mapping can be created to determine d1MRG(x,y) and d1MCRG(x,y) components such that d1MRG(x,y)+d1MCRG(x,y)+dYRG(x,y)=a constant color.
In practice for these specific colorants, we have found that dYRG(x,y) is nearly zero due to yellow having very little unwanted absorption. We have found that acceptable image quality can be obtained by using the approximation that dYRG(x,y)=0, which obviates the need for d1MRG(x,y) and d1CRG(x,y).
Considering only the density components to simplify the discussion, the overall visual density under green and red spectral power distributions corresponds to a constant background density of KRG with the spatially varying density pattern of d2MRG(x,y)+d2CRG(x,y) superimposed. This spatially varying pattern is the one that is seen under red and green spectral power distributions and should therefore represent the second encoded image, which is normalized color, that is to be seen under red and green spectral power distributions.
Since the terms d2MRG(x,y)+d2CRG(x,y) and d2YB(x,y) represent the visual variations in density corresponding to the two spectrally encoded images, we would like to maximize their dynamic range. Since colorants can only add positive density, this requirement translates to minimizing the terms qRG and qB subject to meeting the required equations and the physical constraint that colorants can only add positive density. We would therefore like to determine the smallest feasible values of qRG and qB for which the above equations are feasible.
For the purpose of further illustration we use a first-order approximation, that the amount of colorant added to compensate for unwanted absorption of the other colorant, itself only contributes a negligible amount of unwanted absorption (because of its small value). This assumption implies that the component of yellow used to offset unwanted absorption of cyan and magenta contributes negligibly to unwanted absorption under green and red, and the component of cyan and magenta used to offset unwanted absorption of yellow contributes negligibly to unwanted absorption under blue. This assumption is used for illustration only, in practice, one can iteratively determine the appropriate amounts to account for higher-order effects or use an appropriate model/LUT as outlined subsequently in this disclosure. With this simplifying assumption, the range achievable for the desired spatially varying pattern d2CRG(x,y)+d2MRG(x,y) under red and green illumination is between qRG and dCRG(x,y)+dMRG(x,y) with a total density variation or dynamic range of dCRG(x,y)+dMRG(x,y)−qRG. Likewise the total density range available under yellow illumination is dYB(x,y)−qB.
One set of feasible values for the terms qRG and qB can be determined as:




  
    
      
        
          
            
              
                q
                B
              
              =
              
              ⁢
              
                max
                ⁢
                
                  
                
                ⁢
                density
                ⁢
                
                  
                
                ⁢
                for
                ⁢
                
                  
                
                ⁢
                magenta
                ⁢
                
                  
                
                ⁢
                and
                ⁢
                
                  
                
                ⁢
                cyan
                ⁢
                
                  
                
                ⁢
                under
                ⁢
                
                  
                
                ⁢
                blue
              
            
          
        
        
          
            
              
              ⁢
              Illuminant
            
          
        
        
          
            
              =
              
              ⁢
              
                max
                ⁡
                
                  (
                  
                    
                      
                        d
                        C
                        B
                      
                      ⁡
                      
                        (
                        
                          x
                          ,
                          y
                        
                        )
                      
                    
                    +
                    
                      
                        d
                        M
                        B
                      
                      ⁡
                      
                        (
                        
                          x
                          ,
                          y
                        
                        )
                      
                    
                  
                  )
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    d
                    C
                    B
                  
                  ⁡
                  
                    (
                    255
                    )
                  
                
                +
                
                  
                    d
                    M
                    B
                  
                  ⁡
                  
                    (
                    255
                    )
                  
                
              
            
          
        
      
    
    
      
        (
        33
        )
      
    
  
  
    
      
        
          
            
              
                q
                RG
              
              =
              
              ⁢
              
                max
                ⁢
                
                  
                
                ⁢
                density
                ⁢
                
                  
                
                ⁢
                for
                ⁢
                
                  
                
                ⁢
                Yellow
                ⁢
                
                  
                
                ⁢
                under
                ⁢
                
                  
                
                ⁢
                green
                ⁢
                
                  
                
                ⁢
                and
                ⁢
                
                  
                
                ⁢
                red
              
            
          
        
        
          
            
              
              ⁢
              illuminant
            
          
        
        
          
            
              =
              
              ⁢
              
                max
                ⁡
                
                  (
                  
                    
                      d
                      Y
                      RG
                    
                    ⁡
                    
                      (
                      
                        x
                        ,
                        y
                      
                      )
                    
                  
                  )
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  d
                  Y
                  RG
                
                ⁡
                
                  (
                  255
                  )
                
              
            
          
        
      
    
    
      
        (
        34
        )
      
    
  




This can be thought of as follows: the background density under blue light qB is equal to the maximum unwanted density that one can have from magenta and cyan. The yellow density component d1YB(x,y) is designed carefully so that the combination of d1 for yellow, cyan and magenta at each pixel has a density qB. This can be achieved by depositing zero yellow at pixel locations where deposits of magenta and cyan are 100% (255 digital count) and appropriate amounts of yellow are deposited to make up the density to qB at pixel locations having less than 100% magenta and cyan. A similar scheme applies to the cyan and magenta density components dCRG(x,y) and dMRG(x,y) that compensate for the unwanted absorption of Yellow under red and green illumination.
Image-Dependant Mapping for Improved Dynamic Range in a Normalized Color Image
The method proposed above is independent of the images to be used in creating a composite image; such a method, however, is based on worst case assumptions and may sacrifice some dynamic range in the recovered image.
Accordingly, embodiments of spectral encoding and rendering of composite images may also utilize an image-dependent mapping that avoids such a loss in dynamic range. By determining the terms KB and KRG in an image-dependent fashion, the dynamic range of a recovered source image can be improved.
In particular, we have found that regions of a rendered composite image that are intended to appear dark under plural illuminants will, in most instances, need little or no compensation for unwanted absorptions. Accordingly, a better overlap between the dark regions under plural illuminants can be achieved through suitable design of the source images, or by shifting the images appropriately.
Hence, an improved dynamic range can be obtained by using:

qB=maxover all (x,y)(dCB(iR(x,y)+dMB(iG(x,y))−dYB(iB(x,y)),0)  (35)

qRG=maxover all (x,y)(dYRG(iB(x,y))−dCB(iR(x,y))−dMB(iG(x,y)),0)  (36)

where iR(x,y) represents the digital count for the image desired under red illumination, and iG(x,y) represents the digital count for the image desired under green illumination, and dUV(t) represents the visual density under illuminant V for colorant U at a digital count t.
Note that values of qB and qRG in Eqs. (35), (36) are expected to be smaller than qB and qRG values in Eqs. (33), (34) thereby ensuring a higher dynamic range for the desired density variations d2YB(x,y), d2CRG(x,y), and d2MRG(x,y) corresponding to the rendered composite images; this is a condition that may be advantageous for image quality wherein the rendered composite images are designed or shifted so as to have overlapping dark regions, thereby minimizing contrast degradation. This spatial effect can be seen in Eq. (36), where a spatial transformation of an image i can yield a reduced constant floor density K. Spatial optimization can be performed either computationally or by design.
The foregoing considerations can be extended to instances of images rendered using cyan, magenta, yellow, and black. By setting:

qe=min (qRG, qB)  (37)

and using a spatial value of K(x,y) such that the density corresponding to K(x,y)

d(K(x,y))=max(qe−dCR(iR(x,y)), qe−dMG(iG(x,y))  (38)

the K takes up part of the responsibility for the unwanted absorptions increasing the dynamic range available for the desirable images.
ILLUSTRATED EMBODIMENTS OF THE INVENTION
For a general understanding of the present invention, reference is made to the drawings. In the drawings, like reference numerals have been used throughout to designate identical elements.
FIG. 3 illustrates a system 100 operable in a first mode for spectrally multiplexing a plurality of source images to form a composite image, in a second mode for rendering the composite image, or in a third mode for demultiplexing the spectrally multiplexed composite image so as to recover at least one of the plurality of source images for advantageous viewing by an observer.
As shown in FIG. 3, a plurality of disparate source image arrays 11-1, 11-2, . . . 11-N are presented to an image input device 20 in a spectral multiplexing system 101. Image input device 20 may be equipped to receive plural monochromatic images or a combination of monochromatic and polychromatic images. Image input device 20 may include an image capture device such as a digital scanner coupled to a random access memory, or any type of analog or digital camera coupled to a storage device such as a computer memory or a magnetic or optical recording medium. Image input device 20 may also include a device for receiving an image that had previously been stored in a random access memory, on video tape, or a laser-encoded disk, etc., or for receiving an image created by a computer image generator, or an image encoded in an appropriate format and transmitted on a network.
The illustrative representation of the plural source images in respective image arrays received by the image input device 20 in this example includes a first source image 12-1 represented in a first source image array 11-1 and a second source image 12-2 represented in a second source image array 11-2. The system 101 can optionally receive N source images which are represented in a respective image arrays. In this exemplary embodiment of the invention, the first source image array 11-1 contains image data representative of a polychromatic pictorial image (e.g., first source image 12-1) and the second source image array 11-2 contains image data representative of a monochromatic pictorial image (e.g., second source image 12-2). Furthermore, at least one of the first and second source images 12-1, 12-2 is intended for ultimate recovery (via spectral demultiplexing) from a composite image; in the illustrated embodiment, the first source image 12-1 is illustrated as ultimately being recovered, and thus perceived, by an observer 70.
Once the source image data is received in the input image device 20, it is presented to a spectral multiplexer 30, which encodes a data representation of a composite of at least the first and second source images, so as to provide a composite image 32 on an spectrally multiplexed (SM) image plane. Such encoding may proceed in one embodiment with mapping for every pixel location, or by mapping in localized areas rather than specific pixels, to the composite image 32, so as to multiplex the information necessary for encoding of each corresponding pixel located in each source image.
Next, according to operation of a composite image rendering system 102, data representative of the composite image is provided to a rendering device 40, which can be connected to the spectral multiplexer 30 by any one of a variety of suitable devices for transmitting or storing electronic information. The rendering device 40 records the composite image 32 on a substrate 44 with use of a predetermined array of narrow band colorants, so as to form a rendered composite image 42. The rendered composite image 42 is thereby fixed on the substrate 44.
The rendered composite image 42 is available to an observer 70 for viewing in ambient light. Although the rendered composite image 42 is representative of data encoded in the spectrally multiplexed plane using the method of the invention, the rendered composite image 42 typically exhibits a confused appearance under conventional ambient lighting conditions; at least one of the source images 12-1, 12-2, etc. is thus difficult or impossible to distinguish under conventional ambient lighting conditions. A particular source image is made difficult or impossible to distinguish until a demultiplexer 50 is operated to selectively illuminate the composite image 42 in a manner sufficient to reveal the desired source image. Alternatively, one or more of the source images may be encoded so as avoid visual confusion and therefore be visually apparent in the rendered composite image when the rendered composite image is subjected to conventional ambient lighting conditions, and become confused or difficult to detect when the rendered composite image is subjected to a complementary narrow band illuminant.
According to operation of a spectral demultiplexing system 103, a particular source image (as shown in FIG. 3, source image 12-1) may be recovered and made distinguishable within the composite image 42. In the embodiment illustrated in FIG. 3, the output of the demultiplexer 50 is directed to an observer 70. The recovered image is then distinguishable by the observer 70 as being substantially identical to, or a close approximation of, the particular source image 12-1 initially provided to the image input device 20.
Recovery of a particular source image will be understood to generally proceed according to an exemplary embodiment of the spectral demultiplexing system 103 as follows. The substrate 44 is positioned with respect to an illuminant source operable within the demultiplexer 50, such that a selected illuminant generated by the demultiplexer 50 illuminates the composite image 42 so as to subject the array of colorants in the rendered composite image 42 to the predefined spectral power distribution of the selected illuminant. As a result of the rendered composite image 42 thus being controllably and selectively illuminated by a selected illuminant, a desired source image is then made visually distinguishable to an observer 70. The desired source image 12-1, now recovered, is thereby susceptible to comprehension by the observer 70.
Accordingly, by virtue of the aforementioned interaction of one or more colorants and their complementary illuminants, and due to the visual response of the observer 70 to this particular interaction, each encoded source image may or may not be distinguishable during spectral demultiplexing depending upon the objective of the demultiplexing operation.
FIG. 4 is a simplified schematic diagram of exemplary embodiments of spectral multiplexing, rendering, and spectral demultiplexing methods 61, 62, 63, respectively. In step 61 for multiplexing plural source images, image data representing a source image in a first source image 71 and a second source image 72 are provided to the multiplexer 30, which outputs a composite image data file to a rendering device 40. The output of the rendering device 40 is substrate 90 which has incorporated therein a composite image 92. The first source image 71 is provided in the form of a polychromatic source image and secondary image data is formed to describe at least two color separation images derived from the first source image, for rendering respectively using first and second colorants; in the illustrated embodiment, a cyan colorant and a magenta colorant may be suitable choices. The second source image 72 may be provided in the form of either a monochromatic or a polychromatic source image and secondary image data is formed to describe at least one color separation image derived from the second source image, for rendering respectively using a third colorant; in the illustrated embodiment, a yellow colorant may be a suitable choice. (As there is typically some overlap in absorption bands between practical narrow band colorants, the three separation images are preferably encoded in step 61 to account for the absorption that will occur when plural colorants are utilized to produce the composite image.)
In a rendering step 62, the resulting composite image 82 is used to specify patterns in the cyan, magenta, and yellow colorants that are accordingly rendered on a substrate 90 to form the rendered composite image 92. Those skilled in the art will appreciate that certain portions of the patterns may be co-located and other portions are relatively spatially distinct. Nonetheless, in certain embodiments of the present invention that utilize plural source images, visual recognition of at least one of the plural source images encoded in the composite image may be made difficult or impossible due to the visual confusion in the colorant patterns in the composite image.
In step 63 for demultiplexing the rendered composite image 92, the substrate 90 having the rendered composite image 92 fixed thereon is illuminated by the demultiplexer 50. Controlled illumination of the substrate 90 according to a first mode 51 of illumination causes the first and second separation images corresponding to the first source image 71 to achieve a particular level of density with respect to the remainder of the composite image and thus a normalized version of the first (polychromatic) image 71 becomes detectable on the substrate 90. Controlled illumination of the substrate 90 according to a second mode 52 of illumination causes the third separation image corresponding to the second source image 72 to be similarly detectable on the substrate 90. In the illustrated embodiments, the first source image 71 and the second source image 72 are therefore selectably distinguishable on the substrate 90. Controlled illumination of the substrate 90 according to operation of at least one of first and second modes 51, 52 thereby causes both the corresponding one of the first separation image 71 and the second separation image 72 to be distinguishable. Such operation of the first mode 51 is thus advantageous, for example, in recovering a normalized color image.
FIG. 5 illustrates a schematic simplified representation of the spectral multiplexing system 101 of FIG. 3, in which an image processing unit 130 and associated peripheral devices and subsystems are employed. An image input terminal 120 may include an image capture device 122 such as a scanner, digital camera, or image sensor array; a computer image generator 124 or similar device that converts 2-D data to an image; or an image storage device 126 such as a semiconductor memory or a magnetic, optical, or magneto-optical data storage device. The image input terminal 120 derives or delivers digital image data in the form of, for example, plural monochromatic image files, wherein the picture elements or “pixels” of each image are defined at some gray value. For example, the input terminal 120 may be employed to derive an electronic representation of, for example a document or photograph from image capture device 122, in a format related to the physical characteristics of the device, and commonly with pixels defined at m bits per pixel. If a color document, the image is defined with two or more separation bitmaps, usually with identical resolution and pixel depth. Image data from the input terminal 120 is directed to an image processing unit (IPU) 130 for processing so as to be encoded to create a composite image. It will be recognized that the data representing one or more source images is spectrally encoded by the image processing unit 130 to provide secondary image data representative of a composite image suitable for subsequent rendering.
The image processing unit 130 may include image memory 132 which receives input image data from image input terminal 120 or from another suitable image data source, such as an appropriately programmed general purpose computer (not shown) and stores the input image data in suitable devices such as random access memory (RAM). Image processing unit 130 commonly includes processor 134. The input image data may be processed via a processor 134 to provide image data representative of plural source images defined on respective source image planes in accordance with the present invention. For example, image data signals in the form of RGB or black and white (B/W) images may be processed, and the luminance information derived therefrom may be used to provide data representative of a source image. Image data signals presented in other formats are similarly processed: image data signals in, for example the L*a*b format, may be processed to obtain data representing a source image from the lightness channel. Image data signals that are already formatted in grayscale are generally usable without further processing.
Operation of the image processing unit 130 may proceed according to one or more image processing functions 138, 139 so as to encode the source image data into the composite image file as described hereinabove. Processing may include a color conversion which, if necessary, may be implemented to convert a three component color description to a printer-specific two, three, four or more component color description, and may include a halftoner which converts a c bit digital image signals to d bit digital image signals, suitable for driving a particular printer, where c and d are integer values. In certain embodiments, additional functions may include one or more of color space transformation, color correction, gamut mapping, and under color removal (UCR)/gray component replacement (GCR) functions. Control signals and composite image output data are provided to an interface 136 for output from the image processing unit 130.
The image processing unit 130 may be embodied as an embedded processor, or as part of a general purpose computer. It may include special purpose hardware such as for accomplishing digital signal processing, or merely represent appropriate programs running on a general purpose computer. It may also represent one or more special purpose programs running on a remote computer.
FIG. 6 is a simplified schematic representation of the spectral demultiplexing system 103 of FIG. 3, in which a controller and associated peripheral devices and subsystems are employed to obtain one or more recovered source images 171, 172. FIG. 6 shows a controller 150 connected to an illuminant source 160 that is operable for subjecting the composite image 42 on substrate 44 to at least one of first and second predefined illuminants 161, 162. Firstly, as illustrated with reference to the rendered composite image 42 on substrate 44, under conventional ambient lighting and in the absence of illuminants 161, 162, only the composite image 42 is distinguishable and no source image is easily detected. However, upon activation of the source 160 so as to provide the first predefined illuminant 161, the recovered source image 171 becomes detectable to an observer 170. Alternatively, the mode of operation of the source 160 may be switched so as to provide a second predefined illuminant 162, whereupon the composite image 42 is instead subjected to the second illuminant 162, and the recovered source image 172 becomes detectable.
The controller 150 may be constructed as in the form of a manually-operable illuminant selector switch. Alternatively, as illustrated, the controller 150 may be provided in the form of a computer-based control device having an interface 156 connected to source 160, which offers programmable control of the operation of the illuminant source 160. The controller 150 may thus be operated to cause selective activation and deactivation of the illuminant source 160 so as to provide one or more selected fields of illumination 162. Such control may, for example, the accomplished via manual operation of the illuminant source 160 by a human operator, or by programmable control afforded by a computer or similar device.
The controller 150 is operable for accomplishing tasks such as activation, deactivation, or sequencing of the illuminant source 160, setting illuminant intensity, illuminant frequency, etc. Embodiments of the controller 150 benefit from operation of a programmable control system comprising standard memory 152 and processor 154. The controller 150 may be employed, for example, for supplying uniform R or G or B screen images, or a combination thereof, to the interface 156 for subsequent display on the illuminant source 160 when the latter is constructed in the form of a CRT monitor.
Operation of the illuminant source 160 by the controller 150 may proceed according to certain sequenced control functions so as to provide, for example, controlled operation of the illuminant source 160 to afford a field of illumination that varies according to selective characteristics such as: sequential or simultaneous activation and deactivation of selected illuminants, each having a predefined spectral power distribution; controlled variation of the intensity of selected illuminants; or for interactive control according to intervention by an operator of the particular sequence, intensity, or duration of the illuminants. As noted above, the rendered composite image may be constructed to have a plurality of source images encoded therein; for example, of at least first and second patterns of respective first and second colorants. The rendered composite image may be subjected to a temporal sequencing of illumination by respective first and second narrow band illuminants, thus allowing a respective one of the first and second recovered source images 171, 172 to be sequentially distinguishable.
As mentioned, the illuminant source 160 may be provided in the form of a CRT monitor having a screen positionable with respect to the substrate 44 for generating the requisite field of illumination sufficient to illuminate the rendered composite image 42.
FIG. 7 is a rendered composite image generated according to the present invention. The rendered composite image includes a first (polychromatic) source image encoded primarily in magenta and cyan colorants and a second source image encoded as a monochromatic image in yellow colorant. A normalized version of the first source image becomes perceptible as a normalized color image when the rendered composite image is subject to a first illuminant having a predefined spectral power distribution in the red and green wavelength bands. Alternatively, the second source image becomes perceptible when the rendered composite image is subject to a second illuminant having a predefined spectral power distribution in the blue wavelength band.
To further improve image quality and provide additional features, implementation of the following techniques are contemplated:
Techniques for noise masking as disclosed in U.S. application Ser. No. 10/268,241 filed Oct. 9, 2002 by Yeqing Zhang et al. and respectively entitled “System for spectral multiplexing of source images to provide a composite image with noise encoding to increase image confusion in the composite image, for rendering the composite image, and for spectral demultiplexing of the composite image”.
Techniques for grey component replacement (GCR) as disclosed in U.S. application Ser. No. 10/268,575, filed Oct. 9, 2002 by Gaurav Sharma et al. and respectively entitled “Systems for spectral multiplexing of source images to provide a composite image with gray component replacement, for rendering the composite image, and for spectral demultiplexing of the composite image”. Implementation of GCR would contemplate selective replacement of the common image component at a given spatial location according to a fraction of the minimum of the density of the monochrome image, and according to the perceived neutral component of color in the normalized color image.
Note that one skilled in the art may realize a variety of alternatives are within the scope of this invention for implementing the above described embodiments. Its advantageous use is expected in color printing by various processes including offset lithography, letterpress, gravure, xerography, photography, and any other color reproduction process which uses a defined number of colorants, usually three or four, in various mixtures. Embodiments of the rendering system 102 include apparatus capable of depositing or integrating a defined array of colorants in a substrate, according to the composite image, such that the array of colorants is susceptible to selective reflection or transmission of a selected narrow band illuminant incident thereon. For example, the composite image may be rendered on a transparent film and a desired source image may be recovered when the substrate is backlit by a suitable narrow band illuminant. Examples include hardcopy reprographic devices such as inkjet, dye sublimation, and xerographic printers, lithographic printing systems, silk-screening systems, and photographic printing apparatus; systems for imagewise deposition of discrete quantities of a color on a substrate surface, such as paint, chemical, and film deposition systems; and systems for integration of colorant materials in an exposed surface of a substrate, such as textile printing systems.
Embodiments of exemplary substrates include, but are not limited to, materials such as paper, cardboard, and other pulp-based and printed packaging products, glass; plastic; laminated or fibrous compositions; and textiles. Narrow band colorants other than basic CMYK colorants may also be used for this invention.
The field of illumination for illuminating a rendered composite image may be provided by a variety of illuminant sources that include a narrow band light source responsive to manual control or to program control according to an illuminant source control signal. Various narrow band light sources may include apparatus for providing filtered sunlight, filtered incandescent, or filtered fluorescent light; coherent light sources such as a solid-state laser or laser diode; projection or image display devices such as those incorporating a cathode ray tube (CRT), flat-panel display (FPD), liquid crystal display (LCD), plasma display, or light emitting diode (LED) and organic light emitting (OLED) arrays. Light sources incorporating a cathode ray tube are advantageous in that they have phosphors that exhibit stable and well-understood spectral characteristics that are sufficiently narrow and complementary to common CMY colorants. In addition, such displays are widely available.
Additional familiar components (not shown) may be included such as a keyboard, and a mouse, device(s) for reading data storage media, a speaker for providing aural cues and other information to the observer, and adapters for connection of the systems described herein to a network medium. Computer readable media such as memory, hard disks, CD-ROMs, flash memory, and the like may be used to store a computer program including computer code that implements the control sequences pertinent to present invention. Other systems suitable for use with the present invention may include additional or fewer subsystems.
Embodiments of the invention are contemplated for providing visual stimulation and amusement, particularly by the inclusion of composite images in printed materials such as books or posters, in novelty items, and in software sold to consumers for generating such items. Rendered composite images made using this invention can be distributed to consumers for subsequent demultiplexing when exposed to a field of illumination generated by, for example, a display device connected to a computer according to display control signals directed to the computer from a remote source, such as from an internet site, or according to display control instructions embedded in electronic mail, Internet web pages, or similar transmissions.
Embodiments of the invention may be employed for drawing the attention of an observer to a particular source of information, such as for disseminating news, entertainment, or advertising, or to messages or indicia, such as trademarks or product instructions, on objects; to graphics, art work, and the like displayed at gathering places such cinemas, galleries, museums, commercial venues, and trade shows; or to large-format displays such as signs, posters, billboards, or murals. Still other embodiments of the invention are contemplated for use in publications, merchandising, or advertising vehicles such as newspapers, periodicals, or maps; in boxes, bottles, containers, wrappers, labels, or other packaging or shipping materials; in building materials including wall coverings, floor coverings, lighting systems, and the like.
Other embodiments of the invention are contemplated for implementing specialized visual effects in a public setting, a performance or entertainment venue, or other gathering place where there is control of the ambient lighting. Examples are festivals, theaters, night clubs, and sporting events, where participants may receive printed materials or packaging, clothing, souvenirs, etc. having incorporated thereon one or more rendered composite images. Under the influence of localized fields of illumination provided by suitably-modified zone lighting equipment, such as stage lighting equipment, which may be synchronized or otherwise controlled, a variety of source images having visual interest to the participants may be made visible in a dramatic fashion.
Other embodiments of the invention are contemplated for implementing secure verification of authenticity of a document or other instrument. Such embedded information may be present in the form of a watermark, an indice, or an image useful for validation, secure identification, or the like. For example, the appearance of a, single image or an unchanging (i.e. constant) image viewed under specific, controlled illumination could be used to indicate authenticity of a document. Fraudulent attempts to circumvent the verification, such as by proffering a photocopy or counterfeit of the requisite instrument, may not meet the printer calibration settings necessary for generating an authentic composite image, such that a confused appearance of a composite image on a counterfeit under the controlled lighting would preclude authenticity. Embodiments of the invention are contemplated for providing simple encryption and decryption of embedded information in documents, coupons, game pieces, tickets, certificates, commercial paper, currency, identification cards, and the like.
Still other embodiments of the invention are contemplated for use in textiles and garments such as head coverings, clothing, and outerwear, and in other wearable or personal items such as footwear, timepieces, eyewear, jewelry, appliques, fashion accessories, and the like. Items bearing composite images generated in the course of the practice of this invention may have an artistic, novelty, or collectible nature, such as in a souvenir, book, magazine, poster, educational material, trading card, or toy.
While particular embodiments have been described, alternatives, modifications, variations, improvements, and substantial equivalents that are or may be presently unforeseen may arise to applicants or others skilled in the art. Accordingly, the appended claims as filed and as they may be amended are intended to embrace all such alternatives, modifications variations, improvements, and substantial equivalents.

## Claims

1. A method of processing a plurality of source images, comprising:
receiving image data representative of a polychromatic source image and encoding first and second separation images representing the polychromatic source image in a composite image;
rendering the composite image on a substrate by use of a plurality of colorants; and recovering the encoded separation images from the rendered composite image, such that the polychromatic source image is made distinguishable as a normalized color image, by subjecting the rendered composite image to an illuminant having a predefined spectral power distribution that is selected to reveal the normalized color image.

2. The method of claim 1, wherein the source image encoding step further comprises the step of mapping values representative of each separation image pixel to a corresponding pixel value in a respective colorant image plane.

3. The method of claim 2, wherein the mapped values are determined according to at least one of the following: (a) the trichromacy of human visual response to colorant/illuminant interaction; (b) the spectral characteristics of the colorants selected for rendering the composite image, and (c) the spectral characteristics of the narrow-band illuminant(s) used for recovering the source image.

4. The method of claim 3, wherein the source image encoding step further comprises:
receiving image data representative of a second source image and converting the second source image to a third separation image; and mapping the third separation image to a corresponding colorant image plane in the composite image.

5. The method of claim 4, wherein a narrow band colorant is assigned to a respective colorant image plane of the composite image, and the mapped values in the respective colorant image planes represent the relative amounts of the narrow band colorant to be deposited in the rendered composite image.

6. The method of claim 1, wherein the composite image is rendered as pattern of deposited narrow band colorants, each of which narrow band colorants exhibiting a predefined spectral reflectance characteristic.

7. The method of claim 6, wherein the selected narrow band colorant exhibits a predefined narrow band absorption characteristic.

8. The method of claim 7, wherein the selected narrow band colorant is selected from the group of cyan, magenta, and yellow colorants.

9. The method of claim 1, wherein the predefined spectral power distribution of the illuminant is selected from the group of red, green, and blue wavelength regions of the spectrum.

10. The method of claim 1, wherein the rendered composite image is rendered using a digital color electrophotographic printer.

11. An imaging system, comprising:
a spectral multiplexer for receiving image data representative of a polychromatic source image and for processing the image data to encode at least first and second separation images representing the polychromatic source image in a composite image, and for providing a composite image data signal;
an image rendering device which is responsive to the spectral multiplexer for receiving the composite image data signal and for rendering the composite image on a substrate; and
a spectral demultiplexer for subjecting the rendered composite image on the substrate to illumination by an illuminant having a predefined spectral power distribution for which the polychromatic source image was encoded, such that a normalized color image derived from one of the encoded source images is recovered when the rendered composite image is subjected to the illuminant.

12. The imaging system of claim 11, wherein the spectral multiplexer is operable for mapping values representative of each source image pixel to a corresponding pixel value in a respective colorant image plane.

13. The system of claim 12, wherein the mapped values are determined according to at least one of the following: (a) the trichromacy of human visual response to colorant/illuminant interaction; (b) the spectral characteristics of the colorants selected for rendering the composite image, and (c) the spectral characteristics of the narrow-band illuminant(s) used for recovering the source image.

14. The imaging system of claim 12, wherein the spectral multiplexer is operable for converting the polychromatic source image to an array of respective monochromatic separation images, each of which being mapped to a corresponding colorant image plane in the composite image, and the plurality of separation images being mapped to a corresponding plurality of colorant image planes in the composite image.

15. The imaging system of claim 12, wherein the spectral multiplexer is operable for assigning each colorant to a respective colorant image plane of the composite image, and the colorant values in the respective colorant image planes represent the relative amounts of colorant to be deposited in the rendered composite image.

16. The imaging system of claim 11, wherein the spectral multiplexer is operable for spectrally encoding the polychromatic source image by mapping pixel values representative of plural separation images to a corresponding pixel value in one or more of a plurality of colorant image planes.

17. The imaging system of claim 16, wherein the separation images define the polychromatic source image according to the separation image planes, and wherein the composite image is defined in a spectrally multiplexed (SM) image plane having patterns of pixels, whereby at each location in the SM image plane, a pixel value representing one or more spectral components may be present, and wherein the pixel value patterns are determined according to the gray level of the corresponding pixels in one or more of the separation image planes.

18. The imaging system of claim 17, wherein the spectral multiplexer is operable for is spectrally multiplexing to the SM image plane wherein certain pixels includes color values representative of color separation image data from more than one source image plane.

19. The imaging system of claim 11, wherein the spectral multiplexer is operable for receiving image data representative of the polychromatic source image, and converting, when necessary, the array of image data representative of the polychromatic source image to respective separation images, and wherein the spectral multiplexer is operable for receiving second image data which is representative of a second source image, and for converting, when necessary, the second source data to provide a respective monochromatic image, wherein the separation images and the monochromatic image are mapped to corresponding ones of plural colorant image planes in the composite image, and wherein the resulting composite image incorporates spectrally encoded information representing both the first (polychromatic) source image and a monochromatic version of the second source image.

20. The imaging system of claim 11, wherein a mode of operation is provided for recovering a normalized color version of, the encoded source image from the rendered composite image such that a normalized color image is made distinguishable to an observer.

21. The imaging system of claim 11, wherein the spectral demultiplexer is operable in a first mode wherein the normalized color image is recovered when the rendered composite image is illuminated by a controlled field of illumination of a first illuminant having a selected multiband spectral power distribution.

22. The imaging system of claim 21, wherein the spectral demultiplexer is operable in a second mode wherein a second source image presented in a rendered composite image is recovered when the rendered composite image is illuminated by a controlled field of illumination of a second illuminant having a selected narrowband spectral power distribution.

23. The imaging system of claim 22, wherein the spectral demultiplexer is operable in a first mode of operation to subject the rendered composite image to a first illuminant exhibiting a spectral power distribution located in the spectral power distributions of complementary illuminants for at least first and second respective colorants, such that at least two separation images (representing the first source image) are recoverable so as to form a normalized color image, and in a second, optional, mode of operation wherein the rendered composite image is subjected to a second illuminant exhibiting a spectral power distribution located in the spectral power distribution of the complementary illuminant for a third respective colorant.

24. The imaging system of claim 21, wherein the spectral demultiplexer is operable for subjecting the rendered composite image to an incident light spectrum having a selected spectral power distribution in at least two of three selectable bands of radiant energy.

25. The imaging system of claim 24, wherein the first illuminant is selected from at least two of the long, medium, and short (LMS) wavelength bands of the light spectrum, and the second illuminant is selected from at least the remaining third of the long, medium, and short (LMS) wavelength bands of the light spectrum.

26. The imaging system of claim 11, wherein the spectral demultiplexer includes a controller and an illuminant source responsive to illuminant source control signals provided by the controller, and wherein the illuminant source includes one or more light sources for providing desired spectral power distributions in plural selectable bands of radiant energy.

27. The imaging system of claim 26, wherein the selectable bands correspond to the long, medium, and short (LMS) wavelength bands of the light spectrum.

28. The imaging system of claim 11, wherein the image rendering device employs at least one selected colorant selected for its narrow band absorbing properties so as to appear dark when subjected to a first illuminant having a spectral power distribution that lies substantially within the spectral absorption band of the selected colorant, and to appear light when subjected to a second, differing illuminant having a spectral power distribution that lies substantially outside of the spectral absorption band of the selected colorant.

29. The imaging system of claim 11, wherein the spectral multiplexer is provided in the form of a computer for receiving image data files representative of a plurality of source images and for encoding the image data files as a composite image data file.

30. The imaging system of claim 11, further comprising at least one of a composite image file storage device and a composite image file transmission device.

31. The imaging system of claim 11, wherein the spectral multiplexer is operable to perform a dynamic range determination so as to provide a maximum usable contrast in a recovered normalized image.

32. The imaging system of claim 11, wherein the spectral multiplexer is operable to perform a dynamic range determination by permuting the allocation of the source image to differing monochromatic separations, in an image-dependent fashion, so as to restrict the gamut of the source image only to the extent required by the source image.

33. The imaging system of claim 32, wherein the dynamic range determination includes limiting the gamut of the source image.

34. The imaging system of claim 11, wherein the spectral multiplexer is operable to perform the addition of image masking signals to the source image.

35. The imaging system of claim 11, wherein the image recording device is provided in the form of a printer for printing the composite image on a substrate.

36. The imaging system of claim 35, wherein the printer includes one or more of cyan, magenta, yellow, and black colorants selected for their apparent darkness when exposed to complementary illuminants.