JP5564316B2 - Brightest color arithmetic device and program - Google Patents

Description

  The present invention relates to a technique for calculating the brightest color that represents the theoretical maximum color gamut of an object color under a given illumination, and in particular, calculates the brightest color obtained by a given light source spectrum quickly and accurately. The present invention relates to a brightest color arithmetic device and a program.

  The XYZ color system is used as a standard color space in which colors are represented by tristimulus values. The tristimulus value of the object color can be obtained from the light source spectrum of the light that illuminates the object, the spectral reflectance or spectral transmittance of the object, and the color matching function (for example, see Non-Patent Document 1).

  Further, it has been proved that the brightest color representing the theoretical maximum color gamut of the object color has a band-pass characteristic or a band-stop characteristic in which the spectral reflectance (transmittance) of the object is 0% or 100%. The brightest color gamut is expressed by drawing a locus of equal luminance for several set luminances in the CIE xyY or CIELAB color space.

  The color gamut of the brightest color under a given illumination can be targeted, for example, when developing pigments or dye inks for color printers, color filters for image sensors, and designing primary color points for displays.

  Therefore, in recent years, a technique for calculating the brightest color representing the theoretical maximum color gamut of the object color in a given light source spectrum has attracted attention.

In 2007, Martinez-Verdu published a method for calculating the brightest color of a virtual object from a color matching function and a light source spectrum given at a wavelength of 0.1 nm from 380 nm to 780 nm (for example, non-patented). Reference 2). As shown in FIG. 10, this calculation method is based on a case where a bandpass characteristic or a band stop characteristic indicating a spectral reflectance or a spectral transmittance of a virtual object (theoretical object) is classified according to type (Type). Because errors occur due to calculation without complementing the data, ± 0.01 is recommended as the tolerance of error, and if multiple lightest colors that fall within this tolerance are included, one average value is used. If no output falls within the allowable range, the final brightest color is determined by interpolation from the brightest color in the vicinity.

Noboru Ota "Color Optics", Tokyo Denki University Press Martinez Verdu et al, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source”, Vol. 24, No. 6, June 2007, Optical Society of America, pp. 1501-1515

  However, the calculation method of the brightest color according to Non-Patent Document 1 involves an increase in calculation cost due to the case classification of the bandpass characteristics or the band stop characteristics according to the type (Type), and further sets an allowable error range. In order to determine the final brightest color, it cannot be said that the accuracy of the value obtained as the brightest color is high, and the set allowable range is not effective for all illumination light.

  The object of the present invention has been made in view of the above-described problems, and provides a brightest color computing device and a program for computing the brightest color obtained by a given light source spectrum at high speed and accurately. is there.

That is, the brightest color arithmetic device of the present invention is
A brightest color computing device for computing the brightest color obtained by a predetermined light source spectrum,
The light source spectrum, the color matching function and the luminance to be calculated are input, and both the color matching function and the light source spectrum are interpolated so that the wavelength steps used for the calculation have the same step value. A connected spectral distribution calculator that normalizes each color matching function and connects the normalized spectral distributions;
A bandwidth calculation unit that applies a single band characteristic to the connected spectral distribution, executes an integration process, and determines a bandwidth in which a tristimulus value at a central wavelength is the luminance of the calculation target;
A tristimulus value calculator for calculating a tristimulus value at a central wavelength using the determined bandwidth and the three color matching functions;
About the processing of the bandwidth calculation unit and the tristimulus value calculation unit, iterative calculation is performed over the entire visible range to calculate tristimulus values at each central wavelength, and the calculated tristimulus values are calculated as the light source spectrum to be calculated. And an all-wavelength repetitive calculation unit that determines the brightest color of the luminance to be calculated with respect to.

In the brightest color arithmetic device of the present invention, the one band characteristic has a predetermined band width in which the spectral reflectance is 0% or 100%, or the spectral transmittance is 0% or 100%. And

  In the brightest color arithmetic apparatus according to the present invention, the integration process is a trapezoidal integration process.

Furthermore, the present invention provides a computer configured as a brightest color computing device that computes the brightest color obtained by a predetermined light source spectrum.
(A) A light source spectrum to be calculated, a color matching function and a luminance to be calculated are input, and both the color matching function and the light source spectrum are interpolated so that wavelength steps used for the calculation have the same step value. Applying each color matching function to the light source spectrum to normalize and concatenating each normalized spectral distribution;
(B) applying one band characteristic to the connected spectral distribution, executing an integration process, and determining a bandwidth at which a tristimulus value at a central wavelength becomes the luminance of the calculation target;
(C) calculating a tristimulus value at a central wavelength using the determined bandwidth and the color matching function;
(D) About the process of the said step (b) and the said step (c), it calculates repeatedly the tristimulus value in each center wavelength by performing calculation over the whole visible region, and the calculated tristimulus value is the said calculation object. And a step of determining as the brightest color of the luminance to be calculated for the light source spectrum.

According to the present invention, there is no need to separate the bandpass characteristic or the band stop characteristic indicating the spectral reflectance or spectral transmittance of the object color, which has caused an increase in calculation cost, and the discrete spectral distribution is linear. Since the accuracy can be determined with an arbitrary value desired by the user for complementation, the fastest and most accurate value of the brightest color can be obtained.

It is a figure which shows the brightest color arithmetic unit of one Example by this invention. It is a flowchart which shows operation | movement of the brightest color calculating apparatus of one Example by this invention. It is a figure which illustrates the light source spectrum of D65 light source. It is a figure which illustrates a color matching function. It is a figure which shows the spectral distribution and band characteristic in the brightest color arithmetic unit of one Example by this invention. It is a figure which shows the example of the trapezoid integration process in the brightest color arithmetic unit of one Example by this invention. It is a CIExy chromaticity diagram in the predetermined | prescribed brightness | luminance calculated from the tristimulus value obtained with the brightest color calculating apparatus of one Example by this invention. It is a figure which shows the CIE LAB color space calculated from the tristimulus value obtained with the brightest color arithmetic unit of one Example by this invention. It is a figure which shows the lightness error between the lightness L * and L * const (1, 5, 50, 95). It is a figure which shows the example which performs the case classification by the type (Type) about the band pass characteristic or the band stop characteristic showing the spectral reflectance or spectral transmittance of a virtual object (theoretical object).

  Hereinafter, a brightest color arithmetic apparatus according to an embodiment of the present invention will be described.

  The brightest color calculation device 1 can be configured as a computer, and the parameter input unit 11 can be an arbitrary man-machine interface set by a user. The light source spectrum of the calculation target illumination light, the color matching function And the luminance to be calculated are input and sent to the control unit 12, and the control unit 12 executes each function. In addition, a program describing processing contents for realizing each function of the control unit 12 is stored in the storage unit 13 of the computer, and this program is read and executed by a central processing unit (CPU) of the computer. Can be realized.

  The control unit 12 includes a connected spectral distribution calculation unit 121, a bandwidth calculation unit 122, a tristimulus value calculation unit 123, and an all-wavelength repetition calculation unit 124.

The bandwidth calculation unit 122 has a predetermined bandwidth 2hn with a spectral reflectance of 0% or 100% or a spectral transmittance of 0% or 100% with respect to the connected spectral distribution T (k). A band characteristic is applied, an integration process (for example, a trapezoidal integration process) is executed to determine a bandwidth 2hn at which the tristimulus value Y at the center wavelength λn becomes the luminance Yconst to be calculated, and the tristimulus value calculation unit 123 Send it out.

  The all-wavelength repetition calculation unit 124 calculates the tristimulus value at each central wavelength λn by performing repetition calculation over the entire visible range for the processing of the bandwidth calculation unit 122 and the tristimulus value calculation unit 123 described above. The tristimulus value is determined as the brightest color of the luminance Yconst of the calculation target with respect to the light source spectrum S of the calculation target illumination light.

  The user can input the value of the brightness Yconst to the brightest color calculation device 1 arbitrarily, thereby determining the accuracy with an arbitrary value desired by the user.

  Hereinafter, the operation of the brightest color arithmetic device according to an embodiment of the present invention will be described in more detail.

The brightest color computing device 1 has a predetermined spectral reflectance of 0% or 100% or a spectral transmittance of 0% or 100% with respect to the connected spectral distribution T (k) by the bandwidth calculation unit 122. One band characteristic having a bandwidth 2hn is applied and trapezoidal integration processing is executed to determine a bandwidth 2hn at which the tristimulus value Y at the center wavelength λn becomes the luminance Yconst to be calculated (step S3).

Here, N is the number of samples of wavelength. When the wavelength range is 380-780 nm, N = 4001. The tristimulus value Y of the brightest color is expressed by Equation (2) using the spectral reflectance or the spectral transmittance R (k).

  Equation (4) is represented by trapezoidal integration as in Equation (5).

In searching for the minimum value, hn that minimizes | Yn−Yconst | is searched in the range of 0 ≦ hn ≦ N / 2. Since Yn in equation (5) is a monotonically increasing function, it converges stably. The permissible range for hn here is set to a reasonably small value, for example, 10 ⁻¹⁰ . Note that it is not necessary to set an allowable range in advance as in the technique in Non-Patent Document 2.

  The brightest color computing device 1 performs a repeated calculation over the entire visible range with respect to the processing of the bandwidth calculation unit 122 and the tristimulus value calculation unit 123 by the all-wavelength repetition calculation unit 124, and performs three operations at each central wavelength λn. A stimulus value is calculated (step S5), and the calculated tristimulus value is determined as the brightest color of the luminance Yconst of the calculation target with respect to the light source spectrum S of the calculation target illumination light (step S5).

  The present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the spirit of the present invention.

  According to the present invention, it is possible to obtain the fastest and most accurate value of the brightest color from the light source spectrum to be used. For example, development of color printer pigment or dye ink or image sensor color filter, display primary color point Useful in the field of design.

DESCRIPTION OF SYMBOLS 1 Brightest color calculating apparatus 2 Display apparatus 3 Database 11 Parameter input part 12 Control part 13 Storage part 121 Connection spectral distribution calculation part 122 Bandwidth calculation part 123 Tristimulus value calculation part 124 All wavelength repetition calculation part

Claims (4)

A brightest color computing device for computing the brightest color obtained by a predetermined light source spectrum,
The light source spectrum, the color matching function and the luminance to be calculated are input, and both the color matching function and the light source spectrum are interpolated so that the wavelength steps used for the calculation have the same step value. A connected spectral distribution calculation unit that applies normalization to each color matching function and connects the normalized spectral distributions;
A bandwidth calculation unit that applies a single band characteristic to the connected spectral distribution, executes an integration process, and determines a bandwidth in which a tristimulus value at a central wavelength is the luminance of the calculation target;
A tristimulus value calculation unit for calculating a tristimulus value at a center wavelength using the determined bandwidth and the color matching function;
About the processing of the bandwidth calculation unit and the tristimulus value calculation unit, iterative calculation is performed over the entire visible range to calculate tristimulus values at each central wavelength, and the calculated tristimulus values are calculated as the light source spectrum to be calculated. An all-wavelength repetitive calculation unit that determines the brightest color of the luminance to be calculated for
A brightest color arithmetic device, comprising: 2. The brightest color according to claim 1, wherein the one band characteristic has a predetermined bandwidth with a spectral reflectance of 0% or 100% or a spectral transmittance of 0% or 100%. Arithmetic unit.   2. The brightest color arithmetic device according to claim 1, wherein the integration process comprises a trapezoidal integration process. In a computer configured as a brightest color calculation device for calculating the brightest color obtained by a predetermined light source spectrum,
(A) A light source spectrum to be calculated, a color matching function and a luminance to be calculated are input, and both the color matching function and the light source spectrum are interpolated so that wavelength steps used for the calculation have the same step value. Applying each color matching function to the light source spectrum to normalize and concatenating each normalized spectral distribution;
(B) applying one band characteristic to the connected spectral distribution, executing an integration process, and determining a bandwidth at which the tristimulus value Y at the center wavelength becomes the luminance of the calculation target;
(C) calculating a tristimulus value at a central wavelength using the determined bandwidth and the color matching function;
(D) About the process of the said step (b) and the said step (c), it calculates repeatedly the tristimulus value in each center wavelength by performing calculation over the whole visible region, and the calculated tristimulus value is the said calculation object. Determining as the brightest color of the target luminance for the light source spectrum;
A program for running

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