JP2024017068A - Cone spectral sensitivity estimation device - Google Patents

Abstract

[Problem] The purpose is to accurately estimate the spectral sensitivity of the cones of an individual test subject.
A cone spectral sensitivity estimation device 4 is configured to detect a test color displayed in one area 21 of a screen of a display device 2 and a reference color corrected by a color filter 23 installed in another area 22 of the screen. As experimental data of a conditional color matching experiment in which the subject P adjusts the test color so that the test color becomes the same color, the RGB values of the test color adjusted by the subject P and the RGB values of the reference color displayed in the other area 22 of the screen are combined. and an estimating section 64 that estimates a cone spectral sensitivity function indicating the spectral sensitivity of the cone of the subject P based on the experimental data.
[Selection diagram] Figure 1

Description

The present invention relates to a cone spectral sensitivity estimation device.

It is known that there are individual differences in visual characteristics of people. Visual properties are represented by spectral sensitivity functions (color matching functions), which are curves that indicate the sensitivity of cones to each wavelength of light. The color that humans perceive is determined by the spectral sensitivity function and the spectral radiance of the object to be observed.

Patent Document 1 discloses a selection means for causing a user to select a color closest to a reference color formed on a light-reflecting medium from among a plurality of different colors displayed on a display device; determining means for determining a color to be displayed on the display device next time based on the selected color; and calculating the visual characteristics of the user based on the result of repeating color determination by the determining means and selection by the user multiple times. and, when the user repeatedly selects a combination of two or more colors a certain number of times or more, the calculation means calculates the visual characteristics of the user based on the colors included in the combination. An arithmetic processing device is disclosed.

Japanese Patent Application Publication No. 2016-134683

The arithmetic processing device disclosed in Patent Document 1 allows a subject to select a color close to a reference color chart from a display in a color matching experiment. At this time, the arithmetic processing device disclosed in Patent Document 1 displays a measurement color chart, which is a light source color, on a self-luminous display for the printed reference color. As a result, in the arithmetic processing device disclosed in Patent Document 1, a difference in color gamut or brightness occurs between the reference color and the measurement color patch, making it difficult to perform color matching experiments correctly. Therefore, with the arithmetic processing device disclosed in Patent Document 1, it is difficult to accurately estimate the spectral sensitivity function of the subject's cones from the results of the color matching experiment.

The present invention has been made in view of the above, and an object of the present invention is to accurately estimate the spectral sensitivity of the cones of an individual subject.

In order to solve the above problems, the cone spectral sensitivity estimation device of the present invention corrects a test color displayed in one area of the screen of a display device and a color filter installed in another area of the screen. As experimental data of a conditional color matching experiment in which a subject adjusts the test color so that it becomes the same color as a reference color, the RGB values of the test color adjusted by the subject and the reference color displayed in the other area are used. and an estimator that estimates a cone spectral sensitivity function indicating the spectral sensitivity of the cone of the subject based on the experimental data.

The conditional color matching experiment of the present invention can be carried out by a simple method of installing a color filter in another area of the screen of the display device, and it is also possible to perform the conditional color matching experiment by installing a color filter in another area of the screen of the display device, and by using This can be done under experimental conditions that do not cause any difference. The cone spectral sensitivity estimation device of the present invention is capable of estimating a subject's cone spectral sensitivity function based on the experimental data obtained in such a simple and accurate conditional color matching experiment. can. Therefore, the cone spectral sensitivity estimation device of the present invention can easily and accurately estimate the cone spectral sensitivity of an individual subject.

In a further preferred embodiment, the cone spectral sensitivity function is expressed using a parameter related to visual characteristics of the subject, and the response value of the cone to a stimulus of the reference color is expressed as a spectral radiance of the stimulus of the reference color. and the cone spectral sensitivity function, and the response value of the cone to the stimulus of the test color is expressed using the spectral radiance of the stimulus of the test color and the cone spectral sensitivity function. and the estimation unit is configured to minimize a mean squared error of a relative error between the response value of the cone to the stimulus of the reference color and the response value of the cone to the stimulus of the test color. The cone spectral sensitivity function is estimated by searching the parameters.

With this aspect, the cone spectral sensitivity estimating device of the present invention can avoid a situation where the cone spectral sensitivity function converges to zero in the optimization calculation for minimizing the above-mentioned mean square error, and can also prevent the cone spectral sensitivity function from converging to zero. The influence of the reference stimulus on the estimation accuracy of can be minimized. Therefore, the cone spectral sensitivity estimation device of the present invention can estimate the cone spectral sensitivity function more accurately. Therefore, the cone spectral sensitivity estimation device of the present invention can more accurately estimate the cone spectral sensitivity of an individual subject.

In a further preferred embodiment, the test color is expressed by juxtaposed additive color mixing in which different colors are displayed in adjacent pixel groups within the one area.

With this aspect, it is possible to easily increase the gradation of the test color without performing a conditional color matching experiment using a special display device capable of displaying a high gradation. Therefore, the cone spectral sensitivity estimation device of the present invention can accurately estimate the cone spectral sensitivity function of the subject even if the subject has cones that can perceive subtle differences in color. Therefore, the cone spectral sensitivity estimation device of the present invention can more easily and accurately estimate the cone spectral sensitivity of an individual subject.

In a further preferred embodiment, the estimation unit searches for the parameters using a differential evolution method.

With this aspect, the estimation unit of the present invention can search for parameters using a relatively simple algorithm, and therefore can easily estimate the cone spectral sensitivity function. Therefore, the cone spectral sensitivity estimation device of the present invention can more easily estimate the cone spectral sensitivity of an individual subject.

In a further preferred embodiment, the experimental data acquisition unit acquires a plurality of experimental data obtained by installing a plurality of color filters having different spectral transmittances and performing a plurality of conditional color matching experiments, The estimation unit estimates the cone spectral sensitivity function based on the plurality of experimental data.

According to this aspect, the cone spectral sensitivity estimating device of the present invention can estimate the cone spectral sensitivity function using the subject's cone response values to color stimuli having various wavelength ranges. The spectral sensitivity function can be estimated more accurately. Further, the cone spectral sensitivity estimation device of the present invention can suppress estimation errors of the cone spectral sensitivity function even if there are variations in experimental data of conditional color matching experiments. Therefore, the cone spectral sensitivity estimation device of the present invention can more accurately estimate the cone spectral sensitivity of an individual subject.

According to the present invention, it is possible to accurately estimate the spectral sensitivity of the cone of an individual subject.

FIG. 1 is a diagram showing the configuration of a cone spectral sensitivity estimation system including a cone spectral sensitivity estimation device according to the present embodiment. Flowchart showing the flow of conditional color matching experiment. FIG. 3(a) is a diagram explaining a conditional color matching experiment, and FIG. 3(b) is a diagram showing the spectral transmittance of each color filter. FIG. 3 is a diagram illustrating increasing the gradation of a test color. 5 is a flowchart showing the flow of the cone spectral sensitivity function estimation process performed by the cone spectral sensitivity estimation device. Figure 6(a) shows an example of the results of estimating the cone spectral sensitivity function of a subject using the cone spectral sensitivity estimation device, and Figure 6(b) shows the estimation error of the cone spectral sensitivity function due to variations in experimental data. A diagram showing an example of the occurrence.

Embodiments of the present invention will be described below with reference to the drawings. Structures designated by the same reference numerals in each embodiment have the same functions in each embodiment unless otherwise mentioned, and their explanation will be omitted.

[Configuration of cone spectral sensitivity estimation system]
The configuration of the cone spectral sensitivity estimation system 1 of this embodiment will be described using FIG. 1.

FIG. 1 is a diagram showing the configuration of a cone spectral sensitivity estimation system 1 including a cone spectral sensitivity estimation device 4 of this embodiment.

The cone spectral sensitivity estimation system 1 is a system that estimates the spectral sensitivity of a cone of a subject P as a visual characteristic of the subject P. In particular, the cone spectral sensitivity estimation system 1 is a system that estimates a cone spectral sensitivity function that indicates the spectral sensitivity of the cone of the subject P based on experimental data that is the experimental result of a conditional color matching experiment for the subject P. . The cone spectral sensitivity estimation system 1 includes a display device 2, an input device 3, and a cone spectral sensitivity estimation device 4.

The display device 2 is configured with a display that displays various colors to the subject P in order to perform a conditional color matching experiment. The input device 3 is constituted by a general-purpose input device such as a mouse or a keyboard through which information is input by the operation of the subject P during the conditional color matching experiment. The input device 3 may be configured by a dedicated input device such as a slider that is operated by the subject P during the conditional color matching experiment.

The cone spectral sensitivity estimating device 4 is configured by a computer system that estimates the spectral sensitivity of the cone of the subject P. The cone spectral sensitivity estimation device 4 includes a storage device 5 and an arithmetic processing device 6. The storage device 5 is configured by an SSD, an HDD, or the like. The storage device 5 stores various data used in processing by the arithmetic processing device 6. The arithmetic processing device 6 is composed of a CPU, ROM, RAM, and the like. The arithmetic processing device 6 realizes various functions of the cone spectral sensitivity estimating device 4 by having the CPU execute a program stored in the ROM.

The arithmetic processing device 6 includes a display control unit 61 that controls the display of the display device 2 in the conditional color matching experiment. Furthermore, the arithmetic processing device 6 includes an experiment information acquisition unit 62 that acquires experiment information indicating the experimental conditions of the conditional color matching experiment, and an experiment data acquisition unit 63 that acquires experimental data of the conditional color matching experiment. Furthermore, the arithmetic processing device 6 includes an estimation unit 64 that estimates a cone spectral sensitivity function indicating the spectral sensitivity of the cone of the subject P based on the experimental data acquired by the experimental data acquisition unit 63.

[Conditional color matching experiment]
A conditional color matching experiment of this embodiment will be explained using FIGS. 2 to 4.

FIG. 2 is a flowchart showing the flow of a conditional color matching experiment. FIG. 3(a) is a diagram illustrating a conditional color matching experiment. FIG. 3(b) is a diagram showing the spectral transmittance of each color filter 23. FIG. 4 is a diagram illustrating increasing the gradation of a test color.

In the conditional color matching experiment of this embodiment, a test color displayed in one area 21 of the screen of the display device 2 (on the right side of the screen in FIG. 3(a)) and another area 22 of the screen of the display device 2 (in FIG. In (a), the reference color and the test color are matched by having the subject P adjust the test color so that the reference color corrected by the color filter 23 installed on the left side of the screen is the same color. conduct.

Specifically, in the conditional color matching experiment of this embodiment, the experiment manager or the subject P installs the color filter 23 in the other area 22 of the screen of the display device 2 (step S1 in FIG. 2). The color filter 23 is composed of a plurality of color filters 23 having mutually different spectral transmittances. For example, as shown in FIG. 3(b), the color filter 23 is configured such that the color (corrected color) of achromatic light after passing through the filter is pale blue, green, pink, yellow-green, red, or purple. This is the color filter. That is, the reference colors corrected by the achromatic light passing through the color filter 23 are blue, green, pink, yellow-green, red, or violet.

Subsequently, in the conditional color matching experiment of this embodiment, the display control unit 61 of the cone spectral sensitivity estimation device 4 executes initial display control of one area 21 and other area 22 of the screen of the display device 2 (see FIG. step S2). A test color serving as a light source color is displayed in one area 21 of the screen. The color initially displayed as the test color may be a predetermined achromatic color or a chromatic color. In the other area 22 of the screen, the reference color before correction by the color filter 23 is displayed. The reference color displayed in the other area 22 of the screen is not changed until the color filter 23 is replaced.

Here, the test color is expressed by juxtaposed additive color mixture in which different colors are displayed in adjacent pixel groups within one area 21 of the screen. That is, the display control unit 61 displays the test colors by dividing two or more colors into a checkered pattern, as shown in FIG. 3(a). For example, assume that one area 21 on the screen is composed of 6×6 pixels, as shown in FIG. “0” or “1” in each pixel in FIG. 4 indicates that the light emission of each pixel is “OFF” or “ON”. The emission intensity of each pixel can be set in a range of 0 to 255. The display control unit 61 divides the entire 6×6 pixels into nine parts to create a pixel group of 2×2 pixels. The display control unit 61 sets 2 ⁸ =256 gradation colors for each created pixel group. In this case, 255×9+1=2296 colors can be displayed in one area 21 of the screen. In reality, different colors are displayed for each pixel group, but for the subject P observing from a suitable distance from the display device 2, the different colors displayed for each pixel group are mixed to form a uniform color. appear. In this way, the test color is represented by a juxtaposed additive color mixture. In addition, in FIG. 4, one area 21 of the screen may be configured with 3×3 pixels or 12×12 pixels, and is not particularly limited. The color displayed in each pixel group is not particularly limited as long as it is set within a range in which the subject P does not feel a sense of discontinuity in color.

Subsequently, in the conditional color matching experiment of this embodiment, the display control unit 61 of the cone spectral sensitivity estimation device 4 executes display control to display on the display device 2 a message urging the subject P to perform color matching. . Subject P adjusts the test color so that the test color displayed in one area 21 of the screen and the reference color corrected by the color filter 23 installed in the other area 22 of the screen become the same color (see Fig. 2 step S3). The subject P can arbitrarily adjust the test color by operating the input device 3. The subject P can adjust the test color by inputting the RGB values of the test color using the input device 3 configured with a keyboard. Alternatively, the subject P can adjust the test color by moving the input device 3 configured with a slider or the like. The input device 3 notifies the display control unit 61 of the RGB values of the test color adjusted by the subject P. The display control unit 61 controls the RGB values of each pixel in one area 21 of the screen according to the RGB values notified from the input device 3. Thereby, the test color adjusted by the subject P is displayed in one area 21 of the screen. After the adjustment by the subject P, the display control unit 61 stores the RGB values of the test color adjusted by the subject P in the storage device 5 as input values (R _t , G _t , B _t ). The display control unit 61 stores the RGB values of the reference color displayed in the other area 22 of the screen (the reference color before correction by the color filter 23) in the storage device 5 as input values (R _r , G _r , B _r ). Remember.

Subsequently, in the conditional color matching experiment of this embodiment, the experiment manager or the subject P determines whether the experiment has been completed with all the color filters 23 (step S4 in FIG. 2). If all the color filters 23 have not been tested, the color filters 23 are replaced with ones that have not been tested (step S1), and the conditional color matching experiment is performed again. If all color filters 23 have been tested, the conditional color matching experiment is ended. Note that the display control unit 61 determines whether all the color filters 23 have been tested by checking the RGB values of the test colors and reference colors stored in the storage device 5. You may go. Then, the display control unit 61 executes display control to display on the display device 2 a message to the effect that the conditional color matching experiment has been completed, or a message prompting the experiment manager or the subject P to replace the color filter 23. Good too.

[Estimation process of cone spectral sensitivity function]
The cone spectral sensitivity function estimation process performed by the cone spectral sensitivity estimation device 4 of this embodiment will be described with reference to FIG.

FIG. 5 is a flowchart showing the flow of the cone spectral sensitivity function estimation process performed by the cone spectral sensitivity estimation device 4.

First, the experimental information acquisition unit 62 of the cone spectral sensitivity estimation device 4 acquires experimental information (step S11 in FIG. 5). The experiment information includes the age a [years] of the subject P in the conditional color matching experiment.

Subsequently, the experimental data acquisition unit 63 of the cone spectral sensitivity estimation device 4 acquires experimental data of the conditional color matching experiment (step S12 in FIG. 5). Specifically, the experimental data acquisition unit 63 inputs input values (Rt, Gt, Bt) that are the RGB values of the test color adjusted by the subject P and displays them in the other area 22 of the screen for each conditional color matching experiment. The input values (Rr, Gr, Br) that are the RGB values of the reference color thus obtained are acquired from the storage device 5. When a plurality of color filters 23 having mutually different spectral transmittances are installed and a conditional color matching experiment is performed a plurality of times, the experimental data acquisition unit 63 acquires a plurality of experimental data.

Subsequently, the estimation unit 64 of the cone spectral sensitivity estimation device 4 estimates the cone spectral sensitivity function of the subject P based on the acquired experimental information and experimental data. Specifically, the estimation unit 64 performs the processing shown in steps S13 to S16 in FIG. 5. When the conditional color matching experiment is performed a plurality of times, the estimation unit 64 estimates the cone spectral sensitivity function of the subject P based on the plurality of experimental data.

First, the estimating unit 64 identifies parameters related to the visual characteristics of the subject P (step S13 in FIG. 5). Specifically, the estimation unit 64 calculates the age a [years] of the subject P, the stimulus size ν [deg], the deviation d _lens [%] of the optical density of the eyeball optical medium, the deviation d _{macula [%] of the optical density of the macular} , Deviation of maximum optical density of each cone d _L [%], d _M [%], d _S [%], and deviation of spectral absorbance in the wavelength direction s _L [nm], s _M [nm], s Specify 10 parameters of _S [nm]. Note that the cone spectral sensitivity function shown below is expressed using parameters related to the visual characteristics of the subject P.

The stimulus size ν is the size of the color stimulus seen from the subject P in the conditional color matching experiment. The stimulus size ν is expressed by the visual angle [deg]. The stimulus size ν is not explicitly input as the size of the color stimulus set as an experimental condition, but is set as a parameter related to the visual characteristics of the subject P.

The deviation of the ocular optical medium optical density _dlens is the deviation of the ocular optical medium optical density of the subject P from the ocular optical medium optical density of the standard observer used in defining the standard cone spectral sensitivity. This standard observer may be a standard observer defined by CIE (Commission Internationale de Illumination).

The macular optical density deviation d _macula is the deviation of the subject P's macular optical density from the standard observer's macular optical density.

The maximum optical density deviations d _L , d _M , d _S of each cone are the deviations of the maximum optical density of each cone of subject P from the maximum optical density of each cone of a standard observer.

The deviations of spectral absorbance in the wavelength direction s _L , s _M , s _S are the spectral absorbance of the visual substance in each cone of the subject P in the wavelength direction from the spectral absorbance of the visual substance in each cone of the standard observer. It is a deviation. The spectral sensitivities of the three cones L, M, and S are a function of the wavelength of light, and the waveform thereof can be approximately chevron-shaped. The shifts in the wavelength direction of the spectral absorbances s _L , s _M , s _S can directly affect the wavelength of the maximum value of the spectral sensitivity of each of the three cones. Therefore, the estimating unit 64 at least specifies the deviations s _L , s _M , s _S of the spectral absorbance in the wavelength direction, which can have the greatest influence on the estimation of the cone spectral sensitivity function among the above ten parameters. do.

Next, the estimation unit 64 uses the identified parameters to create a visual model representing the cone spectral sensitivity function of the subject P (step S14 in FIG. 5). Specifically, the estimation unit 64 creates Equation 1 as a visual model representing the cone spectral sensitivity function of the subject P. λ represents wavelength. The spectral sensitivity functions l _q (λ), m _q (λ), s _q (λ) are the spectral absorbance α _j (λ) (j=L, M, S), the macular optical density D _macula , as shown in Equation 1. (λ), the ocular optical medium optical density D _lenses (λ).

When the age a of the subject P is 60 years old or less, the average eyeball optical medium optical density D _lens,ave (λ) is defined by Equation 2. When the age a of the subject P is over 60 years old, the average eyeball optical medium optical density D _lens,ave (λ) is defined by Equation 3. Furthermore, as shown in Equation 4, the deviation _dlens of the optical density of the optical medium of the eyeball is introduced to express individual differences.

The macular optical density D _macula (λ) is calculated by introducing the deviation d macula of the macular optical density into the influence of the average macular optical density D _macula,ave (λ) and the stimulus size ν, as shown in Equations 5 and ₆ . and express individual differences.

The spectral absorbance A _shift,j (λ) of each cone at low optical density reflecting the shift s _j in the wavelength direction is expressed by Equation 8. The maximum value D _max,j of the optical density of each cone reflecting individual differences using the stimulus size ν and the deviations d _L , d _M , d _S of the maximum optical density of each cone is expressed by Equation 9. be done. The spectral absorbance α _j (λ) of each cone is calculated using the spectral absorbance A _shift,j (λ) of each cone at low optical density and the maximum value D _max,j of the optical density of each cone, It is expressed by Equation 7.

As described above, the visual model expressing the cone spectral sensitivity function of the subject P is as follows: the subject P's age a [years], the stimulus size ν [deg], the deviation _dlens [%] of the optical density of the ocular optical medium, and the macular optical density. deviation d _macula [%], deviation of the maximum optical density of each cone d _L [%], d _M [%], d _S [%], and deviation of spectral absorbance in the wavelength direction s _L [nm], Individual differences in cone spectral sensitivity can be expressed using a total of 10 parameters, s _M [nm] and s _S [nm].

Next, the estimation unit 64 calculates each cone response value for the reference color stimulus (also referred to as "reference stimulus") and the test color stimulus (also referred to as "test stimulus") (step S15 in FIG. 5). Each cone response value for the reference stimulus and the test stimulus is calculated by the spectral radiance P _r (λ), P _t (λ) of the reference stimulus and the test stimulus, and the cone spectral sensitivity function l (λ), shown in Equation 1. It is expressed using m(λ) and s(λ).

Let the spectral radiances r(λ), g(λ), and b(λ) be when input values to the RGB channels of the display device 2 are maximized, and the spectral transmittance of the color filter 23 be τ(λ). The input values (R _r , G _r , B _r ), (R _t , G _t , B _t ) in the reference stimulus and test stimulus are 0 to 1. The gamma characteristic of the display device 2 is assumed to be linear (γ=1). In this case, the spectral radiance P _r (λ) of the reference stimulus is expressed by Equation 10. The spectral radiance P _t (λ) of the test stimulus is expressed by Equation 11. The input values (R _r , G _r , B _r ), (R _t , G _t , B _t ) in the reference stimulus and the test stimulus are the values stored in the storage device 5 from the display control unit 61 as described above. be.

Each cone response value L, M, S to the reference stimulus and the test stimulus is expressed by Equation 12. In the conditional color matching experiment, the equation 13 should hold true. However, the equation 13 cannot be solved analytically using linear algebra because of its form. Therefore, the estimation unit 64 needs to estimate the cone spectral sensitivity function by numerically solving the equation 13. At this time, the estimation unit 64 numerically solves the equation of Equation 13 using a plurality of experimental data obtained by performing a plurality of conditional color matching experiments.

Next, the estimation unit 64 searches for parameters related to the visual characteristics of the subject P so that the mean square error of the relative error between the cone response value for the reference stimulus and the cone response value for the test stimulus is minimized (Fig. 5 step S16). Specifically, the cone response values to the reference stimulus and test stimulus in the n-th conditional color matching experiment conducted by subject P are (L _r,n , M _r,n , S _r,n ), (L _{t , n} , M _t,n , S _t,n ). The error (residual difference) between the cone response value for the reference stimulus and the cone response value for the test stimulus is expressed as ΔL _n =L _r,n -L _t,n , ΔM _n =M _r,n -M _t,n , ΔS Let _n = S _{r, n} - S _{t, n} . In this case, when a cone spectral sensitivity function that minimizes the error is determined, the determined cone spectral sensitivity function becomes the individual cone spectral sensitivity function of the subject P.

In this embodiment, the estimating unit 64 searches the above 10 parameters so that the mean square error of the relative error between the cone response value for the reference stimulus and the cone response value for the test stimulus is minimized. , estimate the cone spectral sensitivity function of subject P. The mean squared error RMSE _LMS of the relative error between the cone response value for the reference stimulus and the cone response value for the test stimulus is expressed by Equation 14. In Equation 14, ΔL _n /L _r,n , ΔM _n /M _r,n , ΔS _n /S _r,n represents the relative error between the cone response value to the reference stimulus and the cone response value to the test stimulus. represents.

One reason why the mean square error RMSE _LMS of the relative error is adopted as the evaluation function value rather than the errors ΔL _n , ΔM _n , ΔS _n is that the cone spectral sensitivity function is zero in the optimization calculation to minimize the evaluation function value. This is to avoid a situation where the situation converges. That is, the cone response values for the reference stimulus (L _r,n , M _r,n , S _r,n ) and the cone response values for the test stimulus (L _t,n , M _t,n , S _t,n ) are , is calculated by multiplying each spectral radiance by the same cone spectral sensitivity function (estimation target), and then integrating it in the visible wavelength range (calculated as the sum after multiplying by the wavelength width) . Therefore, when simply adopting the mean square error of the errors ΔL _n , ΔM _n , and ΔS _n as the evaluation function value, if the cone spectral sensitivity function approaches zero over all wavelengths, the mean square error (evaluation function value) also becomes zero. , it is highly likely that the optimization calculation will not work effectively. The inventor actually performed optimization calculations using the mean squared error as the evaluation function value, and confirmed that a cone spectral sensitivity function in which all values are always zero was obtained. On the other hand, when the mean square error RMSE _LMS of the relative error is adopted as the evaluation function value, even if the cone spectral sensitivity function approaches zero, the mean square error RMSE _LMS (the evaluation function value) of the relative error is not only the numerator but also the denominator. also approaches zero, so it is impossible for the cone spectral sensitivity function that minimizes the evaluation function value to converge to a function in which all wavelength ranges are zero. For this reason, the estimation unit 64 employs the mean square error RMSE _LMS of the relative error as the evaluation function value.

Furthermore, another reason for employing the relative mean square error RMSE _LMS as the evaluation function value is to minimize the influence of the reference stimulus on the estimation accuracy. That is, the balance of the response values of the three types of cones (L cone, M cone, and S cone) changes depending on the color of the reference stimulus. For example, for a red reference stimulus, the response value of the L cone is relatively large compared to the response value of the M cone or the response value of the S cone. Therefore, if the mean square error of the errors ΔL _n , ΔM _n , and ΔS _n is simply adopted as the evaluation function value, if the reference stimulus used in the conditional color matching experiment is biased toward the red color system, L in the mean square error Since the error in the response value of the cone has a relatively large weight, there is a possibility that the cone spectral sensitivity function of the M cone or the S cone cannot be estimated properly. The same applies if the reference stimulus is biased toward the green color system or the blue color system. On the other hand, when the mean square error RMSE _LMS of the relative error is adopted as the evaluation function value, it is considered that the cone spectral sensitivity functions of the three types of cones can be estimated in a well-balanced manner without being affected by the color bias of the reference stimulus. It will be done. That is, it is possible to equalize each response value between LMS cones and eliminate the possibility that the spectral sensitivity function of a cone with a large response value dominates the error sum of squares. Furthermore, the error between the cone response value to the reference stimulus and the cone response value to the test stimulus in the conditional color matching experiment is proportional to the size of the color discrimination threshold (the minimum color difference for distinguishing between colors). It is known that this discrimination threshold follows Weber's law, which is proportional to stimulus intensity. Therefore, also from the viewpoint of the characteristics of the experimental data used in the optimization calculation, it is appropriate to employ the mean square error RMSE _LMS of the relative error as the evaluation function value. For this reason, the estimation unit 64 employs the mean square error RMSE _LMS of the relative error as the evaluation function value.

In order to search for parameters that minimize the mean squared error RMSE _LMS expressed by Equation 14, it is necessary to apply some kind of nonlinear optimization method. The mean square error RMSE _LMS expressed by Equation 14 has a complex model and cannot calculate the derivative of the cone spectral sensitivity function. Therefore, in order to search for parameters that minimize the mean square error RMSE _LMS expressed by Equation 14, gradient methods such as the steepest descent method or Newton's method cannot be applied. Furthermore, since there is a possibility that the search will be for a parameter that converges to a local minimum value, a global optimization method is preferable as the optimization method to be applied.

Therefore, in this embodiment, the estimating unit 64 searches for the above parameters by applying a differential evolution method, which is one of evolutionary calculation algorithms with a relatively simple algorithm, as an optimization method. In minimizing a multivariate function using the differential evolution method, a large number of vectors (individuals) with variables as components are generated, and the next generation of individuals is created through mutation and crossover, while minimizing the function value to a smaller value. The minimum value of the function is finally obtained by selectively evolving individuals that become . With this method, the above parameters can be easily obtained, and the cone spectral sensitivity function of the subject P can be derived.

The objective here is not to minimize a multivariate function, but to search for parameters that minimize the mean squared error RMSE _LMS . Therefore, a vector having D parameters as components is treated as an individual. The i-th (i=1, 2, . . . , N _P ) vector (individual) in a population with a total number of N _P in generation G is expressed as x _i,G = (x _1i,G , x _2i,G ,・..., x _{Di, G} ). The mutation vector v _{i,G+1 in generation G+1} is a vector x _r1,G , x _r2,G , x _r3,G (where r1, r2, r3∈{i=1, 2, . . . , N _P }) and a scale factor F∈[0,2].

The trial vector u _{i of generation G+1,} the j-th parameter u _{ji, G+1} (j=1, 2, ..., D) of G+1, the parameter x _{ji, G} of the original vector, and the parameter v _ji of the mutation vector _{, G+1} by an operation called crossover shown in Equation 16. At this time, one integer random number j _r ∈{1, 2, . . . , D} and j random numbers rand _ji ∈ [0, 1] are generated for each parameter. A parameter for which the random number rand _ji is less than or equal to a preset crossover rate CR∈[0,1], or the j-th parameter that matches j _r , is replaced with the parameter v _ji,G+1 of the mutation vector. Otherwise, the parameters x _ji,G of the original vector are preserved.

An evaluation value is calculated using the generated trial vector u _i,G+1 and the original vector x _i,G, and as shown in Equation 17, the vector with the lower evaluation value is set as the next generation vector x _i,G+1. leave. This process is repeated to evolve the parameters that give the minimum evaluation value. _The estimation unit 64 calculates D=10 parameters (a, ν, d _lens , d _macula , d _L , d _M , d _S , s _L , _sM , _sS ).

Next, the estimation unit 64 derives the cone spectral sensitivity function of the subject P from the searched parameters (step S17 in FIG. 5). Specifically, the estimation unit 64 calculates the searched 10 parameters (a, ν, _dlens , _dmacula , _dL , _dM , _dS , _sL , _sM , _sS ) using Equation 1. ～Substitute into Formula 9. Thereby, the estimation unit 64 can derive the cone spectral sensitivity function of the subject P.

[Estimation results of cone spectral sensitivity function]
The estimation results of the cone spectral sensitivity function by the cone spectral sensitivity estimation device 4 of this embodiment will be explained using FIGS. 6(a), 6(b), and Table 1.

FIG. 6A is a diagram showing an example of the result of estimating the cone spectral sensitivity function of the subject P by the cone spectral sensitivity estimation device 4. FIG. 6B is a diagram showing an example in which an error in estimating the cone spectral sensitivity function occurs due to variations in experimental data. Table 1 is a table showing an example of the results of searching for parameters related to the visual characteristics of the subject P using the cone spectral sensitivity estimation device 4.

The CFF (Cone Fundamental Function) on the vertical axis in FIGS. 6A and 6B indicates the value of the cone spectral sensitivity function. The horizontal axis in FIGS. 6(a) and 6(b) indicates wavelength. The solid lines in FIGS. 6(a) and 6(b) indicate the cone spectral sensitivity function estimated by the cone spectral sensitivity estimation device 4. The dashed line * in Figures 6(a) and 6(b) indicates the cone spectral sensitivity function calculated in advance in the simulation, which is an ideal cone with virtually no variation in the experimental data of the conditional color matching experiment. The body spectral sensitivity function is shown.

As shown in FIG. 6(a), the estimation result of the cone spectral sensitivity function by the cone spectral sensitivity estimation device 4 almost matches the simulation result showing an ideal cone spectral sensitivity function. That is, the cone spectral sensitivity estimation device 4 can accurately estimate the cone spectral sensitivity function of the subject P. In other words, the cone spectral sensitivity estimation device 4 can accurately estimate the spectral sensitivity of the cone of an individual subject.

In a conditional color matching experiment, a person performs color matching while observing a reference color and a test color. Experimental data from conditional color matching experiments have considerable errors and variations. These errors and variations can cause estimation errors in the cone spectral sensitivity function. In order to suppress the estimation error of this cone spectral sensitivity function, it is effective to perform conditional color matching experiments multiple times under the same conditions.

FIG. 6A shows the estimation results of the cone spectral sensitivity function when the variation in the experimental data is as small as 0.5% and the number of trials of the conditional color matching experiment is 12 times. FIG. 6(b) shows the estimation results of the cone spectral sensitivity function when the variation in the experimental data is as large as 2% and the number of trials of the conditional color matching experiment is three. In the case of FIG. 6(a), the estimation error of the cone spectral sensitivity function is extremely small. In the case of FIG. 6(b), the estimation error is large for the spectral sensitivity function l(λ) of the L cone. As a result of various studies, the inventor found that even if there is a 1.5% variation in the experimental data, if the number of trials of the conditional color matching experiment is 12, the estimation error of the cone spectral sensitivity function is extremely small. I have confirmed that it will become smaller. The inventor also conducted conditional color matching experiments multiple times for a subject P whose shape of the cone spectral sensitivity function deviated somewhat from the shape of the function shown in Equation 1. We have confirmed that the estimation error can be suppressed to a usable level.

Although the embodiments of the present invention have been described in detail above, 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 as described in the claims. It can be performed. The present invention does not include adding the configuration of one embodiment to the configuration of another embodiment, replacing the configuration of one embodiment with another embodiment, or deleting a part of the configuration of one embodiment. You can

2... Display device, 21... One area, 22... Other area, 23... Color filter, 4... Cone spectral sensitivity estimation device, 63... Experimental data acquisition section, 64... Estimation section, P... Subject

Claims (5)

Conditions for having the subject adjust the test color so that the test color displayed in one area of the screen of the display device and the reference color corrected by a color filter installed in another area of the screen become the same color, etc. an experiment data acquisition unit that acquires the RGB values of the test color adjusted by the subject and the RGB values of the reference color displayed in the other area as experiment data of the color experiment;
A cone spectral sensitivity estimating device comprising: an estimator that estimates a cone spectral sensitivity function indicating the spectral sensitivity of the cone of the subject based on the experimental data. The cone spectral sensitivity function is expressed using parameters related to visual characteristics of the subject,
The response value of the cone to the stimulus of the reference color is expressed using the spectral radiance of the stimulus of the reference color and the cone spectral sensitivity function,
The response value of the cone to the stimulus of the test color is expressed using the spectral radiance of the stimulus of the test color and the cone spectral sensitivity function,
The estimator is configured to calculate the parameter such that the parameter minimizes a mean square error of a relative error between the response value of the cone to the stimulus of the reference color and the response value of the cone to the stimulus of the test color. The cone spectral sensitivity estimation device according to claim 1, wherein the cone spectral sensitivity function is estimated by searching. The cone spectral sensitivity estimating device according to claim 1, wherein the test color is expressed by juxtaposed additive color mixture in which different colors are displayed in adjacent pixel groups within the one region. The cone spectral sensitivity estimating device according to claim 2, wherein the estimator searches for the parameter using a differential evolution method. The experimental data acquisition unit acquires a plurality of experimental data obtained by installing a plurality of color filters having different spectral transmittances and performing a plurality of conditional color matching experiments,
The cone spectral sensitivity estimation device according to claim 1, wherein the estimator estimates the cone spectral sensitivity function based on a plurality of the experimental data.

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