Journal of the Korean Physical Society, Vol. 41, No. 6, December 2002, pp. 865∼871

Design of Advanced Color - Temperature Control Systemfor HDTV Applications

Bongsoon Kang,∗ Ohak Moon and Changhee Hong

Department of Electronic Engineering, Dong-A University, Busan 604-714

Honam Lee, Bonghwan Cho and Youngsun Kim

Core Tech. Group, Visual Display Division, Samsung Electronics Co., LTD., Suwon 442-742

(Received 23 April 2002)

This paper proposes an advanced color-temperature control system for HDTV applications. Com-pared with the X-chromaticity method [1], it improves the capability in color-temperature calcula-tion by using an additional Y-chromaticity coordinate. It also extends the temperature range from3000 K to 1667 K by using new coordinates that are obtained by using a linear regression method.The proposed system requires 32174 bits in ROM size, which is an 88 % reduction in hardwarecompared with the X-chromaticity method. The proposed system is experimentally demonstratedfor color temperatures in the range from 1667 K to 25000 K by using the Xilinx FPGA VirtexXCV2000E-6BG560 device.

PACS numbers: 42.79.Ls, 42.30.VaKeywords: Color Temperature, CIE-XYZ, HDTV, Chromaticity

I. INTRODUCTION

When one watches a scene, one can feel the generalcolor tone from the scene. Under an incandescent lamp,one can feel the reddish color tone while in the case ofdaylight one can feel the bluish color tone. This feelingis different from scene to scene or image to image. Thisdifferent feeling can be converted into figures in the formof chromaticity coordinates. It can be also transformedinto the daylight locus on the chromaticity plane [2]. Aconventional color-converting system changes RGB sig-nals for hue, saturation, and so on [3], fixes the RGB tocertain assumed values without considering the incomingcolor tones, and induces artificial effects on the displayedimage, thereby resulting in color distortion. Another wayuses a gamma correction to compensate for the color dis-tortion caused by the properties of display devices suchas cathode ray tube, thin film transistor-liquid crystaldisplay (TFT-LCD), and so on [4], but it still uses fixed-inverse gamma values for the compensation without con-sidering the color tones.

The term color temperature is applied to highly se-lective radiators, such as electric discharge lamps, whenthe light of the radiator has nearly the same chromaticitycoordinates as a blackbody radiator at a certain temper-ature; this temperature is then called the color tempera-ture of the selective radiator [5]. For example, a filament

∗E-mail: bongsoon@daunet.donga.ac.kr; Fax: +82-51-200-7712

temperature is around 2800 K, the daylight temperatureis around 5400 K, and the blue-sky temperature undera sunny sky is 12000∼18000 K. If one can convert thetemperature, the conversion provides more flexibility forvisual display devices while general display media changethe contrast, hue, and gamma values. A self-luminousarea is an area on the scene that is not perceived as apassive surface reflector [6]. It can be thought of as anactive reflector like a lamp itself or the aperture on awall or some specular reflection from an arbitrary sur-face. This area should be excluded when calculating thecolor temperature of the input scene. For a more nat-ural color tone, the color temperature of the convertedscene should not be fixed at a specific temperature, butchanged in proportion to the color temperature of theinput scene.

One way of calculating color temperatures in perceivedillumination was proposed by Robertson in Ref. 5. Thismethod uses two chromaticity coordinates (x, y) in theillumination (hereafter, called the 2D method). The de-merit of the method is that the required hardware is toobulky and is almost infeasible to implement in real hard-ware. A simple way, which uses only the X-chromaticitycoordinate for the calculation (hereafter, called the 1Dmethod), is proposed in Ref. 1. However, the 1D methodresults in big calculation errors when fundamental colors(especially, red, green, cyan, magenta, yellow, etc.) areinputted. The reasons are that the white point line ofthe color temperature is not linear in the X-chromaticitycoordinate and the deviation of the coordinate from the

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white point line is sometimes large. Therefore, a meanhas to be developed in order to improve the temperature-calculation capability for HDTV applications.

II. COLOR - TEMPERATURECALCULATION

For estimating the color temperature of the scene, onecan use the 2D method in which 31 isotemperature linesare defined in the range from 1667 K to infinity [5]. Themethod uses two chromaticity coordinates (x, y). Thus,one can calculate the color temperature of the sceneby using an interpolation method between two adjacentlines where the chromaticity point of the given sourcelies. If the coordinates of the chromaticity point of thegiven source are denoted by (xs, ys) and (xi, yi) denotesthe chromaticity point through which the i-th isotem-perture line of slope ti passes, the required distance di isobtained from

di =(ys − yi)− ti(xs − xi)

(1 + t2i )1/2. (1)

The chromaticity coordinates (xs, ys) lie between ad-jacent lines i = j and i = j + 1 if the ratio dj/dj+1 isnegative. The reciprocal color temperature is a linearfunction of distance along this arc [5]. It follows that

Tc =[

1Tj

+dj

dj − dj+1

(1

Tj+1− 1Tj

)]−1

. (2)

As one can see, the 2D method uses two chromaticitycoordinates (x, y) for calculating the temperature. Itrequires very huge hardware for implementing the high-precision square root, dividers, multipliers, and so on.

A simple way is proposed in Ref. 1. The correlatedcolor temperature Tc of a given source is related to onlythe X-chromaticity coordinate in the given source by us-ing the equations below. For correlated color tempera-tures from approximately 4000 K to 7000 K and fromapproximately 7000 K to 25000 K,

xD = −4.6070109

T 3c

+ 2.9678106

T 2c

+0.09911103

Tc+ 0.244063

and

xD = −2.0064109

T 3c

+ 1.9018106

T 2c

+0.24748103

Tc+ 0.237040 (3)

respectively. In the 1D method, the lower limit of thetemperature is set to 3000 K by simply extending therange of the equation for 4000 K to 7000 K. The lowerlimit is the area for yellow and red, thereby the methodresults in big errors in color-temperature calculationswhen the given source contains low-temperature infor-mation. In the hardware implementaion of Eq. (3), aROM is used for easy implementation, and the requiredsize is 267752 bits [7]. The demerits of the 1D methodare that the calculation errors become bigger when theinput temperatures are below 3000 K and the ROM sizerequired to implement Eq. (3) increases dramatically inproportion to the temperature precision.

In order to reduce the required ROM size and to ex-tend the temperature range, one can use a linear regres-sion method [8] to derive new coordinates, Pix and y dd,in which the Pix is the X-chromaticity coordinate ofthe given source and the y dd is the value on the whitepoint line corresponding to Piy. The generalization ofthe method of finding a best-fit line to finding a best-fitpolynomial is very straightforward. To see the generalpattern of the results, one can try the third-order modelfunction

Pix = a3T−3ci + a2T

−2ci + a1T

−1ci + a0 (4)

and form the averaged difference S between the 31 pointsf(T−1

ci ) and Eq. (4):

S =131

31∑i=1

{Pix− f(T−1ci )}2

=131

31∑i=1

{a3T−3ci + a2T

−2ci + a1T

−1ci + a0 − f(T−1

ci )}2.

(5)

To minimize the difference, one can easily show that thefour equations

∂S

∂a0=

∂S

∂a1=

∂S

∂a2=

∂S

∂a3= 0 (6)

yield

a0

a1

a2

a3

=

31

∑31i=1 T

−1ci

∑31i=1 T

−2ci

∑31i=1 T

−3ci∑31

i=1 T−1ci

∑31i=1 T

−2ci

∑31i=1 T

−3ci

∑31i=1 T

−4ci∑31

i=1 T−2ci

∑31i=1 T

−3ci

∑31i=1 T

−4ci

∑31i=1 T

−5ci∑31

i=1 T−3ci

∑31i=1 T

−4ci

∑31i=1 T

−5ci

∑31i=1 T

−6ci

−1

∑31i=1 f(T−1

ci )∑31i=1 f(T−1

ci )T−1ci∑31

i=1 f(T−1ci )T−2

ci∑31i=1 f(T−1

ci )T−3ci

(7)

Design of Advanced Color - Temperature Control System · · · – Bongsoon Kang et al. -867-

The values of the coefficients, ak, of the best-fit cubic to the points result in

Pix =

{−3.0258469 109

T 3c

+ 2.1070379 106

T 2c

+ 0.2226347 103

Tc+ 0.24039 for 4000K ≤ Tc ≤ 25000K

−0.2661239 109

T 3c− 0.2343589 106

T 2c

+ 0.8776956 103

Tc+ 0.179910 for 1667K ≤ Tc ≤ 4000K.

(8)

In a similar manner, one can derive

y dd =

3.0817580Pix3 − 5.8733867Pix2 + 3.75112997Pix− 0.37001483 for 4000K ≤ Tc ≤ 25000K−0.9549476Pix3 − 1.37418593Pix2 + 2.09137015Pix− 0.16748867 for 2222K ≤ Tc ≤ 4000K−1.1063814Pix3 − 1.34811020Pix2 + 2.18555832Pix− 0.20219683 for 1667K ≤ Tc ≤ 2222K.

(9)

Figure 1 shows the white point lines obtained by us-ing the 2D method and the proposed method (hereafter,called the 1.5D method). As one can see, the curve ofthe estimated polynomials is almost equal to that of the2D method.

Figure 2 shows the difference between the 2D methodand the 1D method. When an input has a chromaticitycoordinate of (Pix, Piy), the 2D method may give thevalue A on the X-chromaticity axis since the cross sec-tion (x dd, ?) between the isotemperature line and thewhite point line lies on the vertical axis of the value A.Since the value of the notation “?” does not affect thecalculated temperature, it is not calculated. The simpleway proposed in Ref. 1 uses only the X-chromaticity co-ordinate so as to reduce the hardware complexity. Thus,the projection of the source on the X coordinate repre-sents the value B that is the value measured by usingthe 1D method. The difference, denoted as Differ pix,between the values A and B represents the temperatureerror in the calculation. The 1D method works quite wellfor most general images, however, because the chromatic-ity coordinates of the images reside near the white pointline. When the coordinates of the given source residefarther from the white point line, the differences becomebigger and result in larger calculation errors that are

Fig. 1. Comparison of white point lines by using Robert-son’s method (2D) and the proposed method (1.5D).

beyond tolerances. Therefore, a means to compensatefor the differences is required, especially for fundamentalcolors.

Figure 3 shows the relationship between Differ pixand Differ piy denoted in Fig. 2. The range used inPix is from 0.15 to 0.58. The 0.15 represents the colorCyan and the 0.58 denotes the lower limit of Robert-son’s method in Ref. 5. They correspond to color tem-peratures of about 25000 K and 1667 K, respectively.The increment in Pix is 0.02 to see the relationship. Asone can see, there are regular patterns, depending onthe Differ piy values. For example, let’s choose the 16points (−0.125, −0.1, −0.075, −0.05, −0.025, 0, 0.025,0.05, 0.075, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.6) for the dis-crete Differ piy. One can then measure the 22 corre-sponding Differ pix values on the curves shown in Fig.3. As already derived in Eq. (9), y dd is then calcu-

Fig. 2. Plot showing the procedure to calculate the colortemperature by using the proposed method.

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Fig. 3. Relationship between Differ piy and Differ pix.

lated easily since Pix is the input value. Differ piy isobtained by differentiating y dd with respect to Piy.

Let’s assume that the actual Pix lies between Pixiand Pixi+1 and that the actual Differ piy lies betweenDiffer piyi and Differ piyi+1. Once Differ piyis obtained, one can easily extract four adjacentDiffer pix values from the ROM. They are denoted asa, b, c, and d. The actual Differ pix value can then bederived by using the geometry shown in Fig. 4. Let’smake an example. Assume that Pix lies between Pixi= 0.15 and Pixi+1 = 0.17 and that Differ piy lies be-tween 0.4 and 0.5. The e is the Differ pix value of thesource on the 0.4-Differ piy axis and the f is the corre-sponding value on the 0.5-Differ piy axis. The valuesof e and f can be obtained as

e =b− a

Pixi+1 − Pixi(Pix− Pixi) + a,

f =d− c

P ixi+1 − Pixi(Pix− Pixi) + c. (10)

Now, the actual Differ pix value can be calculated eas-ily as

Differ pix =f − e

Differ pixi+1 −Differ pixi(Differ pix−Differ pixi) + e. (11)

The value A in Fig. 2 is obtained by adding the valueof Differ pix to the value B. Thereby, the proposedmethod can compensate for the calculation error thatoccurs when using the 1D method. Figure 5 summarizesthe procedure of the proposed method. As one can see,the compensated Pix value is almost equal to the 2DRobertson’s method.

In Ref. 7, the 1D method required 267752 bits fortemperature conversions since it required 199800 bits (=3 columns×3 rows×12 bits×1850 points) for convertingthe input image to a 6500-K image and 44000 bits (=2 components×12 bits×1850 points) for converting the6500-K image to the target temperature. An additionalROM of 23552 bits (= 46 bits×512 points) were neededto calculate the temperature of the input. A linear re-gression estimate and the method shown in Figs. 3 to5 are used. The required ROM size can be reduced toas small as 32174 bits. The proposed method requires5632 bits (= 16 points×22 values×16 bits) for the calcu-lation since the 16 Differ piy points have 22 values, andeach value is required to have at least a 16-bit width toprovide an accurate calculation. An additional ROM of26524 bits (= 46 bits×577 points) is needed to calculatethe temperature of the input.

III. PERFORMANCE EVALUATIONS

Using a variety of input images tests the performanceof the proposed method. Table 1 shows the results. Forcomparison purposes, the temperatures obtained by us-ing the 2D method are assumed to be the original tem-peratures (ideal case) of the input images. Images 1-3are three different images of multiple objects, houses,trees, sky, and so on. The calculated temperatures are8895 K, 2708 K, and 10308 K, respectively. The tem-perature of image 2 is as low as 2708 K since it is taken

Fig. 4. Geometry to compensate for the X-chromaticitycoordinates.

Design of Advanced Color - Temperature Control System · · · – Bongsoon Kang et al. -869-

Fig. 5. Plot showing the method to compensate for theDiffer pix error.

Table 1. Comparison of color temperatures.

Input Image 2D 1D 1.5D

Image 1 8,895 9,780 8,858

Image 2 2,708 3,000 2,594

Image 3 10,308 12,437 10,430

Red 1,667 3,000 1,667

Green 7,245 25,000 7,254

Blue 25,000 25,000 25,000

Cyan 25,000 25,000 25,000

Magenta 1,979 4,773 2,180

Yellow 3,629 3,000 3,620

in the late evening. As one can see, the temperaturesobtained by using the 1.5D method are close to thoseof the 2D method compared the temperatures obtainedby using the 1D method. Even though the 1D methodhas big errors in the temperature calculations, the ex-perimental tests show that the human eye is insensitiveto errors in general images containing multiple objects.This is expected since the coordinates of the combinationof multiple objects lie close to the white point line. Whenfundamental colors are inputted, the errors become big-ger. When the input is Green, the 1D method calculatesa color temperature of 25000 K while the 1.5D methodcalculates a temperature of 7254 K, which is very closeto value of 7245 K from the 2D method. From the Table1, one can see that the color-temperatures obtained byusing the 1.5D method are very close to those obtainedby using the 2D method. Thus, the performance of theproposed method is superior to that of the 1D method.

Figure 6 shows the images converted by using the threemethods. The original image of Fig. 6(a) represents acolor temperature of 3539 K. When one converts the im-age into a color temperature of 1667 K, Fig. 6(b) showsthe result obtained by using the 2D method, Fig. 6(c)that by using the 1D method, and Fig. 6(d) that by usingthe 1.5D method. One can easily see that the colors con-

Fig. 6. Color-temperature conversions with a target tem-perature of 1667 K: (a) original image (3539 K), (b) convertedimage with the 2D method, (c) converted image with the 1Dmethod, and (d) converted image with the 1.5D method.

verted by using the proposed method are almost equal tothose converted using the 2D method while the colors ob-tained by using the 1D method are distorted due to theinaccuracy in the temperature calculation. This againshows the superiority of the proposed method over the1D method. Distortion is very critical to degradations ofcolor representation in HDTV applications because theresolution in an HDTV system is commonly four timeshigher than that in conventional color TV systems [9].

IV. HARDWARE DESIGNS

Figure 7 shows the block diagram of the proposedsystem for color-temperature conversion. The proposedsystem is comprised of thirteen major building blocks.

Fig. 7. Block diagram of the advanced color-temperaturecontrol system.

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Table 2. Hardware complexity in gate counts.

Logic Modules Gate Counts

I/OFC 1 36,178

EffPixel sel 2,885

Chroma Calc 11,884

WP Calc 8,489

Pix 1 5D 11,137

Temperature Calc 31,429

TP Coeff 20,929

XYZtoRGB Coeff 6,557

I/OFC 2 48,410

Time alignment 3,129

I2C 3,284

Total Gate Counts 184,311

Memory Modules Bits

Differ pix ROM 5,632

Temperature ROM 26,542

Total ROM Size 32,174

The compensated X-chromaticity coordinates proposedin this paper are used in order to increase the accuracy inthe calculation. The I/OFC 1 converts the input RGBdata into XYZ coordinates by using a conversion ma-trix [10]. The EffPixel sel selects effective pixels by ex-cluding the self-luminous area that is not perceived as apassive surface reflector. The Chroma Calc averages theXYZ value in each effective pixel and calculates the coor-dinates. The WP Calc, Pix 1 5D, and Differ pix ROMcalculate the revised X-chromaticity coordinate to com-pensate the Differ pix value. The Temperature Calcand Temperature ROM calculate the color temperatureby using the revised X coordinate. The Tp Coeff andXYZtoRGB Coeff generate the temperature-conversionmatrix of the XY Z coordinates for transforming the tem-perature of the input into a desired target temperature.The I/OFC 2 converts the transformed image of XYZinto the RGB data. By doing so, one can achieve variousimages of different temperatures. The Time alignmentgenerates various timing signals for each block and syn-chronizes the input data to the operating pixel. The pro-grammable values in the hardware design are controlledthrough the I2C protocol.

The proposed method is designed by using VHDLmodels, and the VHDL models are verified by using theSynopsys simulator. Each block in Fig. 7 is designedto operate with a speed of at least 67.4325 MHz in fre-quency for HDTV applications [7] and is synchronizedto the frequency for easy test generation [11,12]. Afterthe verifications are conducted, the models are synthe-sized into gates by using the Synopsys synthesizer withthe TSMC 0.25-µm library. Table 2 summarizes the re-quired hardware for the proposed method. The total gatecount is 184311 where a 2-input nand is counted as one

Fig. 8. Demonstration PCB board of the advanced color-temperature control system.

Fig. 9. Demonstration fLCD-TV set of the advanced color-temperature control system.

gate. The ROM size required in the proposed method is32174 bits, which is an 88 % reduction (= 32174/267752)compared with the 1D method.

The Xilinx FPGA Virtex XCV 2000E-6BG560 deviceis used to demonstrate the performance of the proposedmethod. Figure 8 shows the demonstration PCB board,and Fig. 9 shows a ferro liquid crystal display (fLCD)TV set utilizing the demonstration board. The operat-ing clock is 67.4325 MHz in frequency, and the overallresolution for a frame is 1450 pixels by 775 lines. Theleft side of the scene in Fig. 9 shows the incoming video(bypass), and the right side shows the converted videowith a color temperature of 25000 K. As one can see, onecan feel a more bluish tone on the right than one can onthe left side. This is expected since a higher temper-ature contains bluish tones. Figure 9 again proves theeffectiveness of the proposed method.

V. CONCLUSIONS

Design of Advanced Color - Temperature Control System · · · – Bongsoon Kang et al. -871-

In this paper, an advanced color-temperature controlsystem for HDTV applications is proposed. The cal-culated temperatures were shown to be almost equalto those calculated using the 2D method. This provedthat the proposed method improved the accuracy in thecolor-temperature calculation by using an additional Y-chromaticity coordinate. It also extended the lower limitof the color-temperature range from 3000 K to 1667 K.The ROM size required in the proposed method was re-duced to as little as 32174 bits. Therefore, the proposedmethod can be applied to various display systems, suchas HDTVs, camcorders, printers, TFT-LCDs, and so on.

ACKNOWLEDGMENTS

The authors wish to thank the IC design educationcenter for providing the Synopsys and the Xilinx duringthe completion of this work.

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