QUASI-BI-QUADRATIC INTERPOLATION FOR LUT

IMPLEMENTATION FOR LCD TV

Heebum Park, Guiwon Seo and Chulhee Lee

School of Electrical and Electronics Engineering,Yonsei University, Shinchon dong, Seoul, Korea Rep.

Keywords: LCD, LUT, Interpolation, Overdrive, Quadratic function.

Abstract: Overdriving schemes are used to improve the response time of LCD (Liquid Crystal Display). Typically

they are implemented by using LUT (Look-Up Table) within an image processor. However, the size of LUT

is limited by the physical memory size and system cost. In actual implementation of LUT, final overdriving

values are obtained using interpolation methods. However, interpolation errors may cause some display

artifacts and response time delay. In this paper, we present an improved method for LUT implementation

using linear interpolation and piecewise least-square polynomial regression to reduce such errors. The

proposed method improves LUT performance with reduced memory requirements.

1 INTRODUCTION

Recently, the demand for TFT LCD-TVs has

dramatically increased. TFT-LCD TVs have many

advantages including high resolution, light weight,

slim size and low power consumption. On the other

hand, there are also some problems such as slow

response time. Response time is very important for

LCD TVs since TV monitors need to properly

display moving pictures (Song et al., 2004). The

overdrive technique improves the response time of

TFT-LCDs by enlarging the desired change in the

pixel value to force LC materials (Wubben et al,

2004, Someya et al., 2003, Hartman et al., 1996, Lee

et al, 2001, K. Kawabe and T.Furuhashi, 2001). A

block diagram of overdrive is shown in Figure 1.

Figure 1: Block Diagram of overdrive.

The overall system includes a signal processing unit

which generates a current frame data, a frame

memory to store a previous frame data, an

overdriving unit to generate the current frame data

using the frame memory and the look-up table

(LUT), and a liquid crystal panel configured to

display the frame data.

For each pair of the pixel value of the current frame

and the pixel value of the previous frame, the look-

up table (LUT) is used to compute a compensated

value based on TFT-LCD response time

characteristics. However, most LUT stores a part of

the entire LUT data (256x256 matrix) since the LUT

size is limited by the physical memory size and

fabrication cost. For example, a typical LUT has 8 x

8 matrix format and final overdriving pixel values of

LUT are computed using an interpolation method. In

generally, bilinear interpolation is used due to its

simple implementation. However, bilinear

interpolation may introduce artifacts. In this paper,

we propose a new interpolation method for this LUT

implementation.

2 LUT FOR OVERDRIVE

A complete LUT requires a 256x256 matrix

structure in an 8-bit overdrive scheme. A total of

256x256 LUT values are needed for all possible

combinations of current and previous gray levels and

optimum LUT values for overdrive are determined

by experimental measurements. Figure 2 and Figure

3 show the characteristics of typical LUT data. As

can be seen in the Figure 2, the LUT column data

has non-linear characteristics. However, the LUT

row data (Figure 3) shows more linear

70

Park H., Seo G. and Lee C. (2009).

QUASI-BI-QUADRATIC INTERPOLATION FOR LUT IMPLEMENTATION FOR LCD TV.

In Proceedings of the First International Conference on Computer Imaging Theory and Applications, pages 70-73

DOI: 10.5220/0001807600700073

Copyright

c

SciTePress

characteristics than the LUT column data. In bilinear

implementation, missing values are interpolated

using linear functions. When three data points are

available, one can use a quadratic interpolation

function:

2

210

)( xaxaaxf ++=

.

The three coefficients can be determined from the

three data points and this quadratic function can be

used to fill in missing values between the three

points. We will call this method the quadratic

interpolation method.

Figure 2: LUT column data.

Figure 3: LUT row data.

3 THE PROPOSED ALGORITHM

In the proposed method, linear interpolation and

least-square regression methods are used for LUT

implementation. It can be seen that the column data

of LUT (Figure 2) shows more non-linear

characteristics than the row data of LUT (Figure 3).

Based on these observations, we propose to use a

quadratic regression method to find the best-fit of

the column data of LUT and to use linear

interpolation for the row data of LUT. The proposed

quasi-bi-quadratic interpolation is illustrated in

Figure 4.

Figure 4: Concept of quasi-bi-quadratic interpolation.

In the proposed method, f1 and f2 are first computed

using quadratic polynomials.

2

2101

)( xaxaaxf ++=

(1)

2

2102

)( xbxbbxf ++=

(2)

To obtain the coefficients, the least square method is

used:

exaxaay +++=

2

210

(3)

where

e

is an error. Then, we can compute

r

S

which is the square sum of error e as follows:

2

2

210

11

2

) (

iii

n

i

n

i

ir

xaxaayeS −−−==

∑∑

==

(4)

To find

0

a ,

1

a ,

2

a that minimizes

r

S , we

differentiate

r

S with respect to each coefficient:

) (2

2

210

0

iii

r

xaxaay

a

S

−−−−=

∂

∂

∑

(5)

) (2

2

210

1

iiii

r

xaxaayx

a

S

−−−−=

∂

∂

∑

(6)

) (2

2

210

2

2

iiii

r

xaxaayx

a

S

−−−−=

∂

∂

∑

(7)

By setting the differentiations, we obtain the

following equations:

∑

∑

∑

=++

iii

yaxaxan

2

2

10

)()()(

(8)

QUASI-BI-QUADRATIC INTERPOLATION FOR LUT IMPLEMENTATION FOR LCD TV

71

∑

∑

∑∑

=++

iiiii

yxaxaxax

2

3

1

2

0

)()()(

(9)

∑∑∑∑

=++

iiiii

yxaxaxax

2

2

4

1

3

0

2

)()()(

(10)

The optimal coefficients can be obtained by

simultaneously solving these equations. Then, the

final value is determined from f1 and f2 using linear

interpolation as follows:

X

xff

fF

Δ+

+=

)(

21

1

(11)

4 EXPERIMENTAL RESULTS

Table 1 shows the SNR comparison of the bilinear

interpolation method, the quadratic interpolation

method and the least square quadratic regression

method for the column data. It can be seen that the

quadratic regression method provides noticeably

improved results.

Table 1: The SNR(dB) of LUT column data.

0

gray

32

gray

64

gray

96

gray

128

gray

160

gray

192

gray

224

gray

255

gray

A* 35.4 39.0 40.3 41.4 42.5 42.2 41.1 39.8 41.6

B* 36.2 41.6 43.7 43.0 43.4 43.9 42.2 39.8 35.3

C* 40.5 44.5 47.0 45.8 46.0 50.1 46.9 43.6 44.6

A*: Linear Interpolation (AVG: 40.4)

B*: Quadratic Interpolation (AVG: 41.0)

C*: Least Square Quadratic Regression (AVG: 45.4)

Table 2: Number of LUT coefficients.

Method for LUT Implementation

Number of

Coefficients

Bilinear Interpolation 144

Quadratic Interpolation 108

Least Square Quadratic Regression 108

0

50

100

150

200

250

0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 255

Figure 5: Curve fitting of the column data of LUT using

bilinear interpolation.

0

50

100

150

200

250

0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 255

Figure 6: Curve fitting of the column data of LUT using

quadratic interpolation.

0

50

100

150

200

250

0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 255

Figure 7: Curve fitting of the column data of LUT using

least square quadratic regression.

IMAGAPP 2009 - International Conference on Imaging Theory and Applications

72

In ASIC LUT implementation, the coefficients are

saved in memory for computation efficiency. Table

2 shows the number of LUT coefficients for each

method. It can be seen that the least square quadratic

regression method provides more efficient memory

usage in ASIC implementation. Figure 5-7 show the

curve fitting of the column data for each method. It

can be seen that the least square quadratic regression

method generate curves that have smaller error than

other methods.

After computing the column data, final overdriving

values can be calculated by applying linear

interpolation for the row data. The bilinear

interpolation method, the quadratic interpolation

method and the quadratic regression method used

bilinear interpolation for the row data since the row

data of LUT show linear characteristics (Figure 3).

In the conventional bilinear interpolation method, 64

samples (8 by 8) are selected from the entire LUT

data (256 by 256). The sampling grids are equally

distributed. In the proposed method, every 4-th

sample is chosen for the column data and every 8-th

sample is selected for the row data. Thus, a total of

32 samples are used in the proposed method.

Table 3 shows the SNR comparison for LUT

implementation and Table 4 shows the maximum

error comparison. As can be seen, the proposed

method significantly outperforms the bilinear

method which is widely used in the industry.

Table 3: SNR comparison.

Method of LUT Implementation SNR(dB)

Bilinear Interpolation 38.0

Quadratic Interpolation + Linear

Interpolation

36.7

Quasi-bi-quadratic Interpolation 40.2

Table 4: Maximum Error Comparison.

Method of LUT

Implementation

Response Time

Error

Visual

Distortion Error

Bilinear

Interpolation

5.47 % 3.51 %

Quadratic

Interpolation

+ Linear

Interpolation

5.86 % 2.34 %

Quasi-bi-quadratic

Interpolation

3.51 % 1.56 %

5 CONCLUSIONS

In order to provide improved performance in the

LCD overdrive scheme, we propose to use the quasi-

bi-quadratic interpolation that is based on the least

square error approximation. The proposed method

outperforms the conventional bilinear interpolation

method with reduced memory requirement.

REFERENCES

Song, J.K., et.al., “DCCII: Novel Method for Fast

Response Time in PVA Mode,” SID 04 Digest,

pp.1344-1347, 2004.

Wubben, R. H. M., et. al., “LCD Overdrive Frame

Memory Reduction using scalable DCT-based

Compression,” SID 04 Digest, pp.1348-1351, 2004.

Someya, Jun, et. al., “A new LCD-Controller for

Improvement of Response Time by Compression

FFD,” SID 03 Digest, pp.1346-1349, 2003.

Hartman, R.A. et.al., “Fast Response Electro-Optic

Display Device.” United States Patent US5,495,265,

Feb. 1996.

B.-W. Lee et al., “Reducing Gray-Level Response to One

Frame: Dynamic Capacitance Compensation”, SID

2001 Digest, 51.2L, 2001.

K. Kawabe and T.Furuhashi, “New TFT-LCD Driving

Method for Improved Moving Picture Quality”, SID

2001 Symp. Digest, 2001.

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