Displays 34 (2013) 75–80

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Displays

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Constrained non-negative matrix factorization for multiline addressing schemesof quick-response liquid powder display

Chang-Jing Yang, Yung-Fang Chen ⇑Department of Communication Engineering, National Central University, 320, Taiwan, ROC

a r t i c l e i n f o

Article history:Received 11 January 2012Received in revised form 13 October 2012Accepted 23 January 2013Available online 16 February 2013

Keywords:Quick-response liquid powder display(QR-LPD)Non-negative matrix factorization (NMF)Multiline addressing (MLA)

0141-9382/$ - see front matter � 2013 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.displa.2013.01.004

⇑ Corresponding author. Tel.: +886 3 4262657; fax:E-mail address: yfchen@ce.ncu.edu.tw (Y.-F. Chen)

a b s t r a c t

A quick-response liquid powder display (QR-LPD) is a favorable candidate for flexible electronic papersbecause it can be simply operated by passive-matrix driving. However, the slow image refreshing rateis its major problem. In this study, multiline addressing (MLA) schemes for QR-LPD have been developedfor improving the driving efficiency. Non-negative matrix factorization (NMF) with boundary constraintsis used for the MLA scheme. A hybrid pulse modulation (HPM) is proposed for further shortening the driv-ing waveform. The experimental results reveal that the MLA using NMF produces a noisy image on QR-LPD. The root cause for this is that NMF is a linear factorization but the electro-optical response of QR-LPDis not a linear curve. Therefore, we have proposed a lossless matrix factorization (LMF) method. The MLAscheme using LMF not only improves the image refreshing rate but also shows images without loss.

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1. Introduction

A quick-response liquid powder display (QR-LPD) is a novelbistable reflective display. It has a well-defined threshold andhence, can be easily operated using a less-complicated method ofpassive-matrix addressing [1,2]. This reduces the cost of displayfabrication and increases the feasibility of flexible electronic pa-pers. Low-cost but flexible electronic papers using QR-LPD havebecome a popular electronic device in the consumer market.

The task of improving the image refreshing rate of QR-LPD hasbeen extensively discussed in recent years [3–6]. Although the re-sponse time of 0.2 ms of QR-LPD is faster than that of other electro-phoretic displays, a long driving waveform is required to show animage with high contrast and uniform grayscale distribution. Inour previous work [3], we proposed a programmed driving wave-form based on pulse number modulation (PNM) to optimize theperiod for QR-LPD.

Novel technologies of multiline addressing (MLA) schemes havebeen used for operating passive-matrix liquid crystal displays(LCDs) and organic light-emitting diode (OLED) panels [4,5]. Thesetechnologies have the superior advantages of enhancing the dis-play efficiency and the panel lifetime. In [4], the use of an orthog-onal basis as the row data input enables the root mean square(rms) voltage of the driving waveform of an LCD to determinethe electro-optical state of a pixel. Because the optical behaviorof bistable displays is not a response to the rms voltage, a drivingscheme cannot be used in the bistable displays. In [5], NMF has

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been used for decomposing the original image into a basis matrixand a coefficient matrix. The basis matrix, denoted by the row data,controls the current output, and the coefficient matrix, denoted asthe column matrix, controls the driving time of an OLED pixel.

In [6–8], the authors proposed an MLA method and a minimizedsingle-line addressing (SSLA) method to shorten the QR-LPD imageupdating time, where the multiple rows are scanned simulta-neously while an image is updating. However, in [6], the MLAscheme using non-negative matrix factorization (NMF) has demon-strated a poor image quality in the case of QR-LPD, and the rootcauses for this poor quality have not been discussed in detail. In[7], the MLA scheme has showed an improved image, but the de-tailed algorithm has not been given. In [8], the authors extendthe MLA scheme in [7] for halftone images by using a minimizedMLA method. This method compares the row vectors of the matrixwith one another to find the basis vectors. However, the calcula-tion of the basis vectors in the algorithm dominates the computa-tional resources of the QR-LPD device. This is a critical issue thatshould be dealt with precisely. Moreover, the computational com-plexity of the abovementioned calculation should be analyzed. Inthis paper, the MLA scheme for QR-LPD has been discussed in de-tail. First, we have reviewed the basic operations of QR-LPD and theconventional row-by-row addressing scheme. The root cause of thepoor image quality in the case of QR-LPD by the MLA scheme usingNMF has been discussed. We modify the objective function of NMFfor the boundary of the component of factorization. Moreover, forthe sake of image quality, we propose the fast algorithm of losslessmatrix factorization (LMF). The worst case of the computationaltime of the proposed algorithm for a binary image is O(m2). The ex-tended algorithm for g gray-level images having the worst case of

Fig. 1. Charge mechanism of QR-LPD.

Fig. 2. Pixel voltage between column and row electrodes.

76 C.-J. Yang, Y.-F. Chen / Displays 34 (2013) 75–80

the computational time is O(gm2). Lastly, the experiment resultsand the conclusion are given.

Fig. 3. Block diagram of QR-LPD driver.

2. QR-LPD operation

QR-LPD uses charged pigment powders as the media for display.A powder is a compound particle whose child particles adhere tothe surface of a mother particle [9]. Pigment powders (diameter:0.1–20 lm) are placed into pixels sandwiched between two elec-trodes at a distance of 50–100 lm and partitioned using ribs.When an external electric field is not applied, the powders donot move because the attractive forces between the electrodesand the powders, such as the image charge force, the Van derWaals force, and the Coulomb force are larger than the gravity.In contrast, the powders get transported in air when an electricfield is applied because the repulsive force is greater than theattractive force.

The charging mechanism of these powders is mainly surface-dominated electrification, and the material characteristics deter-mine the charge-holding capacity [10,11]. The basic charge mech-anism of QR-LPD is illustrated in Fig. 1. The powders are chargedfrom the contact surface by an applied electric field, as shown inFig. 1a. When the removal force generated by the applied electricfield, given by F = qE (where q is the charge of the powder and Eis the electric field), exceeds the attractive force, the powders beginto move. As shown in Fig. 1b, frictional charging occurs when thepowders come into contact with one another. The contact areaand the relative velocity determine the triboelectric charge of thepowders. When the powers arrive at the electrode with an oppo-site charge, as shown in Fig. 1c, the powders discharge throughthe contact surface of the electrodes. A powder’s charge accumu-lates when the image refreshes and leaks when the images holds.

A driving waveform performs the sequences of showing an im-age. The first sequence for a bistable display is to erase the priorimage. Let us assume that the white powders with a negativecharge appear on the observation substrate when a positive elec-tric field is applied, and in contrast, the black powders with a po-sitive charge appear when a negative electric field is applied.Fig. 2 shows an example of the pixel voltages between a columnand a row electrode in QR-LPD. The alternate pulses of positiveand negative electric field enhance the performance of image era-sure in order to avoid the effect of shadow images. Further, in order

to obtain a relatively high contrast ratio, the driving waveformwith more than one pulse is used for operating the QR-LPD.

Fig. 3 shows the block diagram of a QR-LPD driver. The encodeddata are serially inputted to the shift register. While the latch sig-nal is enabled, the data in the shift register are outputted to theoutput buffer. The buffer drives the output into the tri-level voltagestates of high voltage (HV), middle voltage (MV), and zero voltage(0 V) of the driver. For example, in a conventional row-by-rowdriving scheme, the MV is lower than the threshold voltage ofQR-LPD. The voltage of the selected row and that of the unselectedrow can be set to HV and MV, respectively, and the voltage of theswitched column and that of the unswitched column can be set to0 V and MV, respectively. The pixels of the unselected rows acrossthe electrodes are given by MV–0 V or MV–MV, which are lowerthan the threshold voltage, and the active and inactive pixels ofthe selected row are given by HV–0 V and HV–MV, respectively.The details of the driving method and the electro-optical responseof the driving method are further discussed in [12,13].

The grayscale rendition of a basic row-by-row driving scheme isshown in Fig. 4. The pulses at a low level denote that the row isunselected, and those at a high level denote that the row is se-lected. The pulse of a column at low and high levels denotes thatthe column is unswitched and switched, respectively. It must benoted that the pulse level does not indicate the voltage level ofthe row and the column but denotes the driver operation status.In a previous study [3], we measured the electro-optical responseof a QR-LPD device. The threshold voltage of the device is approx-imately 35 V. At an applied voltage below the threshold, the QR-LPD shows a clear threshold; only a few particles move to theopposite electrode, and the contrast increases slightly. When theapplied voltage is larger than the threshold, the optical contrastis a function of the applied voltage and the pulse width. Therefore,the voltage levels of 35 V for MV and 70 V for HV are employed.When the column data are inputted, only one row is selected.The conjunction of the pulse levels of the row and the columndetermines the grayscale of the pixel on a display. The formulationis denoted by yij = ri ^ cj, where yij is the grayscale of the pixel at theith row and the jth column. ri and cj are the pulse levels of the ith col-umn and the jth row, respectively. For example, the grayscale of the

Fig. 4. Basic row-by-row driving scheme.

C.-J. Yang, Y.-F. Chen / Displays 34 (2013) 75–80 77

pixel across the first column and the first row is denoted byy11 = r1 ^ c1, where r1 and c1 are the pulse levels of the first columnand the first row, respectively. Let us assume that the QR-LPD iserased to display a white image; y11 is larger than y33 becausethe driving waveform with relatively few pulses is driven.

3. Multiline addressing

When an MLA scheme is employed on a display, the rows arescanned simultaneously and share the same coefficients of the col-umn data. Fig. 5 shows an example of MLA for a bistable displayusing PNM. The conjunction of the row and column vectors deter-mines the grayscale of the pixel. For example, the driving wave-forms of pixels y11 and y21 across the first column c1 obtain 1and 2 pulses, respectively.

An image A shown on a bistable display can be represented asA = WH, where W and H denote the basis data of the rows andthe coefficient data of the columns, respectively. In the conven-tional method of the row-by-row addressing scheme, the basis Wis an identity matrix I, and coefficient H is the image A. Therefore,the MLA scheme of the bistable display can be considered the ma-trix decomposition of image A when the basis matrix is not anidentity matrix.

3.1. MLA scheme using NMF

A low-rank NMF has been utilized in many applications of im-age processing, such as pattern recognition and data mining [14–16]. In this study, an algorithm of NMF with boundaries is usedfor the MLA scheme. The rank of the basis matrix determines thescan times while updating an image. In other words, the imageupdating time decreases when the rank is lowered. Moreover,the non-negative characteristic of the basis and the coefficient

Fig. 5. Multiline addressin

components is apt for operating the driver. Multiple rows arescanned simultaneously, and the pixel grayscale increases by eachrank. By using NMF for an MLA scheme, we can represent the costfunction as

min f ðW;HÞ ¼ 12

Xm

i¼1

Xn

j¼1

Aij � ðWHÞij� �2

st:0 6 Wij 6 Wu

0 6 Hij 6; Hu:

ð1Þ

where Aij, Wij, and Hij are the components of image A, basis matrixW, and column matrix H, respectively. The objective is to minimizethe norm of the difference between the image A and the product ofW and H. The components of the factorization results should be lar-ger than zero and smaller than the upper bound Wu, which is themaximum gray level of the image. We use the gradient algorithmto obtain the solution of (1). Let us assume that the imageA = [a1� � �am] is an n �m matrix. The basis matrix W = [w1� � �wr]and the coefficient H = [h1� � �hr]t are the factorization matrices ofrank r. The update rule is as follows:

W W� lW@f ðW;HÞ@W

H H� lH@f ðW;HÞ

@H

ð2Þ

The step sizes of lW and lH are adaptive parameters. Duringiterations, the components are replaced by the upper bound orzero when they are out-of-range values of the bounds. The itera-tion converges when the objective norm is achieved. When therank of the basis and the coefficient matrix is lowered, the iterationprocess becomes relatively difficult to converge. If we limit thenumber of iterations, then a factorization loss occurs. An NMF

g scheme using PNM.

Fig. 7. Electro-optical response of QR-LPD.

78 C.-J. Yang, Y.-F. Chen / Displays 34 (2013) 75–80

example of character ‘‘E’’ is shown in Fig. 6a. By using Eq. (2), wefactorize the 5 � 4 matrix by a 5 � 2 basis matrix and a 2 � 4 ma-trix. The scan times are reduced by 50% as the rank of the basis ma-trix is lowered.

The optical response of QR-LPD is determined by the area ofblack and white pigment powders on the observation surface. Forexample, a pixel appears to be the lowest grayscale if the observedsurface of the pixel is covered with black powders. On the otherhand, a pixel represents the highest grayscale if the observed sur-face is covered with white particles. The PAM, PWM, and PNMtechniques yield simple grayscale rendition; however, their opticalresponses differ considerably. Fig. 7 shows the average electro-optical response of QR-LPD measured by a densitometer. A drivingwaveform with more than one pulse is used for operating the QR-LPD, and a relatively high contrast ratio is obtained. To simplify thesystem hardware and reduce power consumption, a relatively highapplied voltage of 70 V is employed. For example, with a pulsewidth of 400 ls and a pulse interval of 150 ls, a driving waveformwith five pulses can easily achieve a contrast ratio of close to 8.

NMF is a linear factorization method; however, as shown inFig. 7, the electro-optical response of QR-LPD is not a linear curve.This implies that the MLA scheme using NMF will show a poor per-formance of the grayscale rendition on QR-LPD. For example, witha short pulse width in a driving waveform, a relatively high con-trast ratio is difficult to achieve. In contrast, in the case of a drivingwaveform with a relatively large pulse width, it is difficult to ren-der a low gray level. In Section 4, a hybrid pulse width modulation(HPM) by combining PWM and PNM is proposed for addressingQR-LPD. However, the quantization loss is unavoidable because itis difficult for the driver to represent the non-integer componentsof the basis and the coefficient matrices.

3.2. MLA using LMF

Matrix factorization without loss should be developed when theMLA scheme is employed. When the constraints of (1) are modifiedto A = WH, the factorization loss does not exist. Moreover, thequantization loss is absent when the components of the basisand the coefficient matrices are natural numbers, the objective ismodified to minimize the rank of the basis matrix W, and the rowsto be scanned are reduced. This decreases the image refreshingtime. The cost function of LMF is represented as

min RankðWÞst:

A ¼WHWij;Hij 2 N

ð3Þ

where Wij and Hij are the components of basis matrix W and col-umn matrix H, respectively. N is a natural number. Let us assumethat the image A = [a1� � �am] is an n �m matrix, and the basis matrixW = [w1� � �wr] and the coefficient H = [h1� � �hr]t are factorization

Fig. 6. Factorization example of character ‘‘E’’ with (a) NMF and (b) LMF.

matrices of rank r. The update rules in the proposed algorithmcan be given as follows:

Algorithm: Allocate W and H with the constraints in (3)

1. W = 0; H = 02. for i = 1:m

key = ai; j = 0

while key – 0if wj – ai and wj = 0wj = ai; Hj,i = 1

break

else if wj = keyHj+1,i = 1; j = j + 1break

j = j + 1

The proposed algorithm finds the independent vectors of image A.When the column vector ai of image A is identical to vector wj ofbasis matrix W, we allocate a weight to Hj,i of the coefficient matrix.In contrast, the column vector ai is added to the basis matrix whenit is independent of the vectors of W and a weight is allocated to Hj,i

as well.The algorithm searches m vectors of A, which are matched with

the basis vectors of W. The worst case of the computational time ofthe proposed algorithm is O(m2). The proposed algorithm lowersthe rank of the basis matrix by eliminating the redundancy ofthe basis vectors. The lowered rank depends on the independentbasis vectors of image A. In practice, the basis matrix can be com-posed by the row or column vector of image A. An LMF example ofcharacter ‘‘E’’ is shown in Fig. 6b. By using the proposed algorithm,we can factorize the 5 � 4 matrix by a 5 � 2 basis matrix and a2 � 4 matrix. The scan times are also shortened by 50% since therank of the basis matrix is lowered. Moreover, the factorization lossdoes not exist when LMF is used.

The QR-LPD is only capable of rendering fewer than 16 gray lev-els because the number of particles on the observation surface of apixel is difficult to control precisely [17,18] and false contours oc-cur as a result of the quantization errors. Therefore, a quantizedimage ought to be half-toned before being displayed on QR-LPD.In this paper, the half-toned image with 16 gray levels is regardedas 16 binary images. We repeat the proposed algorithm 16 times tofind the basis matrices in each binary image. For example, whenthe basis matrix and the column matrix of the gth binary imageare found by the proposed algorithm, a binary image will be

Fig. 8. Block diagrams of implementation architecture: (a) MLA scheme using NMF;and (b) MLA scheme using LMF.

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addressed. We repeat the process g times to obtain the gray-levelimage. The computational complexity in this case is O(gm2).Consider the applications of electronic paper. Some applications,such as E-tag that shows simple text on the display, need few basisvectors. In contrast, the applications for showing images requiremore basis vectors.

4. Implementation architecture

The block diagram of the implementation architecture for theMLA scheme using NMF is shown in Fig. 8a. As we impose the con-straints with the upper bound and the lower bound of NMF, thequantization level is the gray level of the image. As discussed inSection 3, the quantization loss is unavoidable because the compo-nents of the factorization result are non-integers.

In [6], PNM has been used for modulating the quantization datawhen the driving waveform is 256 times longer than the drivingwaveform in a conventional method. In our previous work [3], arelatively high density is achieved when PNM is used because ofthe repulsive force between particles. In the interval betweentwo consecutive driving pulses, the repulsive force moves the par-ticles, and more spaces appear among them. When the next driving

Fig. 9. Hybrid pulse m

pulse is applied, more particles squeeze into these spaces. There-fore, a relatively high particle density within a pixel is achievedgradually when multiple driving pulses are used. Further, we ob-served the optical response in the interval between two consecu-tive driving pulses. It altered rapidly at first and tended to slowdown gradually; finally, the optical response remained steadywhen the interval was longer than 150 ls.

In this paper, we have proposed HPM to address QR-LPD. TheHPM, shown in Fig. 9, combines PNM and PWM in order to shortenthe driving waveform. Various pulse widths and pulse numberscan be implemented in HPM. The driving waveforms of the pixelsin different rows may comprise various pulse widths, and the onesin different columns may comprise various pulse numbers. Forexample, if we employ 50 ls as the pulse width of a single pulsein Fig. 9, the driving waveform of pixel y12 comprises two pulseswith a pulse width of 50 ls. Refer to the optical response inFig. 7, we can achieve a contrast close to 2. Moreover, the drivingwaveform of pixel y21 comprises a single pulse with a pulse widthof 100 ls. A contrast of close to 2.5 is achieved. Although these twopixels have the same total pulse width in their driving waveform,they achieve different optical responses because of the differentmodulation types.

In [3], the algorithm of the programmed driving waveformachieved a successful tradeoff between image contrast and drivingtime. In Fig. 8b, the MLA scheme using LMF is presented, whichemploys the algorithm to determine the pulse width and the num-ber of the driving waveform.

5. Experiment results

MLA schemes using NMF and LMF are employed in 4.1-in. QR-LPD. The rank of NMF is designed to be 64, and HPM is also em-ployed. As the electro-optical response is the nonlinear responseof QR-LPD, the gray-scale rendition by using NMF is not presented.Figs. 10 and 11 illustrate the test images shown on QR-LPD byusing NMF and LMF, respectively. When NMF is employed inMLA, a simple text image of one row shows only a minor loss, aspresented in Fig. 10a; however, a fatal image loss is perceived, asshown in Fig. 10b, when more rows of text are involved in the im-age. Crosstalk is also observed between the active rows/columnsand the inactive ones because the threshold voltage is not uniform

odulation scheme.

Fig. 10. Black and white image displayed on QR-LPD by using NMF: (a) text in asingle row; and (b) text in three rows.

Fig. 11. Black and white image and gray image displayed on QR-LPD using LMF: (a)three text rows; and (b) gray image.

Table 1Comparison of driving schemes.

Driving scheme Rank Image quality

R-R r GoodNMF k PoorLMF 6r Good

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in the QR-LPD. Moreover, the QR-LPD displays a lossless image, asillustrated in Fig. 11a and b, when the proposed algorithm of LMF isemployed in MLA. In addition, an image of 16 gray levels is shownin Fig. 11b. By comparing the image refreshing time of the address-ing schemes, we have found that the rank of the basis matrix deter-mines the driving time if we assume that the scan durations areidentical for each driving scheme. Table 1 presents the comparisonof the driving schemes, where r is the rank of image and k is therank of NMF.

The rank of the basis matrix determines the scan times whileupdating an image. In other words, the image updating time is de-creased when the rank is lowered. However, the rank of a basis ma-trix is determined by the independent vectors of an image. Asimple text image has fewer independent vectors than a gray im-age does. For example, Fig. 11a shows an image of a text in threerows whose resolution is 320 � 240 pixels. In the conventionalrow-by-row method, the image should be addressed in 240 lines.When we use LMF to show the image on QR-LPD, the addressing

lines can be reduced to 27% of the conventional row-by-row meth-od since the rank of the image is 65. Fig. 11b shows an image of 16gray levels with 320 � 240 pixels. As discussed in III, the imagewith 16 gray levels is regarded as 16 binary images. We repeatthe proposed algorithm 16 times to find the basis matrices in eachbinary image. The average rank is 163. Therefore, the addressingtime is reduced to 68% of the conventional row-by-row method.

6. Conclusions

In this study, the MLA schemes using NMF and LMF for QR-LPDhave been developed. Compared with the conventional row-by-row scheme, MLA is observed to improve the image refreshing rateby lowering the rank of the basis matrix. Although the MLA schemeusing NMF is not a suitable method for displaying images on QR-LPD because of the nonlinear electro-optical response, it is stillan attractive method for display with a linear electro-optical re-sponse. With a lower rank than the original image, the MLAscheme using LMF not only improves the image refreshing ratebut also shows images without any loss.

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