CANCELLATION OF SHOW-THROUGH IN DUPLEX SCANNING

Gaurav Sharma

Dig. Imaging Tech. Ctr., Xerox Corp., MS0128-27E, 800 Phillips Rd, Webster, NY 14580.Email: g.sharma@ieee.org

ABSTRACT

When scanning a page with printing on both sides,the printing on the back-side often shows through inthe scan of the front-side because the page is not com-pletely opaque. This phenomenon of show-through isanalyzed and an image processing method for removalof this commonly encountered degradation is devel-oped. A simplified mathematical model is obtainedfrom first physical principles. The model is linearizedusing suitable transformations and simplifying approx-imations. Based on the linearized model, an adaptivelinear-filtering scheme is developed for the electronicremoval of show-through using scans of both sides ofthe document. Experimental results demonstrating theeffectiveness of the method developed are presented.

1. INTRODUCTION

The phenomenon of show-through is a common arti-fact encountered while scanning duplex (double-sided)printed pages. Since the page is not completely opaque,the scanner receives light that is transmitted throughthe paper, reflected from the scanner backing and trans-mitted back through the paper. If there is no printingon the back side of the paper, this light produces no un-desirable artifacts. If, however, the back side also hasprinting, then due to transmission through the paper,the scan of the front side contains a residual (trans-posed) image of the back side, which is referred to asshow-through [1].

Figure 2 and 3, respectively, are the images ob-tained by scanning the two sides of a duplex printedpage. In each scan, show-through from the (corre-sponding) back side can be clearly seen as a low con-trast transposed image of the printing on the backside. The show-through is most visible in the regionsin which there is no printing on the front side, thoughit can also be seen in light gray regions of the imageside.

Show-through is clearly an unwanted artifact thatone would like to eliminate. If the original informa-tion consists of simple black and white printed text,

show-through can be removed by a simple process ofthresholding. The thresholding method, however, doesnot work for prints containing images or text that havegray levels other than pure black and white. For re-gions with light gray printing on the front side, thethresholding either does not remove the show-through,or inadvertently eliminates the information in these re-gions by converting them to white.

2. SHOW-THROUGH MODEL ANDANALYSIS

Consider the simplified cross-sectional view of a scan-ner shown in Fig 1, where a duplex printed documentis being scanned. The printing on the two sides maybe viewed as separate layers on either side of the page,with the printed information represented as the spatialtransmittance profile of these layers. The light reach-ing the sensor has two main components: light that isscattered by the paper substrate and light that is trans-mitted through the paper, reflected by the backing andtransmitted again through the paper. Both these com-ponents encounter the transmittance of the front-sideprint layer but only the latter encounters the transmit-tance of the back-side print layer. If Tf(x, y) representsthe transmittance of the “print layer” on the front sideand Tb(x, y) represents the transmittance of the “printlayer” on the back side, the reflectance detected by thesensor when scanning the front side is given by

Rsf (x, y) = T2f (x, y)(Sp + T

2pRbkT

2b (x, y)) (1)

where x and y represent the two-dimensional spatialcoordinates on the paper being scanned, Sp is the frac-tion of light scattered by the paper (in the forwarddirection), Tp is the transmittance of paper, Rbk isthe reflectance of the backing, the subscript f denotesthe front side, and the superscript s is used to de-note that this is the “scanned” reflectance. Note that,the reflectance of unprinted paper is given by Rwp =Sp + T

2pRbk.

Equation (1) indicates that the reflectance Rsf (x, y)detected by the scanner sensor depends on the front-

side print layer transmittance, the paper scattering andtransmittance parameters, the reflectance of the back-ing, and the back-side print layer transmittance. Inparticular, the dependence of the scanned reflectanceRsf (x, y) for the front side on the transmittance Tb(x, y)of the back side print layer represents the undesiredshow-through in the front side scan.

If the scan of the back-side is also available, thenthe scanned reflectance for the back side can be writtenin a manner analogous to (1) as

Rsb(x, y) = T2b (x, y)(Sp + T

2pRbkT

2f (x, y)) (2)

where the terms on the right hand side are as definedearlier. This yields a system of two equations in thetwo unknowns Tf (x, y) and Tb(x, y). Therefore, onecan expect to remove the show-thorough if scans ofboth sides of the page are available and if these twoequations can be solved for these unknowns.

3. LINEARIZED SHOW-THROUGHMODEL

The nonlinear nature of equations (1) and (2), and thelack of knowledge of the parameters Sp and Tp makea direct analytic or numerical solution infeasible. Inorder to simplify these equations, it is advantageous toexpress them in terms of optical density by dividing bythe paper reflectance and taking the (negative) naturallogarithm

Dsf (x, y) ≡ − lnRsf (x, y)

Rwp(3)

= Df (x, y)−

ln

(1−

T 2pRbk

Sp + T 2pRbk(1− T 2b (x, y))

)

≈ Df (x, y) +T 2pRbk

Sp + T 2pRbkAb(x, y) (4)

where Dsf (x, y) is the paper-normalized density for thefront-side scan, Rwp denotes the reflectance of white(unprinted on either side) paper,

Df (x, y) ≡ − ln(T 2f (x, y))

= − lnRf (x, y)(Sp + T

2pRbk)

Rwp(5)

represents the front-side density that would be obtainedif there was no printing on the back-side, i.e., the show-through corrected density; Ab(x, y) ≡ (1− T 2b (x, y)) =1 − Rb(x,y)

Rwpis the absorptance of the back side “print

layer”; and in (4) we have used the fact that for typ-ical paper substrates, the fraction of light transmit-ted is much smaller than the fraction of light scat-tered, i.e., T 2p << Sp, which allows the approximationln(1− t) ≈ −t for |t| << 1.

Equation (4) states that the paper-normalized den-sity of the front side scan can be approximated bythe sum of the paper-normalized density of the show-through corrected front side and the absorptance ofthe back-side print layer weighted by a small factor.It is clear that the second term represents the show-through. A similar result can be obtained for the backside. The major significance of these equations is thatin the density domain the show-through separates intoan additive distortion, which is further characterized asbeing a scalar multiple of the opposite side print layer’sabsorptance.

4. SHOW-THROUGH CORRECTION

In practice, light undergoes spreading in the paper sothe interaction between the front and the back sides isnot purely point-wise as implied by (4). This spread-ing can be incorporated into the show-through model

by replacing the scalar termT 2pRbk

Sp+T 2pRbkin (4) with an

empirical “show-through” point spread function (PSF)to obtain

Dsf (x, y) = Df (x, y) + h(x, y) ⊗Ab(x, y)≈ Df (x, y) + h(x, y) ⊗Asb(x, y) (6)

where h(x, y) is the “show-through point spread func-tion (PSF)”, ⊗ represents the convolution operator,and the approximation in (6) replaces the absorptancefor the back side “image layer”, i.e., Ab(x, y), by thecorresponding absorptances from the scan, given by

Asb(x, y) ≡ 1− Rsb(x, y)

Rwp(7)

Note that the show-through PSF represents the termT 2pRbk

Sp+T 2pRbkin the physical model. The show-through

PSF is therefore expected to be nonnegative and smallin comparison to unity. Furthermore, it is determinedby the scattering and transmission characteristics ofthe paper and the reflectance of the backing.

If the show-through PSF and the relative alignmentof the front and back side images is known precisely, theshow-through corrected image can be obtained fromthe scans of the two sides using (6). In practice, how-ever, both the above assumptions are unrealistic. Us-ing methods from adaptive signal processing, however,the show-through correction can be performed with-out these unrealistic constraints. Since equation (6) is

linear, the problem of show-through correction can beviewed as the two-dimensional equivalent of the one-dimensional echo-cancellation problem in speech tele-phony [2, pp. 53-56]. As in speech echo-cancellation,adaptive linear filters [2] can be used for automaticallyestimating and tracking the show-through PSF and im-plicitly the alignment between the front and the backside images.

The complete process of show-through correction isdescribed as follows. First, approximate alignment forthe front and back side scans is determined by identify-ing corresponding image features in the front side show-through and the back side scan. The reflectance Rwp ofwhite paper unprinted on both sides (with the scannerbacking) is estimated by averaging the reflectance val-ues over a region of the scan that has no printing oneither side.

Using the estimate of Rwp , scan data from the frontside is converted to density relative to paper white asper (3) and data for the back side is converted to ab-sorptance using (7). The image pixels are processedone at a time. At each pixel location (m,n), the show-through corrected density is computed as

Df (m,n) = Dsf(m,n)−M∑

k=−M

N∑l=−N

wm,n(k, l)×

Asb(k −m, l − n) (8)

where wm,n(k, l) is a two-dimensional adaptive FIR fil-ter with support [−M . . .M ]×[−N×N ] that representsthe show-through point spread function.

The scanned image values for the front and backside images are then examined and compared to thepaper white reflectance to determine if the local neigh-borhood about the current pixel location (and includ-ing it) contains any printing on either side. If the lo-cal neighborhood has printing on the back-side but noprinting on the front-side (this corresponds to “far-endsingle-talk” in the speech-telephony echo-cancellationanalogy), the filter coefficients wm,n(k, l) are adapted.The adaptation of the filter coefficients can be done inaccordance with any of the several known algorithmsin adaptive filter theory [2]. For the following descrip-tion, the simplest and perhaps best-known least-meansquare (LMS) algorithm [2, pp. 302] will be used. Forthe LMS algorithm, the filter coefficients for the nextpixel location (m′, n′) are computed as

wm′,n′(k, l) = wm,n(k, l) + µDf (m,n)×

Asb(k −m, l − n) (9)

where µ is the LMS adaptation step-size parameter. Atpixels where the filter coefficients are adapted, there

is no printing on the front side, therefore, the desiredshow-through corrected density at the pixel (m,n) iszero and the valueDf(m,n) computed in (8) representsthe error term used in the more general specification ofthe LMS algorithm [2, pp. 302].

The processing is then repeated for the next pixellocation, continuing until the complete image has beenprocessed. The show-through corrected density for thefront-side Df (m,n) is converted to reflectance by in-verting the relation of (5) to obtain the output show-through corrected image. Note that the show-throughcorrection of (8) is applied at each pixel, though theadaptation is performed only in regions where the back-side has printing and the front-side does not. Since thedesired output is not known for regions with printing onthe front side, the filter coefficients cannot be adaptedin those regions. No adaptation is performed for re-gions that have no printing on either side to keep thefilter coefficients from drifting due to the noise (and nosignal) in these regions.

5. EXPERIMENTAL RESULTS

The show-through model and the cancellation algo-rithm developed here were tested using a UMAX pow-erlook desktop scanner. The scanner was operated in amode for which the scanner output is linearly related toscanned reflectance. The two sides of a duplex-printedpage were scanned at 600 dpi resolution as 8-bit gray-scale images. The resulting scanned images are shownin Fig 2 and 3. In both images, show-through from theother side, can clearly be seen as mentioned earlier.

The relative alignment between the scanned imagesfor the two sides was obtained by locating the positionof the intersection of the two lower 45-degree strokelines at the bottom of the upper case “X” on the firstline (the first “X” in “The Document Company Xerox).The (scaled) reflectance Rwp of white paper unprintedon either side was computed by averaging the scannedvalues over a 400 pixel by 400 pixel square in the topcorner of the image-side scan.

Using the alignment information and the estimatedwhite reflectance, the images were processed using theLMS adaptive-filtering algorithm presented earlier. Suc-cessive pixels to be processed were chosen along a ser-pentine raster so as to preserves spatial contiguity andthereby allow the adaptive filter to track the inevitablechanges in alignment between the front and back sideimages over the page. The filter size was chosen to be31× 31 (i.e., M = N = 15), the filter was initialized toall zeros at the start, and the LMS adaptation parame-ter µ was set to 0.001. For checking for the presence ofprinting on either side (detecting “far-end single talk”),

a 15× 15 neighborhood was used.The show-through corrected images for the text-

side and the image-side obtained from the show-throughcancellation algorithm developed are shown in Fig. 4and 5, respectively. The results clearly indicate thatthe algorithm is successful in cancelling show-through.In comparison to the original scans, both the correctedimages have almost no show-through and very minorprocessing artifacts (these minor artifacts can be seenbetter in the electronic versions of these images whendisplayed on a monitor).

6. REFERENCES

[1] K. T. Knox, “Show-through correction fortwo-sided documents,” United States Patent No.5832137, 3 Nov. 1998.

[2] S. Haykin, Adaptive Filter Theory, Prentice Hall,Englewood Cliffs, NJ, second edition, 1991.

Scanner Backing

Printing on back side(Duplex-printed) pagePrinting on front side

LampSensor

Figure 1: Scan of Duplex Printed Page.

Figure 2: Scan of Side 1 of a two sided page, demon-strating show-through from Side 2.

Figure 3: Scan of Side 2 of a two sided page, demon-strating show-through from Side 1.

Figure 4: Side 1 scanned data after show-through cor-rection.

Figure 5: Side 2 scanned data after show-through cor-rection.