375

Film Digitization Aliasing Artifacts Caused by Grid Line Patterns

Jun Wang and H. K. Huang, Senior Member, IEEE

Abstract- Sampling a radiographic film containing grid line patterns during digitization may produce aliasing artifacts (Moire pattern). We propose a mathematical model based on the laser spot size of the digitizer, the sampling distance and the angle between the grid line and the sampling direction to predict the amplitudes and the frequencies of aliasing artifacts. The predicted results are compared to the experimental results. Effective ways of avoiding or reducing aliasing artifacts without sacrificing too much image quality are proposed.

f i x , Y)

I. NOMENCLATURE is the film image of an object with a grid pattem. is the film image of an object without a grid pattem. is the film image of a grid pattem. is the Fourier transform of gimg(z, y). is the laser spot size smoothed grid image. is the Fourier transform of gavg (2, y). is the frequency response of the PMT and AMP system. is the Fourier transform of the image before A D converter.

ssix: Y) is the G,(u, w) is the w(x,y) is the W(u,w) is the W*(u, U) is the H ( u , v ) is the T is the fo = 1/T is the a is the

digitized grid image. Fourier transform of g ( x , y). intensity distribution of the laser spot. Fourier transform of w(z , y). conjugate of wizc, y). reconstruction filter. grid interval. grid frequency. laser spot size.

d, and d, fx = l/dx and f , = l/d, are the sampling frequencies in

6

cp

41

are the sampling distance in z and y directions.

x and y directions. is the angle between the grid line and the x direction. is the angle between the Moir6 pattem and the 3: direction. is the phase of the grid lines. is the phase of the PMT-AMP response. f o 3 0)

Manuscript received December 30, 1992; revised May 15, 1993. The associate editor responsible for coordinating the review of this paper and recommending its publication was A. E. Burgess.

J. Wang is with the Department of Radiological Sciences, UCLA School of Medicine, Los Angeles, CA 90024-1721 USA.

H. K. Huang is with the Department of Radiology, UCSF School of Medicine, San Francisco, CA 94143-0628 USA.

IEEE Log Number 9401076.

11. INTRODUCTION IGITAL IMAGES, compared with analog images, have D the potential of improving image quality, reducing image

storage, speeding up retrieval process and as a means of developing expert diagnostic systems. Currently, about 70% of examinations in a radiology department still rely on con- ventional screedfilm detector as a method of acquiring the image [ 11. In order to take advantage of the potential of digital images, we have to consider how to obtain high quality digital images from films. Previous studies indicated that a laser film digitizer is commonly accepted as one of the best choices to obtain high quality digital images [2], [3]. However, aliasing artifacts may occur in the digitized image if the sampling is inadequately performed. Aliasing artifacts may become very prominent when the film image contains line patterns due to scatter reducing grids for two reasons. First, lower frequency aliasing artifacts change the local contrast of the original image. As a result, it will affect the diagnosis of some disease related to the contrast difference. Second, higher frequency aliasing artifacts will affect the diagnosis of the diseases that have fine details. Choosing the appropriate parameters during digitization is very important to avoid the artifacts.

In this study, Fourier theory is used to derive the relationship between a sampled image and an original grid image. The effects of the laser spot size of the digitizer, the sampling distance, and the angle between the grid lines and the direction perpendicular to the laser beam scanning direction on aliasing artifacts are derived. X-ray films with grid lines were digi- tized varying these three parameters. The amplitude and the frequency of the aliasing artifacts under each condition are calculated and compared with the theoretical results. Finally, we propose methods to avoid and to minimize aliasing by choosing appropriate parameters during the digitizing process.

111. MATERIALS AND METHODS

A . Theoretical Calculations

The projectional image of an object with a grid pattem, for the local approximation can be written as

f(z, Y) = . f img(z , Y) + gimg(x:r Y) (1)

where f i m g ( z , y ) is an image without the grid pattem, and gimg(z,y) is the grid pattem image. Since our interest is in the grid line aliasing artifacts, we will only consider the grid line image gimg(z, y) in this paper.

02784062/94$04.00 0 1994 IEEE

376 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 13, NO. 2, JUNE 1994

Aluminum

Fig. 1. two lead strips.

The cross-section of an antiscatter grid. T is the distance between

An ideal stationary anti-scatter grid is made of transmis- sive material (e.g. aluminum) interspersed with opaque (e.g. lead) in an alternating pattern of period T . (see Fig. 1) [4]. The Fourier series of an one-dimensional periodic function gimg(z + T ) = gimg(Z) is

33

gimg(z) = a0 + U, cos(27rnfoz + &) (2) n = l

where uo. a, and dl, are constants, f a = 1/T is the grid frequency. The frequency spectrum of the grid is discrete with the frequencies f o , 2 f 0 > 3.fo. . . .. Conventional X-ray imaging systems normally have cutoff frequencies of about 5 lp/mm. If the grid frequency f o used is from 2.5 lp/mm to 4 lp/mm, the harmonic frequencies 2 f 0 , 3 f o , . . . will be larger than the cutoff frequencies of these imaging systems. Only the fundamental frequency fo will be left on the film. Even if the cutoff frequency of an X-ray imaging system is greater than 5 lp/mm, the amplitudes of the higher harmonic components of the grid lines will still be less than that of the fundamental frequency due to high frequency attenuation of the MTF of the X-ray imaging system. To the first order approximation, we will only consider the fundamental frequency. If we ignore the DC component (1.0 and tilt the film so that the grid lines have an angle 6' with respect to the x-axis (Fig. 2), then the grid lines on the film can be written as

gjmg(z, y) = A cos[Z.rr(fo sin 6' . 3 : - f o cos H . y) + 411 (3)

The z-axis is defined such that when 6' = 0" the grid lines lie along the 2-direction. A is a constant and 41 is a phase factor.

The simplified digitization process of a laser film digitizer is shown in Fig. 3. A laser beam scans the film in the horizontal (y) direction and the film moves in the vertical (2) direction. After each horizontal scan, the film is advanced one step and the laser beam scans the next line. This process continues until the entire film is scanned. A photomultiplier tube (PMT) receives the transmitted light beam and converts the light signals to the electrical signals. The electrical signals go through amplifiers (AMP) and then to an analog to digital converter (AD). For simplicity, we consider the digitization as a three stage process. In the first stage, a laser beam scans through the film. In the second stage, the PMT and the amplifiers function as a low pass filter along the scanning direction. We call it PMT-AMP component. In the third stage, the A D converter samples the signals.

Fig. 2. the grid lines and the .Y-axis.

The coordinates of the grid line orientation. H is the angle between

first stage

second stage

third stage

Fig. 3. the digitizing process.

A simplified schematic laser film digitizer and the three stages of

In the first stage, the intensity of the light transmitted through the film is proportional to the average light passing through the area where the laser spot scans. This corresponds to averaging the image with a finite focal spot, such that

gavg(z!Y) = g i m g ( . + ~ , ~ + 8 ) . m ( a , ~ ) d a d p (4) 1.1 where gavg(x,y) is the smoothed grid image, w ( I x , / ~ ) is the intensity distribution of the laser spot. Taking the Fourier transforms of both sides of (4), we obtain

( 5 )

where Gavg(z, y) and G;,,(u. U) are the Fourier transforms of gavg(z, y) and yi,,(z. y), respectively, W * ( ~ L , U ) is the conjugate of the Fourier transform of ,w(z, 9).

In the second stage, the PMT-AMP component, the light signals are converted to the electrical signals and then go through the amplifiers. We assume that this part of the system is linear and it only affects the signals in the scanning direction (y direction). If the frequency response of this component is S(v) , the signal spectrum after this stage is

Gavg(U. U) = G j m g ( U , U ) ' W*(U, U)

G(u. U ) = GaYg( U. U ) . S(V)

(6) = Ginlg(?~, U ) . W * ( ~ L . I I ) . S(71)

WANG AND HUANG: FILM DIGITIZATION ALIASING ARTIFACTS CAUSED BY GRID LINE PAlTERNS 311

0 2 4 6 8 Sampling frequency (pixeVmm)

0 1 2 3 4 5 6 Sampling frequency (pixeVmm)

(b)

Fig. 4. of the grid frequency. (a) Grid frequency = 4.0 Ip/mm. (b) Grid frequency = 3.0 Ip/mm.

Effect of the sampling frequency on the aliasing frequency. The minimum aliasing frequency is when the sampling frequency equals to the fractions

The third step, A/D converter converts analog values to discrete values. Discrete sampling in the frequency domain, according to the sampling theory [SI, is given by

where G,(u, U ) is the Fourier transform of the sampled image, d, and d, are the sampling distances in z and y directions respectively, and fZ = & and f, = & are the corresponding sampling frequencies.

To obtain the final analytical results, let's go back to G(u, v ) in (6). The Fourier transform of the grid image gimg(.x: y) (see (3)) is

A 2

+ e C J C I S ( u + fo sin 8 , v - f o cos 0)]

Gimg(u,v) = - [ e J m l b ( u - fosinOlw+focosO)

(8) Substituting (8) into (6), we obtain

~

378

\

0 A 0 W

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 13, NO. 2, JUNE 1994

grid frequency sampling frequency (lP/") (pixeVmm) (4.00, 4.00) (2.86 2.86) ..... ....... I..."

grid frequency sampling frequency (lp/mm) (pixeumm) (4.00, (2.86, 3.33) (2.22, 2.50)

.._ -......-...

/-....--

_*---. ....-."/

/.......' -*e+

* - - e C

e.--". ... ..ee ._"..e /.'.

-.... C"... _--- c--

.......e ......... " ._.*........... ...... "..."."- _---.-*-

-___-- - -* --

0 5 10 15 20 Angle (")

(b)

Fig. 5. = grid frequency. (b) Sampling frequency does not equal to the grid frequency.

Effect of the angle between the grid lines and the direction perpendicular to the scanning direction on the aliasing frequency. (a) Sampling frequency

If we assume that the laser spot intensity has a Gaussian where L represents the phase angle and q ( f 0 , 0 ) is used here distribution, for simplicity.

Substituting (1 1) and (12) into (9), we obtain

A w(z; y) = B exp (- 2(2zaz ")) (IO)

where B is a normalized constant, a is a constant which determines the size of the laser spot. The Fourier transform

G(u,w) = - 2 exp [-y(fi)] ~ ~ ( f , , c o s ~ ) l

of w(z ,y ) is

If the PMT-AMP component impulse response is real, its TO reconstruct the sampling image, substituting (13) into Fourier transform S(w) is conjugate symmetric, i.e. (7), multiplying (7) by a square reconstruction filter H ( u : w )

IS( fo cos 0) I = IS( - f o cos 0) 1, and H(.u,w) = dzd, 1uI < f z / 2 IV I < fy /2 Ls( focose) = - L S ( - ~ - ~ ~ ~ ~ B ) = q ( f o , e ) (12) = 0 elsewhere

WANG AND HUANG: FILM DIGITIZATION ALIASING ARTIFACTS CAUSED BY GRID LINE PATTERNS 379

1 .o

0.8

0.6

0.4

0.2

0.0

grid frequency 4.0 lp/mm 3.0 lp/mm 2.5 lp/mm

.................. -----

0 100

Fig. 6. Effect of the laser spot size on the aliasing amplitude.

and taking an inverse Fourier transform, the sampled grid line image becomes

gs(GY) = A w [-+-;I] I s ( focose) l

AI N x

+ 2 4 - f o cos0 + 71fy)rJ + 41 - d f o , 011 (14)

cos[2a(jo sin B - 7 r i f , ) z

m = - h f n=-N

Here M . N are determined so that when Iml < M and In1 < N

f s If0 sin B - mfz I < -

2 f

I f O C O S B - nfyl < -2 2 (15)

Equation (14) is the summation of many cosine terms. Each cosine term represents a single frequency Moire pattem with the spatial frequency f m 1 2 , a phase factor $1 - 7)(f0, B ) , and a tilt of angle cp with respect to :I: direction, where

f o sin B - m f, fo COS B - r i f ,

tan cp =

The final digitized grid pattem image g,(z,y) should be the superposition of all these cosine terms. The aliasing frequency is defined as f m n which is a function of the sampling frequency and angle 8. When the aliasing frequency f m n is close to zero, the contribution of the first two terms inside the cosine in (14) becomes very small, and the phase factor 41 - 7 / ( f 0 , 8 ) contributes significantly to the aliasing artifacts. In this case, the aliasing appearance is a slow varied background. The background level is dependent on the phase factor. Otherwise, the phase factor does not affect the

200 300 400

Laser spot size (pm)

amplitude, and has no effect the Moire pattem visibility in most of the cases. The aliasing amplitude

exponentially decreases with the laser spot size a and depends on the angle B.

B . Experiments

Two X-ray films, one from a chest anthropomorphic phan- tom (Radiology Support Device Inc., Long Beach, CA) [2] and the other from a 8.25 cm uniform plastic block, were taken with a 1.5 mm focal spot size X-ray tube at 90 kVp, 15 mAs and 152 cm FFD (focus to film distance). The film cassette was FUJI AW with medium 200 screen and the Kyokko GM- 1 films were used. Both films were obtained with an anti-scatter grid. The grid (MXE Inc., Culver City, CA) was 14 x 17 inches, 4 Ip/mm and with a grid ratio 6: 1. The films were then digitized with a Lumiscan 100 scanner (Luminsys, Sunnyvale, CA) with different laser spot sizes (50, 70, 105, and 210 pm) and sampling distances (200, 250, 300, and 350 pm) at different angles (OD, 5" and 10"). The images from the uniform plastic block and the grid pattem were used to calculate the frequencies and amplitudes of the artifacts. The 2-D Fourier transforms of these images were calculated first. The Fourier transformed images had a well defined pattem close to a single frequency. The frequency and the amplitude of each image were calculated from the Fourier spectrum.

IV. RESULTS

A. Theoretical Calculations In this section, we plot the relationships between the aliasing

frequency and the sampling frequency, the aliasing frequency and the film angle tilted, and the aliasing amplitude and the laser spot size, by using (14)-(17). It is easy to prove that

380

2

1 -

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 13. NO. 2, JUNE 1994

film angle = 0"

theOEtiCal experimental

\///// 2

1 -

U '

2

film angle = 5"

theoretical experimental

3 I I I

4 5 6 Sampling frequency (pixel/")

0 : I I I

2

2.0

1.5

1 .o

film angle = 10"

theoretical experimental film angle = 10"

theoretical experimental

0.5 ! I I I

2 3 4 5 6 Sampling frequency (pixel/mm)

(C)

Fig. 7. The minimum aliasing frequency occur5 when the sampling frequency = 3.82 pixel/mm. (a) Film angle = O n , (b) Film angle = so. (I,) Film angle = 10'.

Comparison of the theoretical and the experimental results of the aliasing frequency versus the sampling frequency. Grid frequency = 3.82 Ip/mm.

there is only one pair of ( r n . 71) which satisfies (15) for each sampling frequency, so that the aliasing artifacts are always a single frequency. The indices rrL and 7) representing the aliasing frequency were selected depending on the sampling conditions.

The effects of the sampling distance on the aliasing fre- quency are illustrated in Fig. 4(a) and 4(bj which were calcu- lated from (16). In these calculations, we assume that d, = d,, so that the digital imaging has the same magnification in the r and :y directions, and H was kept constant for each curve.

WANG AND HUANG: FILM DIGITIZATION ALIASING ARTIFACTS CAUSED BY GRID LINE PATTERNS 38 I

2 3 3.82 4 5 6

Sampling frequency (pixel/")

Fig. 8. Comparison of the theoretical and experimental results of the angle of the aliasing patterns versus the sampling frequency. Grid frequency = 3.82 Ip/mm. Note the sudden change of the angle when the sampling frequency is above and below 3.82 pixel/mm, this corresponds to the orientation change of the Moire pattern.

The grid frequencies in Fig. 4(a) and 4(b) are 4 Ip/mm and 3 Ip/mm, respectively. For each grid frequency, three angles 0'. so, and 10' were used to calculate the aliasing frequency. Note that when the sampling frequency is equal to, half, or one third of the grid frequency, the aliasing frequency is the minimum. The aliasing frequency oscillates with the sampling frequency until the sampling frequency reaches the Nyquist frequency.

Fig. S(a) and 5(b) demonstrate the variation of the aliasing frequency with the angle H. The curves were calculated from (16), where angle H was varied with fx and f y kept constant. In Fig. 5(a), the sampling frequency and the grid frequency are equal for each curve, and they are different in Fig. 5(b). The aliasing frequency increases with the angle. This can be explained as follows: when the film is tilted a small angle, the apparent grid frequency in the ?J direction decreases, whereas the grid frequency in the :I' direction increases (Fig. 2). Be- cause the grid frequency in the :r direction increases from zero, we assume that there is no aliasing problem in this direction. As the angle increases, the grid frequency in the y direction (:os H decreases. Since the sampling f y frequency was kept constant. the aliasing frequency I jocosH - f Y l increases.

Fig. 6 shows the effect of the laser spot size on the ampli- tude of the aliasing artifact, assuming that all other parameters remain unchanged. From ( 18) we notice that the spot size U does not affect the aliasing frequency, but strongly influences the amplitude. As the laser spot size IL increases the amplitude decreases. The reason for this is that the laser spot is behaving as a low pass filter. The larger the laser spot is, the narrower the pass band is. If the grid frequency is fixed, the amplitude of the grid frequency reduces as the filter becomes narrower, i.e. as the laser spot size increases.

B. Comparing Theoretical and Esperiment Results

After digitizing the film with a grid pattem, the frequencies and the amplitudes of aliasing artifacts were calculated and compared with the theoretical results. The experimental and the theoretical results of the sampling frequency on the aliasing frequency are shown in the Fig. 7(a), 7(b) and 7(c). The grid frequency used for the theoretical curve was 3.82 lp/mm which was different from 4 lp/mm, the nominal number of the grid frequency. This difference may be contributed by many factors, including the error of the calibration of the laser scanner, and the accuracy of the grid frequency given. The true grid frequency 3.82 Ip/mm was calculated from the Fourier spectrum of the digitized image which was obtained by sampling the film with 100 pm (10 pixel/"). The experimental results are very close to the theoretical results. The tilted angle cp of the aliasing pattem with respect to the .r direction were also calculated from the frequency components f x and f , obtained from the digitized images. These results, together with the theoretical results from (17) are shown in Fig. 8. Note the change of the orientation of the angle of the aliasing line when the sampling frequencies are above and below the grid frequency 3.82 Ip/mm. (see also Figs. 1 I, 12)

The experimental results of the laser spot size of the digitizer on the aliasing amplitude are shown in Fig. 9. They do not fit well with the theoretical curve. The reason is that we assume the laser spot is Gaussian, but the true laser spot may not be strictly circularly symmetric Gaussian 161.

Fig. 10 shows a chest phantom film with a grid line pattem (4 Ip/mm). The grid line pattem is hardly seen from this image. The region in the square including the left lung and mediastinum was digitized with different parameters to appreciate the visual effect of the Moir6 pattern (Figs. 11 and

382

1.0

0.8 -

0.6 -

0.4 -

0.2 -

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 13. NO. 2. JUNE 1994

distance

98pm 156pm 332pm - theoretical

0.0 : I I

0 100 200 300 Laser spot size (pn)

Fig. 9. for the visualization of the aliasing artifacts.

Comparison of the theoretical and experimental results of the aliasing amplitude versus laser spot size. The high amplitude value is responsible

Fig. IO. The chest phantom film with a grid line pattem. The small square is the digitization region. The grid line pattem is not visible.

12). The laser spot size used was 105 pm in the Fig. 11 and 210 p m in the Fig. 12. The Moir6 pattern appears on most of the images when the sampling spot size is 105 ,um (Fig. I l ) , and is hardly seen on the images with 210 pm sampling spot size due to the decreased amplitude of the Moir6 pattern. This

effect can be explained from Fig. 9, as we notice that the amplitude of the Moire pattern sampled with 105 pm is about 4-5 times larger than that of 210 /Lm.

On both Figs. 11 and 12, the sampling distances are 200 pm, 254 pm, 293 pm and 352 pm from the first to the

WANG AND HUANC;: f . 1 I . V I)ICilTI%Xl~lOh AI.IASING AKTIFAC'TS CAUSED BY GRID LINE t ?~ l~E .K 'US 383

Fig. 11. Digital image\ digiti74 \ \ i t h a 105 / r i m focal \pot \im at different sampling distances and angles. Image\ i n row\ 1-3 from top IO bottom were digitizcd with rhc film r i l l ed 5" and 1 O'respeclivcly. Images in columns 1 4 from the left to right were digitired \vith sampling distance?, 200 Iim, 254 jrm, 293 { r n i and 357- / j t i i rerpc.cti\cly. The aliahing artifacts are most prominent at 254 /rni and 293 I'm. Some aliazing ;inifact\ are seen at 200 p m with 0' and io Oh\cr\e h, iihriipl change o f the Moire pattern orientation in column 2.

fourth column, and the angles are 0'. 5" and I O o from the first to the third I O W respectively. With a 105 /bm spot size, when the sampling distance is equal to 254 //mi (the second column) which is the closest to the grid interval 262 /im (3.82 Ip/mm), the aliasing frequency i \ the smallest, i.e. the distance between the lines is largest, and the artifact appears stronger. As the sampling distance moves away from the grid interval, the aliasing frequency increases and the line pattern becomes closer and the artifacts are less prominent (the first and the fourth columns). The aliasing frequency also increases with the increase of the angle (comparing each column from the top to the bottom).

The visibility of' the aliasing artifacts is dependent on three factors: the amplilude o f the aliasing in (14), the frequency response of the display, and the human visual sensitivity. The amplitude of the aliasing artifacts is independent of the sam- pling frequency. hut may depend on the orientation of the grid line pattern. The effect of the angle H on the amplitude depends on the bandwidth of the PMT-AMP frequency response, S(v ) . If the cutoff frequency of S( , t i ) is high enough, H will not affect the amplitude. The amplitude is always the minimum when 0 = 0". Generally \peaking. the smaller the amplitude is, the

less dominate the aliasing artifacts. We will not discuss various display systems in detail, only assume that i t functions as a low pass filter. The human visual response varies with the grid frequency 171, and i t was reported that the highest response of the human eyes is around 1-2 Ip/nim and decreases on both sides.

It is also observed from Fig. 1 1 that the orientation of the MoirC pattern is different for a givzn \et of digitizing parameters. (Note: the images shown here are in an anatomical position which is !NIG clocki\ise rotated v,.ith repect to the digitizing position). This can he explaincd by ( 17) and from Fig. 8. The first row of image5 have aliajing patterns almost parallel to the . I ' direction. The second row of images were digitized with the film tilted .5'. and the angles of aliasing pattems vary from -70" to :5'. The third row of images were digitized with the film tilted 1P. and the angles of the aliasing pattems vary from -80' lo T,.>". These angles can be predicted from (17). Note that the magnifications of the digitized images with different sampling distance:, shown in Figs. I 1 and 12 are different. This is because all images are 512 x 512 pixels, using a smaller \ampling distance will cover a snialler area on the tilni, but the Files displayed on the

384 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 13. NO. 2, JUNE 1994

Fig. 12. Digital image digitized with a 210 p m focal spot size at different sampling distances and angles. Images in rows 1-3 from top to bottom were digitized with the film tilted 0'. 5'and 10' respectively. Images in columns I4from the left to right were digitized with sampling distances 200 p m , 254 Itm, 293 p m and 352 p m respectively. For this large focal spot size, no appreciable aliasing artifacts are seen regardless the sampling distance and the tilted angle.

screen are the same size as those images sampled with larger sampling distances. Thus, the images appear to have different magnifications.

V. DISCUSSION

We presented a mathematical model to explain the aliasing artifacts (Moire pattern) caused by digitizing of an X-ray film with a grid pattern. The model includes three parameters: the laser spot size of the digitizer, the sampling distance, and the angle between the grid line and the sampling direction. The results derived from this model compare favorably with experimental values.

The results of this work show that the digitization process cannot totally eliminate the aliasing artifacts by using the current system without losing the imaging resolution. But a proper choice of the digitization parameters will have an effect on the visibility of the aliasing artifacts and the future processing for removing artifacts.

We recommend that during the digitization process, the film is positioned such that the grid lines are perpendicular to the scanning direction. This way we can possibly utilize the high frequency attenuation characteristic of the digitizer PMT-AMP component to reduce the amplitude of the gird

lines. The amplitude of the aliasing artifacts is independent of the sampling frequency. We cannot reduce the aliasing amplitude by varying the sampling frequency. If the Nyquist frequency condition cannot be satisfied, we would select a sampling frequency from Fig. 4 which will give a higher aliasing frequency. The reason for this is that the display system functions as a low pass filter. The aliasing artifacts will be less prominent due to the high frequency attenuation characteristic of the display system. In addition, a digital image can be post-processed. The high frequency aliasing artifacts are more easily to be removed than the low frequency components because the original image is dominated by low frequency components. Once the sampling distance is selected, the laser spot size should be selected to be the same as the sampling distance.

Since it is difficult to remove the grid line aliasing artifacts in the digitizing process, it would be more desirable to remove them from the digitized image. One method is to implement the Fourier transform and search for the sharp peaks and implement a filter to remove those peaks.

This model also explains two phenomena which had been puzzling us during the past several years. First, why do the aliasing artifacts appear to be more prominent under certain digitization conditions? Second, why does the orientation of

WANG AND HUANG: FILM DIGITIZATION ALIASING ARTIFACTS CAUSED BY GRID LINE PATTERNS

the Moir6 pattem change abruptly when there is only a slight change in the digitization condition? Fig. 11 allows us to understand the characteristics of the Moire pattem under various digitization conditions. Results from this study can be used to guide us to minimize aliasing artifacts using current generation digitizers and to design film scanners of the next generation .

ACKNO w LEDGMENT

The authors thank Brent Liu for providing the two X- ray films and Hisashi Yonekawa for his assistance in the digitization process.

385

REFERENCES

[ I ] E. R. Miller. E. M. McCury, and B. B. Hruska, “Immediate hospital wide access to x-ray film image,” Rudiolo,yy, vol. 192, pp. 13-16, 1969.

[ 2 ] H. K. Huang. Elemenrs of Di,yitu/ Rudiolo,yy. Englewood Cliffs, NJ: Prentice-Hall, 1987.

[3] S. C. Lo, R. K. Taira. N. J. Mankovich, H. K. Huang, and H. Takeuchi, “Performance characteristic of a laser scanner and laser printer system for radiological imaging,” Computerized Radiology, vol. 10, no. 5, pp. 227-237, 1986.

[41 T. S. Cuny 111, J . E. Dowdey, and R. C. Muny Jr, Chrisrensen’s Physics of Diagnostic Radiolog!. 4th ed., Lea & Febiger 1990.

151 A. Rosenfeld and C. Kak. Digirul Picture Processing. San Diego, CA: Academic Press Inc. 1976.

[6] H. K. Huang, Elemenrs of Digirul Rudiolocyj. Englewood Cliffs, NJ: Prentice-Hall. 1987. p. 318.

[71 C. R. Carlson, R. W. Cohen. and I . Gorog “Visual processing of simple two dimensional sinewave luminance grating.” Vision Res. vol. 17, pp. 351-358, 1977.