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Title:

Image quality characteristic of a novel X-ray detector with multiple screen - CCD sensors for real-time diagnostic imaging Authors: Cornelis H. Slump, Geert Jan Laanstra, Henny Kuipers, Mark A. Boer, Alex G.J. Nijmeijer, Mark J. Bentum, Ruud Kemner, Henk J. Meulenbrugge, Ruud M. Snoeren In: Medical Imaging 1997: Physics of Medical Imaging, Richard L. Van Metter, Jacob Beutel, Eds., Proc. SPIE, Vol. 3032, 1997.

Image quality characteristic of a novel X-ray detector with multiple screen - CCD sensors for real-time diagnostic imaging Cornelis H. Slumpa , Geert Jan Laanstraa , Henny Kuipersa , Mark A. Boerb , Alex G.J. Nijmeijerb, Mark J. Bentuma , Ruud Kemnerc , Henk J. Meulenbruggec , Ruud M. Snoerenc a University of Twente, Enschede, The Netherlands b Aemics B.V., Hengelo, The Netherlands c Philips Medical Systems, Best, The Netherlands In1

ABSTRACT

we have presented the principle of an X-ray detector based upon a screen coupled to an array of multiple CCD sensors. We now focus on the characterization of the image quality: resolution (MTF) and noise behavior in the overlap area. Simple (and cheap) low F# lenses likely show distortion which means that not all imaged pixels have the same magnication. This may a ect resolution. In the overlap area the image is reconstructed by interpolation between two sensors. Interpolation a ects the noise properties so care must taken in order to avoid that the noise characterization of the reconstructed image mosaic becomes spatially non uniform. We present an analysis of the in uence of lens distortion and interpolation in the overlap area on the image mosaic. The image processing appears not to diminish the image quality provided the processing parameters are set correctly. We therefore present a robust extraction algorithm. In order to evaluate in real-time the image quality of the proposed detector system, we are building an 2 by 2 lens-CCD sensor system as a lab prototype. The main interest is on MTF and quantum noise properties. The hardware is designed such (cubic spline interpolation) that also the lens distortion can be compensated. This enables relative cheap optical components with low F# and a short building length. We have obtained and will present radiographic exposures of static phantoms. Keywords: image quality, radiographic imaging, optical coupling, CCD sensors, real time processing, parameter extraction, distortion

1. INTRODUCTION

The realization of a digital X-ray image detector with input size of 40 40 cm at a resolution of 2k 2k or even 4k squared is not feasible with the conventional II-TV techniques at a reasonable cost. Promising new technology is a full solid state detector based upon amorphous silicon.2{7 In1 we have presented an alternative techniques based upon multiple screen-CCD sensor combinations. In the present paper we will characterize the image quality. As our alternative relies heavily on image processing we investigate the in uence on the image quality of the system. We focus on resolution (MTF) and noise. The X-ray quanta are detected by a scintilator screen and converted to light photons. The conversion of this optical image with one single high resolution CCD would lead to a poor quantum eciency due to the high minication or to expensive and bulky optics. See also the ne paper8 about the DQE of the optically coupled screen to CCD setup. Instead of one (expensive) CCD, we propose a number of lens-CCD sensors of standard resolution. Due to the smaller demagnication the coupling eciency is better even with moderate quality (F#) lenses. We now have a matrix of partially overlapping subimages. With image processing we construct from the subimages a single high quality image. In between images the pixels in the overlap area are interpolated, resulting in a seamless total image. Per subimage the following is necessary, see Figure 1:

o set and gain calibration, correction for vignetting and low frequency drop rotation and magnication (ane transform) correction due to CCD positioning compensation of tolerances and optical afterfocussing requirements. Correspondence to C.H. Slump, Laboratory for Network Theory and VLSI-Design, Dept. of Electrical Engineering, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. E-mail: [email protected]

1 / SPIE Vol. 3032 Medical Imaging 1997: Physics of Medical Imaging

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In Figure 1 also the calibration is indicated by the parameter extraction block. The optical lens coupling can be relatively simple if we allow for some distortion. With a lens design of a small number of spherical surfaces we can practically eliminate spherical aberration, coma and astigmatism. In principle distortion may a ect resolution. In the overlap area the image is reconstructed by interpolation between two or even four sensors. Interpolation a ects the noise properties so care must be taken to avoid a spatially non uniform noise pattern in the reconstructed image mosaic. We present an analysis of the in uence of lens distortion, sensor position and interpolation on the image quality of the image mosaic.

Figure 1.

Schematic diagram of the multiple CCD sensor system.

We will show that the image processing has no negative in uence on the image quality if all parameters are set correctly. However, due to improper parameter extraction residual matching errors may show up. Therefore in this paper we describe a robust method for parameter extraction characterizing lens distortion and sensor position. Vignetting Compensation

Source MEMORY

Image Resampling

Distortion Correction

Target MEMORY

Image Combination

Figure 2.

Overview of the dataow.

In order to evaluate in real-time the image quality of the proposed detector system, we are building an 2 by 2 lens-CCD sensor system as a lab prototype, see Figure 2. The main interest is on MTF and quantum noise properties. The hardware is designed such (cubic spline interpolation) that also the lens distortion can be compensated. This enables relative cheap optical components with low F# and a short building length. We have obtained and will present radiographic exposures of static phantoms.

2. IMAGE FORMATION, PROCESSING AND QUALITY

In this section we investigate the optical image formation between intensifying screen and CCD sensor. From1 we know that the magnication should not be too small, m;1 5. The (F#) is important and also the focal length because the building length should not be too large. Our purpose is to satisfy our imaging requirements with as few optical surfaces as possible. We have also the vignetting e ect to cope with. This means that the o axis intensity prole drops proportionally to cos4 () with the half angle of the optical system. In order to simplify the discussion we limit the discussion here to screens with one major spectral contribution, e.g. Gd2 O2 S so that we can neglect the chromatic aberrations of the imaging lens system. 2 / SPIE Vol. 3032 Medical Imaging 1997: Physics of Medical Imaging

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Distortion can be characterized by a two dimensional third order polynomial. Tolerances in sensor positions and orientation between the pertinent imaging pipes are implicitly taken into account. Distortion is third order in the spatial coordinates9 and can be expressed as follows: x = r2 (Dx ; dy ) y = r2 (Dy + dx ) i

o

o

o

i

o

o

o

(1)

With x y the coordinates of the transformed image and x y the coordinates in the object plane, r is the distance in the corrected image from the optical axis. Distortions do not blur the image, but merely destroy the proportionality between image and object coordinates. Therefore it can be corrected by means of digital signal processing. Distortions can be divided into two categories, isotropic and anisotropic distortion. In Figure 3 three kinds of distortion can be seen: pincushion, barrel (both isotropic) and pocket-handkerchief (anisotropic) distortion. We apply here centered optical systems, symmetrical around the respective optical axis. Therefore the anisotropic distortion coecient d is zero. This coecient is only of importance for electro optical components in the presence of magnetic elds. o

Figure 3.

o

o

Three kinds of distortion.

We characterize distortion by the two dimensional third order polynomial Eq. 1. Correction can be made by the operator T, see Figure 4 which is the inverse of this polynomial, also a two dimensional third order polynomial10,11 :

x(u v) = (a + e v + i v2 + m v3 ) + (b + f v + j v2 + n v3 )u + (c + g v + k v2 + o v3 )u2 + (d + h v + l v2 + p v3 )u3 and a similar equation for y(u v). x

x

x

x

x

x

Figure 4.

x

x

x

x

x

x

x

x

x

x

(2)

Image transformation.

Figure 4 shows the reverse address computation procedure. The target image is the corrected output image, the source image is the acquired distorted image. For every pixel and thus u v coordinate in the target image, the corresponding coordinates in the input image are computed. The source image is characterized by a matrix of numbers representing the pixel intensity in the center of the pixel, the so-called gridpoint. The pixel intensities of computed coordinates in the source image not identical to gridpoints are interpolated, see the next section. 3 / SPIE Vol. 3032 Medical Imaging 1997: Physics of Medical Imaging

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The transformation viz. Equation 2 is easily executed o -line by a computer but we have also implemented it in hardware for real time applications by forward di erence accumulation.10 The source coordinates x and y are expressed by a 16 terms equation as a third order polynomial of the target address. Each of the 16 terms is given by the partial derivative:

+ k l = 0 3 u v

(3)

MTF ( ) = exp(;( ) )

(4)

k

l

k

l

Let us assume that we want to construct an X-ray detector with an input screen of 20 20 cm with a resolution of 1024 1024 pixels. We have a limiting resolution of 2:5 lp=mm. In12 it has been pointed out that in many electro-optical imaging cases the MTF can be modeled in one dimension by the expression: n

c

with the one-dimensional spatial frequency and and n device constants. With n = 2 and = 2:12 lp=mm we have at the spatial Nyquist frequency a modulation of 0.25. This value is a reasonable compromize between screen sensitivity and resolution in the clinically relevant area and spatial aliasing due to the discrete pixels. A higher modulation value would increase the aliasing and reduce the sensitivity due to the requirement of a slower high resolution screen. We apply a reduced demagnication equal to 5 as required in1 for DQE reasons and let us for example image a screen part of 5 5 cm2 on a CCD of 1 1 cm2 , we have for a standard sensor of 512 512 pixels, a limiting spatial Nyquist frequency of 5 lp=mm. This resolution is not supported by the intensifying screen, also because we want the screen to be fast in order to have as much photons as possible. From the detector we require a limiting resolution of 2:5 lp=mm so we appear to oversample the MTF by a factor of two. his is a convenient situation and this allows us also the correction of some mild barrel distortion. A detailed analysis will be presented elsewhere but the base line is that from an oversampled image a high quality image representation is constructed by means of spatially - varying multi - sampling rate techniques. This solves our potential resolution problem. Noise may be something di erent. The most likely situation in which noise structural artifacts may show up due to image processing is the case of imaging a uniform object. In that case the image is a realization of a stochastic process.13 Random variables will be underlined. The number n representing the X-ray photons impinging on the intensifying screen per mm2 is Poisson distributed according to: c

c

P fn = kg = exp(;) k!

k

k = 0 1 2 3

(5)

with the average number of photons per mm2 . With h(x y) the pointspread function characterizing the optical system coupled to screen and CCD we obtain for the output shot noise process14 s(x y) the expectation value:

E fs(x y)g = c and the variance:

2 fs(x y)g = c2

Z1Z1

;1 ;1

Z1Z1

;1 ;1

h(x y)dxdy

(6)

h2 (x y)dxdy

(7)

The DQE at frequency zero is denoted by and the total detection gain is equal to c. The autocovariance of s(x y) is given by: Z1Z1 C ( ) = c h(x y)h(x + y + )dxdy (8) x

y

x

;1 ;1

y

The CCD averages the signal s(x,y) over the pixel area. Because the pixel areas are small (typ. 12 12 m2 ) we model the acquired image by multiplying the signal s(x y) at the center of the pertinent pixel with its area. The CCD adds electrical noise (readout noise, dark current shot noise etcetera) that we model by a Gaussian distributed random process with a constant mean r and variance 2 : r

n = s(x y ) + N (r 2 ) ij

x

y

i

j


r

(9) PREPRINT

The recorded image consists of a correlated part due to the X-ray photons ltered by the systems MTF and an uncorrelated electrical noise part. With

h(x y) =

Z1Z1

;1 ;1

MTF ( )exp(2 j( ) ; 2 j ( x + y))dxdy x

y

x

y

x

y

(10)

where MTF ( ) is the modulus and ( ) is the phase of the optical transform function associated with the impulse response function h(x y), we obtain for the autocovariance function: x

y

x

C ( ) = x

Z1Z1

y

;1 ;1

y

MTF 2( ) exp(;2 j ( x + y))d d x

y

x

y

x

y

(11)

With the MTF of Equation 4 we arrive at the following result:

C ( ) = 0:5 2 exp(; 4 2 2 )exp(; 4 2 2 ) x

y

x

c

c

y

c

(12)

from which we can compute the correlation of neighboring pixels. This equation shows that neighboring pixels are heavily correlated apart from the electrical noise as indicated in Equation 9. The interpolation process1 required for the correction is a linear combination of pixels in the neighborhood of the computed address according to Equation 2. If the pixel intensities are uncorrelated the interpolation results in a reduction of the noise variance. In case the computed address coincides with an original pixel this noise reduction does not occur and we may have a noise breakthrough. In our case the electrical noise power is much below the quantum noise contribution due to the multiple CCD approach. Due to the correlation between the pixels the noise variance is not reduced in the interpolation process and the have a similar visual appearance of the noise texture in the image.

3. PARAMETER EXTRACTION

In this section we describe how the 2 16 parameters of Equation 2 required for the correction of distortion and sensor position are obtained. Each lens sensor combination is presented a testpattern, from the acquired image the set of parameters is computed. Due to the distortion relative to the sensor position and orientation the testpattern will be deformed. In our approach the testpattern consists of a number of markers. The distortion will shift the relative location of the markers. The parameters are determined by least-squares tting of the distance between the original and the shifted locations. The markers need to be easily recognizable and an accurate determination of the center positions of the markers is necessary. A simple example of the three most common markers, spots, crosses and lines is presented in Figure 5.

(a)

Figure 5.

(b)

(c)

Three grid patterns with the marker: (a)spots, (b) crosses, (c) wire grid.

The advantage of using spots is the shape is almost not sensitive to distortion and rotation. In case the CCD pixels are not square but rectangular as in many consumer TV applications the spots will be elliptical in the output window. In noisy and low contrast images, spots are hard to nd. For crosses we have more constraints for the search algorithm, but the shape is sensitive to rotation and distortion, see Figure 6. A similar situation applies for the wire grid where the wire crossings are used as markers. Our choice is for the wire grid because it enables a robust search and center computation. The testpattern is presented in Figure 12, note the extra lines added to detect the center of the grid. This is very useful for the seamless combining of the subimages. 5 / SPIE Vol. 3032 Medical Imaging 1997: Physics of Medical Imaging

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(a)

Figure 6.

(b)

(c)

(d)

(a) undistorted cross, (b) rotated cross, (c) distorted cross (d) distorted and rotated cross. Image

f(n+a,m+b)

g(a,b)

SUM

S(a,b)

Threshold

correlation

h(a,b)

Implementation of template matching.

Figure 7.

The marker search algorithm applies template matching. The algorithm is outlined in Figure 7 and consists of image correlation, summation and thresholding. The algorithm uses the pixel values of the acquired test pattern f (n + a m + b) and the corresponding template values h(a b). The test pattern is constructed such that in a 20 20 pixel image part the template, see Figure 8, can be detected. 10 8 6 4 2 0 20 20

15 15

10 10

5 0

Figure 8.

(a)

5

(b)

0

Cross template. (a) 3D representation, (b) 2D representation.

For each pixel (n m) of the test pattern a 20 20 pixel kernel is multiplied with the template and the contributions are summed:

S (n m) =

20 X 20 X =1 b=1

f (n + a ; 10 m + b ; 10)h(a b)

(13)

a

By thresholding S the marker location is found. An example of a template matching is presented in Figure 9. A recorded marker is shown and the correlation with the template of Figure 8. The marker search algorithm results in a 20 20 pixel size image area for the location of a marker. The next step is to nd the exact center position with subpixel accuracy. Basically two methods can be applied. With the rst method we nd the center by computing the row and column sums and dene the center coordinates corresponding to the row and column respectively with the maximum values. The accuracy of the method can be increased by computation of the center over a larger area or even by applying the resampling techniques in order to obtain subpixel accuracy. In the second method a rst order approximation of the horizontal and vertical line segment is derived from which the coordinates of the center point are computed, see Figure 11. A line k(n m) is drawn through the vertical line of the marker and l(n m) is drawn through the horizontal line. From the rst order line equations the center point is computed. The second method is found to be more accurate than the rst and is therefore preferred. After the location of the markers in the distorted image, the parameters of the polynomials of Equation 2 must be determined. All 32 parameters are computed by minimizing the mean squared di erences between actual and desired marker locations. The algorithm consists of the following steps: 6 / SPIE Vol. 3032 Medical Imaging 1997: Physics of Medical Imaging

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250

2500

200

2000

150

1500

100

1000

50

500

0 20

0 20 20

15

20

15

15

10

15

10

10

5

5 0

0

(a)

Figure 9.

10

5

5 0

0

(b)

(a) recorded cross marker, (b) correlation between marker and template. n 1 1 2 2 m 2 2 9 2 2 2 9 2

Figure 10.

2 2 2 2 9 2 2 2 2

2 2 2 2 9 2 2 2 2

2 2 2 2 9 2 2 2 2

9 9 9 9 9 9 9 9 9

2 2 2 2 9 2 2 2 2

2 2 2 2 9 2 2 2 2

2 2 2 2 9 2 2 2 2

9 2 2 2 2 9 2 2 2 2

A 9 9 image part containing the ideal positioned marker.

1. Normalizing all desired marker locations in the range which results in a better conditioned transformation matrix T. 2. We create two sets of linear equations:

c c

T

x

T

y

= m = m

(14) (15)

x y

with m and m vectors containing the measured x and y marker locations, respectively. The vectors c and c are the transformation parameters to be solved. The transformation matrix T is dened as: 0 1 u u2 u3 v 1 BB 1 u12 u122 u132 v12 CC x

y

x

y

T

= B .. .. @. . 1 u

.. .

n

.. .

u2 u3 n2 n

CA

(16)

n

3. The vectors c and c are are solved by the least squares algorithm15 provided the number n of measured markers is larger than 16. ;1 T m T T = T m c = (T T) (17) x

y

t

t

t

x x

t

x

4. Denormalization of the computed sets of coecients c and c . x

y

In the next section we will apply the correction processing to static imaging examples.

4. RESULTS

In this section we present two results of the multi sensor image processing applied to static objects. For the rst experiment we have positioned a laserhardcopy transparency of the SMPTE testpattern on a lightbox. Four quadrants of this image are subsequently imaged by a CCD camera. The image sensor is the Philips Frame Transfer sensor FT800P, camera module FTM800 50 Hz 754 (H) pixels horizontally and 580 (V) vertically, pixelsize 8:5 m horizontally and 16:8 m vertically. The optical coupling is by means of a Fujinon 25/0.85 lens. We have applied the aperture of 1.0. The lens shows a moderate but noticeable amount of barrel distortion. The images are acquired in the 5122 mode and digitized by means of a Matrox framegrabber in 8 bits / pixel. 7 / SPIE Vol. 3032 Medical Imaging 1997: Physics of Medical Imaging

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k(n,m)

l(n,m) m n

Figure 11.

First order line estimation.

(a) Acquired grid Figure 12.

(b) Corrected grid

Example of camera calibration pattern.

The procedure is as follows. The camera rst images an overlaying gridpattern see Figure 12 from which the geometrical imaging parameters are determined by the procedures outlined in the previous section. Based on the acquired grid image the camera calibration parameters are calculated. Without changing the camera position the pertinent quadrant image is acquired. The four quadrant images are shown in Figure 13. In Table 4. the computed parameters are shown required for the compensation of the registration of the respective subimages. After the overlaying gridpattern has been recorded it is removed and the pertinent quadrant of the image is x parameters x0

x u 2x u2 3x u3 x v 2x u v 3x u2 v 4x u3 v 2x v2 3x u v2 4x u2 v2 5x u3 v2 3x v3 4x u v3 5x u2 v3 6x u3 v3

Table 1.

presented.

upper left 18.506682 0.925395 0.000126 -0.00001 -0.003782 -0.000042 0.000001

upper right 20.848218 0.908433 0.000232 -0.000001 -0.010987 0.000075 -0.000001

lower left 18.526048 0.923626 0.000153 -0.000001 -0.006712

lower right 19.371885 0.902219 0.000282 -0.000001 -0.013530 0.000179 -0.000001

-0.000022 0.000001

0.000059 -0.000001

0.000023

-0.000001 -0.000001

The 2

y parameters y0

y u 2y u2 3y u3 y v 2y u v 3y u2 v 4y u3 v 2y v2 3y u v2 4y u2 v2 5y u3 v2 3y v3 4y u v3 5y u2 v3 6y u3 v3

upper left 13.4772022 -0.028314 0.000125

upper right 8.325975 -0.027998 0.000157

lower left 16.534916 -0.015400 0.000010

lower right 12.543546 -0.027232 0.000131

0.924847 0.000174 -0.000001

0.929512 0.000163 -0.000001

0.931489 -0.000018 0.000001

0.916292 0.000153 -0.000001

0.000102 -0.000001

0.000086 -0.000001

-0.000008 0.000001

0.000152 -0.000001

16 registration parameters obtained from the four subimages. Only the non zero values are


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acquired. The four original quadrants are presented in Figure 13.

(a) Upper left quadrant

(b) Upper right quadrant

(c) Lower left quadrant

(d) Lower right quadrant

Figure 13.

The four original quadrants.

With the processing of the four subimages with the parameters according to Table 4., we obtain the four corrected images shown in Figure 14. With the overlap processing over 12 pixels a seamless total image is obtained, see Figure 15. In our next experiment we have imaged a circular aperture of 15.5 cm in a leadbox containing an X-ray source. We have covered the hole with an intensifying screen of 20 20 cm. We have positioned three standard X-ray resolution phantoms against the intensifying screen. The images are recorded at 25 frames/s in 512 512 mode by a Matrox framegrabber, without averaging or integration. The uoroscopy X-ray parameters are 70 kV and 3:8 mA. The Source Image Distance (SID) is 42 cm. The lens in this experiment was a simple TV lens 16/1.6, applied with diaphragm 2. Again four quadrant images are recorded sequentially after that a registration grid has been recorded rst for each subimage. The four X-ray subimages are presented in Figure 16. After correction and overlap processing of 12 pixels we obtain the resulting nal image of Figure 17. p

5. CONCLUSIONS

The results presented in this paper show that for the two radiological applications exposure and uoroscopy the multi - CCD processing leads to a satisfactory Image Quality. The experiments conrm the analysis that the image processing required for corrections is not limiting the Image Quality of the resulting nal image. Exposure characterized by high dose low noise is well mimicked by the imaging setup with the optical lightbox. On the other hand the experiment with the intensifying screen is a good model for the photon starved uoroscopy imaging. Our work continues with the realization of a real - time lab. prototype.


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Figure 14.

The four corrected quadrants.

REFERENCES

1. C. H. Slump, G. J. Laanstra, H. Kuipers, M. A. Boer, A. G. J. Nijmeijer, and M. J. Bentum, \A novel x-ray detector with multiple screen-CCD sensors for real-time diagnostic imaging," in Medical Imaging 1996: Physics of Medical Imaging, R. L. Van Metter and J. Beutel, eds., Proc. SPIE 2780, pp. 450{461, Apr. 1996. 2. L. E. Antonuk, J. M. Boudry, Y. El-Mohri, W. Huang, J. H. Siewerdsen, J. Yorkston, and R. A. Street, \Largearea at-panel amorphous silicon imagers," in Medical Imaging 1995: Physics of Medical Imaging, R. L. Van Metter and J. Beutel, eds., Proc. SPIE 2432, pp. 216{227, 1995. 3. U. W. Schiebel, N. Conrads, N. Jung, M. Weibrecht, H. Wieczorek, T. T. Zaengel, M. J. Powell, I. D. French, and C. Glasse, \Fluoroscopic x-ray imaging with amorphous silicon thin-lm arrays," in Medical Imaging 1994: Physics of Medical Imaging, R. L. Van Metter and J. Beutel, eds., Proc. SPIE 2163, pp. 129{140, 1994. 4. P. K. Rieppo, B. Bahadur, and J. A. Rowlands, \An amorphous selenium liquid crystal light valve for x-ray imaging," in Medical Imaging 1995: Physics of Medical Imaging, R. L. Van Metter and J. Beutel, eds., Proc. SPIE 2432, pp. 228{236, 1995. 5. J. M. Henry, M. J. Ya e, B. Pi, J. Venzon, F. Augustine, and T. Tumer, \Solid state x-ray detectors for digital mammography," in Medical Imaging 1995: Physics of Medical Imaging, R. L. Van Metter and J. Beutel, eds., Proc. SPIE 2432, pp. 392{401, 1995. 6. E. M. Kutlubay, R. M. Wasserman, D. C. Wobschall, R. S. Acharya, S. Rudin, and D. R. Bednarek, \Cost e ectieve, high resolution portable digital x-ray imager," in Medical Imaging 1995: Physics of Medical Imaging, R. L. Van Metter and J. Beutel, eds., Proc. SPIE 2432, pp. 554{558, 1995. 7. W. Zhao, J. A. Rowlands, S. Germann, D. Waechter, and Z. Huang, \Digital radiology using self-scanned readout of amorphous selenium: design considerations for mammography," in Medical Imaging 1995: Physics of Medical Imaging, R. L. Van Metter and J. Beutel, eds., Proc. SPIE 2432, pp. 250{259, 1995. 8. S. Hejazi and D. P. Trauernicht, \Potential image quality in scintillator ccd-based x-ray imaging systems for digital radiography and digital mammography," in Medical Imaging 1995: Physics of Medical Imaging, R. L. Van Metter and J. Beutel, eds., Proc. SPIE 2708, pp. 440{449, 1995. 10 / SPIE Vol. 3032 Medical Imaging 1997: Physics of Medical Imaging

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Figure 15.

Combined image based upon 12 pixels overlap.

9. P. W. Hawkes and E. Kasper, Principles of Electron Optics, Volume 1, Basic Geometrical Optics, Academic Press, London, 1989. 10. A. G. J. Nijmeijer, M. A. Boer, C. H. Slump, M. M. Samsom, M. J. Bentum, G. J. Laanstra, H. Snijders, J. Smit, and O. E. Herrmann, \Correction of lens distortion for real-time image processing systems," in Proceedings of the 1993 IEEE Workshop on VLSI Signal Processing, vol. VI, pp. 316{324, 1993. 11. M. J. Bentum, Interactive Visualization of Volume Data. PhD thesis, University of Twente, Enschede, The Netherlands, Dec. 1995.





Figure 16.

The four X-ray original quadrants.


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12. C. B. Johnson, \Classication of electron-optical device modulation transfer functions," Advances in Electronics and Electron Physics 35, pp. 579{584, 1972. 13. M. Brok and C. Slump, \Automatic determination of image quality parameters in digital radiographic imaging systems," in Medical Imaging III: Image Formation, R. Shaw, ed., Proc. SPIE 1090, pp. 246{256, 1989. 14. A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York, 1965. 15. A. K. Jain, Fundamentals of Digital Image Processing, Prentice-Hall, Englewood Cli s, 1989.

Figure 17.

Combined X-ray image based upon 12 pixels overlap.


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