Adv. Radio Sci., 9, 135–138, 2011 www.adv-radio-sci.net/9/135/2011/ doi:10.5194/ars-9-135-2011 © Author(s) 2011. CC Attribution 3.0 License.
Advances in Radio Science
Inverse filtering for time, delay and integration X-ray imaging M. Rosenbaum, W. Sauer-Greff, and R. Urbansky TU Kaiserslautern, Institute of Communications Engineering, 67653 Kaiserslautern, Germany
Abstract. In food industry, most finished products are scanned by X-ray for contaminations. These X-ray machines continuously scan the product passing through. To minimize the required X-ray power, a Time, Delay and Integration (TDI) CCD sensor is used to capture the image. While the product moves across the sensor area, the angle of the X-rays changes during the pass. This can be compensated for by adjusting the sensor shift speed to focus on a single plane of the product. If the product has a significant thickness, the image will show artifacts due to the laminographic effect. In this contribution we demonstrate that by the use of inverse filtering images which are focused on planes of different height can be generated out of a single X-ray image.
1
Introduction
In food industry, there is a need to prevent contaminated products from leaving the production site. Metal detectors are widely used for this task, but they fail for non-metallic objects. Glass splinters and ceramic objects such as broken ceramic knife blades or ceramic ball bearing balls can not be detected. Continous X-ray imaging allows to detect all these objects and the machine can simply be fitted in the production process. The product passes the X-ray machine continously on a belt with an overhead X-ray source. After passing the product, the X-rays are converted to visible light by a szintillating foil. The light emitted by this foil is projected on a lineaccumulating CCD sensor. A typical sensor has 128 lines which are shifted synchronously to the transport belt and the charges are moved from line to line over the sensor accumulating more and more X-ray light. Each image leaving the sensor is exposed 128 times. This allows for a high efficiency and low noise, however the angle of the X-ray beam passing through the product changes slightly from shift to shift. This produces a so-called laminographic effect. By Correspondence to: M. Rosenbaum (
[email protected])
this effect, object edges get washed out, the sharpness of the image is reduced in general. Because of the imaging process, it is not possible to distinguish between a flat, dense object and a high, less dense object – e.g. metallic washer ring versus macaroni noodle. Figure 1 shows a schematic drawing of such an X-ray scanner. Currently, it is necessary to use laminographic techniques (Gondrom, 1999; Rooks, 1995) in conjunction with the Radon Transform (Popularikas, 1996) if depth information is needed. This requires two X-ray sources and two sensor assemblies which deliver images of the product under different angles. This is not only expensive, in addition the second X-ray tube also needs cooling and better shielding against X-rays leaving the machine is required. In this paper, we propose the use inverse filtering of the single X-ray sensor image to calculate images focussed on arbitrary planes of the product. The paper is organized as follows: first, we give an short introduction into the X-ray imaging process. After that, the inverse filtering is discussed, followed by the description of the test setup and the results. 2
Imaging process
The product is transported through the X-ray scanner on a conveyor belt. Above the belt, an X-ray source is located, the imaging equipment can be found below the belt. Because large CCD sensors are very expensive and subject to damage by X-ray radiation, a szintillation foil which converts X-rays into visible light is located below the conveyor belt. The light is focussed by optic lenses and digitalised by a CCD sensor. This CCD sensor has a typical resolution of 128×1024 pixel. The electrical charge generated by photons hitting the sensor is shifted from line to line and read out after it reaches the last line (in this case line 128). Each line which enters the analsysis system has been exposed 128 times, which can be modeled as a superposition of 128 complete images. Figure 1 shows a schematical drawing of such an apparatus. The angle under which the X-rays enter the product changes as the belt moves the product across the sensor. Therefor the image gets blurred in movement direction. This
Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.
n
needed, two scans have to be performed. Also, there is nos(x,y) = a(x,y) ∗ h(x,y) + n (2) Product depth information in the resulting image Transport and Belt no differences Fig. 2. Calculated impulse response The inverse filtering takes advantage of the frequency do- : Sensor (with lines) between flat and CCD non-flat objects are visible. 136 M. Rosenbaum et al.: Inverse filtering for time, delay and integration X-ray imaging Fig. 1. Schematic drawing of the X-ray scanner
main. A pure inversion of the transfer function H(f x ,fy ) requires to take the reciprocal of it yielding H w (fx ,fy ) = H −1 (fx ,fy ), but this poses new problems because of spec3 Inverse Filtering tral zeros and noise contained in the X-ray image will be amplified. To deal with this, Wiener filtering (Madisetti (1998)) This blurring caused by the laminographic effect can b can be used. Equation 3 shows the parametric form of the inverse filtering since Wienerfectively filter. K addressed accounts forbynoise influence, ideally it isit can b garded as a convolution ofofthe with the p choosen as the spectral power density the real whiteimage noise conspread-function of the imaging system corrupted with tained in the X-ray image.
X-rayline tube which enters the ne (in this case line 128). Each ysis system has been exposed 128 times, which can be Because of the of width the opticalimages. active area, the object led as a superposition 128ofcomplete Figure is X-rayed atdrawing differentof angles. Theapparatus. charge shift can be modws a schematical such an eled as the superposition of 128 separate images taken under e angledifferent underangles. whichHow thelarge X-rays enteris depends the product this angle on the spees as cific the belt moves the product across thebelow sensor. scanner setup, but in general an angle 5 degrees for theisimage in movement Thisangles used. gets This blurred superposition of imagesdirection. under different n. H ∗ (fx ,fy ) makesleads it difficult to the reliably detect edges. For one to blurring, so-called laminographic effect. (3) Hw (fx ,fy ) = 2 +K s(x,y) |H(f = a(x,y) +n Thisthis effect modeledProduct as aby convolution ofbetheBeltreal fice height, cancan bebecompensated an offsetTransport x ,fy )|∗ h(x,y) a(x,y) with the pointIfspread function of theare imaging belt- image and sensor-shift-speed. two sharp planes Figure shows thefiltering imagingtakes and reconstruction The3 inverse advantage ofprocess, the frequenc CCD Sensoran (withimage lines) system h(x,y), yielding s(x,y). d, two scans have to be performed. Also, there is no ˆ of the unknown original image A producing an estimate A main. A pure inversion of the transfer function H(f Fig. 2. Calculated impulse response. information resulting image and no differences Fig.in 1. the Schematic drawing of the X-ray scanner. Fig. 2. Calculated impulse response Fig. 1. Schematic drawing of the X-ray scanner requires to take the reciprocal of it yielding H w (fx ,f = a(x,y) ∗ h(x,y) (1) en flats(x,y) and non-flat objects are visible. H −1 (fx ,fy ), but this poses new problems because of Ineffect general, thisit function is reliably two-dimensional, but For in our makes difficult to detect edges. one tral zeros and noise contained in the X-ray image will b X-ray tube specifice this can by an offset beBecause the width of be thecompensated optical area, the object case there isof aheight, significant contribution onlyactive in direction of the To deal with this, Wiener filtering (Madisetti (1 Inverseplified. Filtering tween beltand sensor-shift-speed. If sharp are3modmovement, which can be modeled astwo a one-dimensional isbelt X-rayed at different angles. The charge shiftplanes can be can be used. Equation 3 shows the parametric form o needed, two scans have to be performed. Also, is no impulse response. This impulse heightthere variant, eled as the superposition of 128response separateisimages taken under Wiener filter. K laminographic accounts for noise This Fig. blurring caused by the effectinfluence, can be ef-ideally information resulting image and object no differences 3. Block diagram. so itdepth is only validHow forinlarge athegiven height ofisthe above different angles. this angle depends on the spechoosen asbytheinverse spectral power density the be white betweenplane. flat andThis non-flat objects visible. filtering since itofcan re- noise the sensor means thatare only flat objects can befectively Fig. 3.addressed Block diagram cific scanner setup, but in general an angle below 5 degrees Because opticalonly active area, thewould objectgarded as tained in the X-ray image. a convolution of the real image with the pointdiplayed sharp.ofIf the thewidth objectofisthe non-flat, one slice isbeused. This superposition of images under different angles is X-rayed at different angles. The charge shift can be modpoint-spread-function of the imaging system corrupted withnoise diplayed sharp, and the parts of the object out of focusspread-function of the imaging∗ system corrupted with eled as the superposition of 128laminographic separate images taken under (f ,f ) H noise n. x y leads to blurring, the so-called effect. produce blurring. In the response is only n. Hreconstruction w (fx ,fy ) = process, an impulse different angles. Howmodeled large this as angle is depends on the spe2 +K |H(fin This effect can the be a convolution of the realvalid for a single focal plane x ,f y )| the X-ray image. The characFigure 2 depicts calculated impulse response for a discific scanner setup, but in general an angle below 5 degrees s(x,y) =of a(x,y) · h(x,y)+ +n n (2) (2) s(x,y) = a(x,y) ∗ h(x,y) image a(x,y) with the point spread function of the imaging teristics the imaging process allow to calculate an impulse tanceisof 8 cm between object and sensor plane. This impulse Product Transport Belt different angles used. This superposition of images under Figure 3 shows the imaging and reconstruction pro response for every focal plan out of one known impulse reresponse can be yielding calculated the s(x,y). X-ray image of a well system h(x,y), anfrom image leads to blurring, the so-called laminographic effect. ˆ The inverse filtering takes advantage of the frequency doThe inverse filtering takes advantage of the frequency doCCD Sensor (with lines) producing an estimate A of the unknown original imag sponse by using algorithms also known in image processing knownThis object. effect can be modeled as a convolution of the real main. A pure inversionof of the the transfer H (fH(f x ,fy ) ,f ) main. A pure inversion transferfunction function x y image a(x,y) ∗with the point spread function of the imaging (1)requires s(x,y) = a(x,y) h(x,y) to take the reciprocal of it yielding H (f ,f w x y) = Schematicsystem drawing of the X-ray scanner requires to take the reciprocal of it yielding H (f ,f w specx y) = h(x,y), yielding an image s(x,y). H −1 (fx ,fy ), but this poses new problems because of −1 H (fx ,fy ), but this poses new problems because of specIn s(x,y) general, this ·function in ourtral zeros and noise contained in the X-ray image will be am= a(x,y) h(x,y) is two-dimensional, but (1) tral zeros and contained in the X-ray(Madisetti, image will be amplified. Tonoise deal with this, Wiener filtering 1998) there is aof significant contribution direction of thecan be used. Equation (3) shows the parametric form of the cause case of the width the optical active area,only thein object In general, this function isbe two-dimensional, in our caseplified. To deal with this, Wiener filtering (Madisetti (1998)) movement, which can modeled asbe abut one-dimensional Wiener K accounts for noise ideally it is ayed belt at different angles. The charge shift can modused.filter. Equation 3 shows the influence, parametric form of the there is a significant contribution only in direction of the beltcan be response. This impulse response is height variant, choosen as the spectral power density of the white noise cons the impulse superposition of 128 separate images taken under movement, which can be modeled as a one-dimensional im-Wiener filter. K accounts for noise influence, ideally it is so it pulse is only valid for a given height ofthe thevariant, object abovetained in the X-ray image. response. This impulse response ison height so it ent angles. How large this angle is depends spechoosen as the spectral power density of the white noise conthesetup, sensor means objects can be is only valid for This a given height ofbelow theonly object above the senFig. 3. Block canner butplane. in general an anglethat 5 flat degrees ∗ (fdiagram tained in the X-ray H image. x ,fy ) sor plane. This means that only flat objects canone be diplayed diplayed sharp. If the object is non-flat, only slice would H (f ,f ) = (3) w x y d. This superposition of images under different angles 2 |H (f ,f x y )| + K sharp. If the object is non-flat, only one slice would be ∗ be diplayed sharp, and the parts of the object out of focus H (fx ,fy ) to blurring, the so-called laminographic diplayed sharp, and the parts of the effect. object out of focus pro-Hw (fx ,fy ) = (3) produce blurring. 2 K reconstruction In the reconstruction process, anprocess, impulse Figure 3 shows the imaging pro-response is |H(f s effect can modeled as a convolution of the real ducebeblurring. x ,f y )| +and ˆ of thefocal for a A single plane in theimage X-ray 2 depicts thethecalculated impulse response an estimate unknown original A. image. The ch 2 depicts calculated for afor dis-a dis-ducing valid e a(x,y)Figure withFigure the point spread functionimpulse of theresponse imaging Figure 3 shows the imaging and reconstruction process,an im In the reconstruction process, an impulse response only teristics of the imaging process allow toiscalculate tanceyielding of 8ofcm between sensorplane. plane. impulse tance 8 cm between object and and sensor ThisThis impulse m h(x,y), an imageobject s(x,y). ˆ valid for a single focal plane in the X-ray image. The characresponse calculated from from the image of aof well an estimate of thefocal unknown original image A impuls response forAevery plan out of one known response cancan be be calculated theX-ray X-ray image aproducing well teristics of the imaging process allow to calculate an impulse known object. sponse by using algorithms also known in image proce known∗ h(x,y) object. ) = a(x,y) (1) 15
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response for every focal plan out of one known impulse response by using algorithms also known in image processing as bilinear or bicubic scaling (Keys, 1981). To generate a depth map of the objects, overlapping focal planes need to be calculated and tested if an object is sharp in one focal plane. If this is the case, the object is flat and its height is known. If the object is non-flat, it is not sharp in any focal plane.
3 Inverse filtering general, this function is two-dimensional, but in our here is a significant contribution only in direction of the This blurring caused by the laminographic effect can be movement, effectively which canaddressed be modeled as a one-dimensional by inverse filtering since it can be se response. This as impulse response variant, regarded a convolution of istheheight real image with the is only valid for a given height of the object above nsor plane. means only2011 flat objects can be Fig. 3. Block diagram Adv.This Radio Sci., 9,that 135–138, yed sharp. If the object is non-flat, only one slice would played sharp, and the parts of the object out of focus
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shows schematically the setup used for the simulations. The impulse response was estimated by geometrical calculations, K in equation 3 was choosen to 10 −4 .
M. Rosenbaum et al.: Inverse filtering for time, delay and integration X-ray4 imaging
137
light source
objects
screen
3
4. Simulation setup. Fig. 4.Fig. Simulation setup (1981)). To gnerate a
Keys pping focal planes need to be t is sharp in one focal plane. at and its height is known. If arp in any focal plane.
4
:
Figure 5 depicts a blurred image of the 3 objects which results after adding up all 128 rendered images.
ategy, test images were genare. The test setup contains ces to the screen and a long the rings. 128 images were ce the final image. This imfiltering strategy. Figure 4 sed for the simulations. The by geometrical calculations, 10 −4 .
Fig. 5. Simulated X-ray image
5 Results Fig. 6. Focus lower ring. Fig. 6.on Focus on lower ring
This allows a classification of targets into flat and no objects and also to calculate the height of a flat object a and Signal Processing 29, 1981 the conveyor Thisof Flip technique is easy to impleme S. Rooks and T. Sack: belt. X-ray Inspection Chip Attach Using Digital Tomosynthesis, Circuit World, Vol. 21 Iss: 3, pp.51 - 55, it works with already existing sensors and machinery, 1995 S. Gondrom and S. Schr¨opfer: Digital computed laminography and the analysis software needs to applications, be modified. This allow tomosynthesis - functional principles and industrial Proceedings of International Symposium on Computed Tomogsubsequent classification algorithms a more reliable dec raphy and Application, Berlin, Germany, 1999 Fig. 7. Focus on upper ring whether an object belongs to the product or is a contam tion.
The generated source image was inversely filtered with an estimated impulse response as shown in figure 2. The first image (figure 6) shows the result if focussed to the lower ring. The upper ring and the cylinder are distorted by a lot of artifacts. As opposed to fig. 6, figure 7 shows the result if focussed to the upper ring. This was done by scaling the impulse response used before. As expected, flat objects can be focussed, high objects are not sharp in any focal plane. The slight artifacts visible even in the sharp rings result from inacmage of the 3 objects which curacies in theFig.estimation procedure of the impulse response. ndered images. 5. Simulated X-ray image
ource
screen
References
Fig. 5. Simulated X-ray image.
This allows a classification of targets into flat and non-flat as inversely filtered with an objects and also to calculate the of aonflat object setup Fig.height 6. Focus lower ringabove shown in figure 2.4The Simulation first the conveyor belt. This technique is easy to implement as ult if focussed to the lower it works with already existing sensors and machinery, only nder are distorted by a lot of To demonstrate thesoftware proposed the analysis needs tostrategy, be modified.test This images allows the were gensubsequent classification algorithms a more reliable decision and Signal Processing 29, 1981 contains erated using a ray-tracing software. The test setup shows the result if focussed whether an object belongs toS.the product a contaminaRooks and or T. is Sack: X-ray Inspection of Flip Chip Attach Using one by scaling the impulse two thin rings at different distances to the screen long tion. Digital Tomosynthesis, Circuitand World,aVol. 21 Iss: 3, pp.51 - 55, cted, flat objects can be fo1995 tubeThe with the same diameter S.asGondrom the rings. 128 images were arp in any focal plane. and S. Schr¨opfer: Digital computed laminography and sharp rings result from inacReferences rendered and overlayed to produce the final image. This tomosynthesis - functional principles and imindustrial applications, dure of the impulse response. Proceedings of International Symposium on Computed Tomogage was used to testandthe filtering V. K. Madisetti D.B. inverse Williams (eds): The Digitalstrategy. Signal Pro- Figure 4 raphy and Application, Berlin, Germany, 1999 Fig. 7.
6 Conclusions
The presented technique allows it to gain depth information out of a single image corrupted by the laminographic effect.
cessing Handbook, CRC Press, 1998 shows schematically usedand forApplications the simulations. The A. D. Popularikas the (ed): setup The Transforms Handbook, CRCwas Press,estimated 1996 impulse response by geometrical calculations, it to gain depth information R. Keys: Cubic convolution interpolation for digital image processtoSignal 10−4 . K effect. in Eq. (3)ing,was by the laminographic IEEEchoosen Transactions on Processing, Acoustics, Speech, Figure 5 depicts a blurred image of the 3 objects which results after adding up all 128 rendered images.
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5
V. K. Madisetti and D.B. Williams (eds): The Digital Signa cessing Handbook, CRC Press, 1998 A. D. Popularikas (ed): The Transforms and Applications book, CRC Press, 1996 R. Keys: Cubic convolution interpolation for digital image pr ing, IEEE Transactions on Signal Processing, Acoustics, S
Focus upper ring. Fig. 7.on Focus on upper ring
Results
The generated source image was inversely filtered with an estimated impulse response as shown in Fig. 2. The first image (Fig. 6) shows the result if focussed to the lower ring. The upper ring and the cylinder are distorted by a lot of artifacts. Adv. Radio Sci., 9, 135–138, 2011
138
M. Rosenbaum et al.: Inverse filtering for time, delay and integration X-ray imaging
As opposed to Fig. 6, Fig. 7 shows the result if focussed to the upper ring. This was done by scaling the impulse response used before. As expected, flat objects can be focussed, high objects are not sharp in any focal plane. The slight artifacts visible even in the sharp rings result from inaccuracies in the estimation procedure of the impulse response. 6
Conclusions
The presented technique allows it to gain depth information out of a single image corrupted by the laminographic effect. This allows a classification of targets into flat and non-flat objects and also to calculate the height of a flat object above the conveyor belt. This technique is easy to implement as it works with already existing sensors and machinery, only the analysis software needs to be modified. This allows the subsequent classification algorithms a more reliable decision whether an object belongs to the product or is a contamination.
Adv. Radio Sci., 9, 135–138, 2011
References Gondrom, S. and Schr¨opfer, S.: Digital computed laminography and tomosynthesis – functional principles and industrial applications, Proceedings of International Symposium on Computed Tomography and Application, Berlin, Germany, 1999. Keys, R.: Cubic convolution interpolation for digital image processing, IEEE Transactions on Signal Processing, Acoustics, Speech, and Signal Processing 29, 1981. Madisetti, V. K. and Williams, D. B. (Eds.): The Digital Signal Processing Handbook, CRC Press, 1998. Popularikas, A. D. (Ed.): The Transforms and Applications Handbook, CRC Press, 1996. Rooks, S. and Sack, T.: X-ray Inspection of Flip Chip Attach Using Digital Tomosynthesis, Circuit World, 21(3), 51–55, 1995.
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