Summary

View-interpolation method

Seungwoo Haa, Daecheon Kima, Jonghee Yuna, and Ho Kyung Kima,b*

aSchool of Mechanical Engineering, Pusan National University, Busan, Republic of KoreabCenter for Advanced Medical Engineering Research, Pusan National University, Busan, Republic of Korea

* Corresponding author: hokyung@pusan.ac.kr

Digital X-ray Tomosynthesis of Planar Objects Using the View-Interpolation Method

Poster #: 3 KSNT 2017, Deagu, Republic of Korea

This work was supported by the National Research Foundation of Korea (NRF)grant funded by the Korea government (MSIP) (No. 2013M2A2A9046313).{http://bml.pusan.ac.kr}

Radiation Imaging Laboratory

Background Introduction

Results

Objective

Discussion & conclusion

• Augmenting a few number of projectionimages by view-interpolation (VI) method1. To reduce the time for the inspection of

planar objects2. To gain higher image quality than the

conventional reconstruction image

• In the manufacturing process, the defects detection in thin-slab objects is regarded as an indispensableprocedure and the digital tomosynthesis (DTS) method can be appropriately used for this application

• The DTS method needs a wide scan angular scope and a small step angle for less out-of-plane artifact andless noise in the reconstruction image [Timothy et al. SPIE. (2007)]

• The DTS method in a step-and-shoot fashion can suffer from the trade-off between the image quality andthe inspection time

• For the interpolation, two projection images are used• However, when the arbitrary voxels of object are irradiated,

they are positioned on the detector plane depending on theprojection angle

• For this reason, the re-position process is required for theinterpolation

30 mm

4 m

m

10 mm

1 mmAl disc

• The results of SDNR have shown that the reconstruction images with the VI process gain,on the average, 1.3 times higher performance than the conventional reconstructionimages

• The ASF graphs indicate that the step angle for the inspection has no influence on theASF whether the VI method is used or not

• The VI method can improve the signal characteristic but not beneficial enough to compare with the reference reconstruction image. Therefore, it is properto use the VI method where the top priority is the inspection time

• As scan angle increases, the SDNR increases as well. Using this information, we expect that the VI method can be applied to the computed tomography

�𝒙𝒙, �𝒚𝒚,𝒂𝒂𝒂𝒂𝒂𝒂 �𝒛𝒛 The global coordinates

�𝒖𝒖 𝒂𝒂𝒂𝒂𝒂𝒂 �𝒗𝒗 The local coordinates

𝒙𝒙𝟎𝟎,𝒚𝒚𝟎𝟎,𝒂𝒂𝒂𝒂𝒂𝒂 𝒛𝒛𝟎𝟎A target voxel in the global

coordinates

𝒖𝒖𝟎𝟎 𝒂𝒂𝒂𝒂𝒂𝒂 𝒗𝒗𝟎𝟎The position of a projected target

voxel on the detector plane

𝒖𝒖′ 𝒂𝒂𝒂𝒂𝒂𝒂 𝒗𝒗′ The position of the re-positioned projected target voxel

• Simulation geometry

• Analysis method• Signal-Difference-to-Noise Ratio (SDNR)

- Signal performance is measured

𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒 =𝑺𝑺𝑹𝑹 − 𝑺𝑺𝑩𝑩

𝝈𝝈𝑩𝑩• Artifact Spread Function (ASF)

- Artifact performance is measured

𝐀𝐀𝐒𝐒𝐀𝐀 =𝑺𝑺𝑹𝑹 𝒛𝒛 − 𝑺𝑺𝑩𝑩(𝒛𝒛)𝑺𝑺𝑹𝑹 𝒛𝒛𝟎𝟎 − 𝑺𝑺𝑩𝑩(𝒛𝒛𝟎𝟎)

• Quantitative performances

• Parameters• Coordinates

𝜶𝜶 𝒂𝒂𝒂𝒂𝒂𝒂 𝜽𝜽 The projection angles

𝒓𝒓 The source to object distance

𝒂𝒂 The source to detector distance

𝒎𝒎𝜶𝜶The magnification of a target

voxel at 𝛼𝛼°

𝒘𝒘𝜽𝜽The weighting factor depending

on 𝜃𝜃°

𝑹𝑹𝜶𝜶𝜽𝜽The re-positioning operator from

the detector plane at 𝛼𝛼° to 𝜃𝜃°

𝑷𝑷𝜶𝜶(𝒖𝒖,𝒗𝒗) A pixel value at the point of (𝑢𝑢, 𝑣𝑣)on the detector plane at 𝛼𝛼°

• Single values

• Operators

Experimental setupSDD SOD Al-filter

665.86 mm 443.91 mm 2.5 mmAlkVp mA Integration time

45 kVp 0.9 mA 275 msDet. size Pixel size Voxel size

1548 x 1032 0.099 mm 0.066 mmRecon. size Scan angle Step/interpolation angle

512 x 512 120° 10°/1°

• Numerical disc phantom for the analysis

• Experimental resultsPhantom Interpolation 10° Interpolation 10°

• Re-position process• Coordinates conversion relation

�𝒖𝒖 = �𝒙𝒙 𝐬𝐬𝐬𝐬𝐬𝐬𝜶𝜶 + �𝒚𝒚 𝐜𝐜𝐜𝐜𝐬𝐬𝜶𝜶 , �𝒗𝒗 = �𝒛𝒛• Position of a target voxel on the detector plane

𝒖𝒖𝟎𝟎 =𝒂𝒂(𝒙𝒙𝟎𝟎 𝐬𝐬𝐬𝐬𝐬𝐬𝜶𝜶 + 𝒚𝒚𝟎𝟎 𝐜𝐜𝐜𝐜𝐬𝐬𝜶𝜶)𝒓𝒓 − 𝒙𝒙𝟎𝟎 𝐜𝐜𝐜𝐜𝐬𝐬𝜶𝜶 + 𝒚𝒚𝟎𝟎 𝐬𝐬𝐬𝐬𝐬𝐬𝜶𝜶

𝒗𝒗𝟎𝟎 =𝒂𝒂𝒛𝒛𝟎𝟎

𝒓𝒓 − 𝒙𝒙𝟎𝟎 𝐜𝐜𝐜𝐜𝐬𝐬𝜶𝜶 + 𝒚𝒚𝟎𝟎 𝐬𝐬𝐬𝐬𝐬𝐬𝜶𝜶• Correlation of the coordinates at 𝛼𝛼° with 𝜃𝜃°

- 𝒙𝒙𝟎𝟎 can be assumed to zero at thin objects

𝒖𝒖′ = 𝒖𝒖𝟎𝟎𝒎𝒎𝜽𝜽 𝐜𝐜𝐜𝐜𝐬𝐬𝜽𝜽𝒎𝒎𝜶𝜶 𝐜𝐜𝐜𝐜𝐬𝐬𝜶𝜶

,𝒗𝒗′ = 𝒗𝒗𝟎𝟎𝒎𝒎𝜽𝜽

𝒎𝒎𝜶𝜶

• Re-positioning operator

𝑹𝑹𝜶𝜶𝜽𝜽 𝑷𝑷𝜶𝜶 𝒖𝒖,𝒗𝒗 = 𝑷𝑷𝜶𝜶(𝒖𝒖𝒎𝒎𝜽𝜽 𝐜𝐜𝐜𝐜𝐬𝐬𝜽𝜽𝒎𝒎𝜶𝜶 𝐜𝐜𝐜𝐜𝐬𝐬𝜶𝜶

,𝒗𝒗𝒎𝒎𝜽𝜽

𝒎𝒎𝜶𝜶)

• Interpolation process• Applying the weighting factor to neighboring images𝑷𝑷𝜽𝜽 𝒖𝒖,𝒗𝒗 = 𝒘𝒘𝜽𝜽𝑹𝑹𝜶𝜶𝜽𝜽 𝑷𝑷𝜶𝜶 𝒖𝒖,𝒗𝒗 + 𝟏𝟏 −𝒘𝒘𝜽𝜽 𝑹𝑹𝜶𝜶+∆𝜶𝜶𝜽𝜽 {𝑷𝑷𝜶𝜶+∆𝜶𝜶 𝒖𝒖,𝒗𝒗 }