1. 3D Reconstruction of
Solder Balls
Zhejian Peng
Department of Computer Science and Information
Engineering,
National Taiwan University,
Taipei, Taiwan

2. Introduction
• Computer Tomography (CT) is a way to
analyze shapes and the internals of objects
non-invasively.
• It aims to search for defects in objects
during the manufacturing process without
needing to damage these objects.

3. Introduction
• One obvious example:

4. Introduction
• X-ray images of Printed Circuit Boards (PCB) from
Test Research, Inc. (TRI德律科技股份有限公司),
a company specializing in testing and inspecting
PCBs.

5. Introduction
• Our application
here:
• The white spots
shows the defects
(voids) of this PCB.
• Cavity exists
• Shorten lifetime
• Short Circuit

6. Procedure
• 360 degrees, We shoot 128 images.
• Every 2.81 degrees.
• SART: Simultaneous Algebraic Reconstruction
Technique

7. ART
• ART: Algebraic Reconstruction Technique
• Widely used to reconstruct the cross-section of
an object.
179o
0o

8. 1100Iterations

9. 2200 Iterations

10. 5500 Iterations

11. Final Result

12. Comparison

13. SART
• SART: Simultaneous Algebraic Reconstruction
Technique
• Considers all projection rays in one iteration,
instead of one projection ray per iteration in ART.
• Resist noise and can generate better
reconstructed image.

14. Procedure
• Determine the center position of solder ball
using Bounding Box technique.

15. • We need to
calculate the
fitness.
• Fitness indicates
how well our
model matches
the actual PCB.
Procedure
Fitness =
shadow image
shadow image



16. 3D Reconstruction Using Unity
• Unity3D is a famous software mostly used to
generate visualized 3D model. It’s widely used in
video game industry.
• We use it to build a 3D model of PCB.

17. Google Cardboard VR
• We use Google Cardboard VR to generate a user-
friendly application and visualization tool on
mobile phone
VR: Virtual Reality

18. Result
• A well functioned 3D model as iOS application in
VR.
• Function of zoom-in and zoom-out.
• Fitness value on top of each solder ball.
• Write a TextLookAt.cs C# script so that the
fitness value will always face the observer.

19. Result

20. • Managing the normal vector of the text plane,
we achieve this goal.
void Update () {
transform.LookAt (transform.position
- Camera.main.transform.position);
Result

21. Result: Fitness

22. Result: View from All Angles

23. Problems and Solutions
• When you zoom-in all the way to the limit, the
application will be stuck.
• Solve this problem by rewriting the whole
problem according to latest version of Unity3D,
and Google Cardboad VR library, and Xcode.
• Improve our prototype to an applicable
industrial application.

24. Reference
• [1] Unity Technologies, “Unity,” http://unity3d.com/, 2016.
•
• [2] MathWorks, “Matlab,” http://www.mathworks.com, 2016.
•
• [3] Google, “Google Cardboard,”
• https://vr.google.com/cardboard/index.html, 2016.
•
• [4] H. K. Lin, “Algebraic Reconstruction Technique,” Technical Report, Department of
Computer Science and Information Engineering, National Taiwan University, 2016.
•
• [5] H. K. Lin, “Algebraic Reconstruction Technique,” Technical Report, Department of
Computer Science and Information Engineering, National Taiwan University, 2016.
•
• [6] Ligong Han, “Tools for 2-D Tomographic Reconstruction
• ,” http://www.mathworks.com/matlabcentral/fileexchange/43008-tools-for-2-d-
tomographic-reconstruction?s_tid=srchtitle, 2015.
•
• [7] Kyungsang Kim, “3D Cone beam CT (CBCT) projection backprojection FDK, iterative
reconstruction Matlab examples,”
http://www.mathworks.com/matlabcentral/fileexchange/35548-3d-cone-beam-ct--cbct--
projection-backprojection-fdk--iterative-reconstruction-matlab-examples?s_tid=srchtitle,
2016.

25. Reference
• REFERENCES
•
• [1] S. Gondrom, S. Schröpfer, FhG ITFP, Saarbrücken, “Digital Computed Laminography and Tomosynthesis - Functional Principles and
Industrial Applications,” http://www.ndt.net/article/v04n07/bb67_11/bb67_11.htm
•
• [2] Frank Tabak, “Robust Algorithms for Discrete Tomography,” Technical Report, Delft Institute of Applied Mathematics, Delft University
of Technology, 2012.
•
• [3] Wolfram MathWorld, “Gauss-Seidel Method," http://mathworld.wolfram.com/Gauss-SeidelMethod.html, 2016.
•
• [4] Wolfram MathWorld, “Jacobi Method," http://mathworld.wolfram.com/JacobiMethod.html, 2016.
•
• [5] A. C. Kak and Malcolm Slaney, “Principles of Computerized Tomographic Imaging,” 1988.
•
• [6] Unity Technologies, “Unity,” http://unity3d.com/, 2016.
•
• [7] Adobe, “Photoshop CS6,” http://ww.adobe.com/, 2016.
•
• [8] OpenCV, “OpenCV,” http://opencv.org/, 2016.
•
• [9] Google, “Google Cardboard,”
• https://vr.google.com/cardboard/index.html, 2016.
•
• [10] Charles L. Hamberg and Ronald Vavrinek, “Shoelace Algorithm,” Illinois Mathematics and Science Academy, 2016.
•
• [11] Y. B. Zhang, “3D Reconstruction of Solder Balls,” submitted to IPPR Conference on Computer Vision, Graphics, and Image Processing,
Keelung, Taiwan, 2016.
•
• [12] OpenCV, “Canny Edge Detection,” http://docs.opencv.org/master/da/d22/tutorial_py_canny.html, 2016
•
• [13] Point Cloud Library, “Point Cloud Library,” http://pointclouds.org/, 2016

26. Thank You and Q & A