1. Image Restoration Juan Navarro Sorroche Phys-6314 Physics Department The University of Texas at Dallas Fall 2010 School of Natural Sciences & Mathematics Department of Physics

2. School of Natural Sciences & Mathematics Department of Physics Image Restoration 1.Motivations for image restoration 2.Pin-hole camera model 3. Sources of image distortion 4.Distortion models 5.Correcting algorithms and implementation

3. School of Natural Sciences & Mathematics Department of Physics Image Distortion Motivations for image restoration 8’x4’ camera calibration board Introduction

4. School of Natural Sciences & Mathematics Department of Physics Image Distortion Close up view of 8’x4’ camera calibration board Introduction

5. School of Natural Sciences & Mathematics Department of Physics Any DAQ system where images are created requires restoration of images Oscilloscopes Microscopes X-rays machines Robotic vision CCD/CMOS sensors Medical imaging equipment Ionization chambers Mass spectrometers Any projective type of detector Introduction

6. Projective Transformation X Y Z C World coordinates to pixels transformation Pin-Hole Camera ModelSchool of Natural Sciences & Mathematics Department of Physics CCD/CMOS camera sensor pixel’s coordinates n, n0, m, m0 = # of pixels px, py = pixel size

7. Projective Transformation X Y Z C World coordinates to pixels transformation: general case School of Natural Sciences & Mathematics Department of Physics General expression for the camera transform xw,yw,zw homogenous 4-vector K= Camera calibration matrix R=Rotation matrix C=camera center coordinates P=Projective Transformation matrix For the case of camera rotation and translation Pin-Hole Camera Model

8. School of Natural Sciences & Mathematics Department of Physics Image Distortion Sources 1.Intrinsic Radial distortion Tangential distortion Skew distortion 2.Extrinsic Projection distortion Perspective distortion Skew distortion

9. School of Natural Sciences & Mathematics Department of Physics Image Distortion Sources Perspective Distortion

10. Distortion Models School of Natural Sciences & Mathematics Department of Physics Distortion Correction Models Model Radial functions Most used Best approximation Easiest. Good approximation Radial distortion Perspective distortion Commercial packages  Adobe  RoboRealm  PhotoModeller  FireWorks Open Source  GIMP Professional metrology  Halcon

11. Calibration Board Pixel Plot School of Natural Sciences & Mathematics Department of Physics Correcting Algorithms & Implementation

12. Radial Points - Fitting Function Plot School of Natural Sciences & Mathematics Department of Physics Correcting Algorithms & Implementation

13. Pin-hole Vs. Radial Distortion Corrected Pixel Plot School of Natural Sciences & Mathematics Department of Physics Correcting Algorithms & Implementation

14. Pin-hole Vs. Rad/Persp. Corrected Pixel Plot School of Natural Sciences & Mathematics Department of Physics Correcting Algorithms & Implementation

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16. School of Natural Sciences & Mathematics Department of Physics Correcting Algorithms & Implementation

17. School of Natural Sciences & Mathematics Department of Physics Correcting Algorithms & Implementation

18. School of Natural Sciences & Mathematics Department of Physics Correcting Algorithms & Implementation

19. Conclusions School of Natural Sciences & Mathematics Department of Physics Images must be corrected from optical system distortions prior of making any measurement Radial distortion affects object’s position determination & other derived variables Perspective distortion can leads to large errors in position determination depending on angle of tilt Distortions must be removed before ideal (pin-hole) camera transformations are made Conclusions