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Image Restoration

School of Natural Sciences & Mathematics Department of Physics. 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. Image Restoration.

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Image Restoration

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

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

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

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

  5. School of Natural Sciences & Mathematics Department of Physics Introduction • 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

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

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

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

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

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

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

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

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

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

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

  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. School of Natural Sciences & Mathematics Department of Physics Conclusions Conclusions 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

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