Focused Image Creation Algorithms for Digital Holograms of Macroscopic Three-Dimensional Objects<br />Conor Mc Elhinney, B...
Outline<br /><ul><li>Introduction
Focus
Focus Detection
Depth-From-Focus
Extended Focused Imaging
Pointwise Approach
Neighbourhood Approach
Results
Conclusion</li></ul>DH and Three-Dimensional Imaging  -- 18th March 2008<br />
Outline<br /><ul><li>Introduction
Focus
Focus Detection
Depth-From-Focus
Extended Focused Imaging
Pointwise Approach
Neighbourhood Approach
Results
Conclusion</li></ul>DH and Three-Dimensional Imaging  -- 18th March 2008<br />
Why digital holography?<br />Using digital holography we can record a scene in a complex valued data structure which retai...
Why not 2D Image Processsing?<br />2D<br />	Standard 2D image processing techniques can be applied to individual digital h...
Reconstructing with digital holography<br />Digital Hologram<br />Digital Reconstruction<br />Discrete <br />Fresnel<br />...
Reconstructing with digital holography<br />Digital Hologram<br />Digital Reconstruction<br />d1<br />Discrete <br />Fresn...
Numerical focusing of digital holograms<br />Holograms can be numerically reconstructed at an arbitrary depth away from th...
Outline<br /><ul><li>Introduction
Focus
Focus Detection
Depth-From-Focus
Extended Focused Imaging
Pointwise Approach
Neighbourhood Approach
Results
Conclusion</li></ul>DH and Three-Dimensional Imaging  -- 18th March 2008<br />
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Focused Image Creation Algorithms for digital holography

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Focused Image Creation Algorithms for digital holography

  1. 1. Focused Image Creation Algorithms for Digital Holograms of Macroscopic Three-Dimensional Objects<br />Conor Mc Elhinney, Bryan M. Hennelly, Thomas J. Naughton<br />Tuesday 18th March<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  2. 2. Outline<br /><ul><li>Introduction
  3. 3. Focus
  4. 4. Focus Detection
  5. 5. Depth-From-Focus
  6. 6. Extended Focused Imaging
  7. 7. Pointwise Approach
  8. 8. Neighbourhood Approach
  9. 9. Results
  10. 10. Conclusion</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  11. 11. Outline<br /><ul><li>Introduction
  12. 12. Focus
  13. 13. Focus Detection
  14. 14. Depth-From-Focus
  15. 15. Extended Focused Imaging
  16. 16. Pointwise Approach
  17. 17. Neighbourhood Approach
  18. 18. Results
  19. 19. Conclusion</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  20. 20. Why digital holography?<br />Using digital holography we can record a scene in a complex valued data structure which retains some of the scene's 3D information. A standard image obtained with a camera records a 2D focused image of the scene from one perspective.<br />Reconstructions<br />Why do we need image processing?<br /> However reconstructing a digital hologram returns a 2D image of the scene at a specific depth (300mm from the camera) from an individual perspective (along the optical axis). Algorithms and processing techniques need to be developed to extract the 3D information from digital holograms by processing multiple (volumes of) reconstructions.<br />Image Processing<br />Depth Map<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  21. 21. Why not 2D Image Processsing?<br />2D<br /> Standard 2D image processing techniques can be applied to individual digital holographic reconstructions with varying success.<br />2D<br />Image<br />Processing<br />3D<br />Digital Holographic<br />Image<br />Processing<br />However, we are interested in developing the field of digital holographic image processing (DHIP) where we use volumes of reconstructions to extract 3D information from digital holograms.<br />Using this information we can develop techniques which are more accurate than standard 2D approaches.<br />Reconstructions<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  22. 22. Reconstructing with digital holography<br />Digital Hologram<br />Digital Reconstruction<br />Discrete <br />Fresnel<br />Transform<br />Distance d<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  23. 23. Reconstructing with digital holography<br />Digital Hologram<br />Digital Reconstruction<br />d1<br />Discrete <br />Fresnel<br />Transform<br />d2<br />d3<br />d4<br />d5<br />d6<br />Set of distances {d1,d2,d3,d4,d5,d6}<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  24. 24. Numerical focusing of digital holograms<br />Holograms can be numerically reconstructed at an arbitrary depth away from the camera.<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  25. 25. Outline<br /><ul><li>Introduction
  26. 26. Focus
  27. 27. Focus Detection
  28. 28. Depth-From-Focus
  29. 29. Extended Focused Imaging
  30. 30. Pointwise Approach
  31. 31. Neighbourhood Approach
  32. 32. Results
  33. 33. Conclusion</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  34. 34. Focus Measures<br /><ul><li>Focus measures are functions which attempt to determine the relative level of focus of sets of images, or regions within sets of images. The accepted image property maximized by these functions is the high spatial frequency energy of the image.</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  35. 35. High Spatial Frequency<br /><ul><li>High spatial frequency in images is equivalent to edges, so the more defined an edge is in an image the higher the spatial frequency.
  36. 36. One function which has been shown to be both a sound focus measure and successfully applicable to reconstructions from digital holograms is variance: </li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  37. 37. Focus Detection<br />Image 2<br />Image 4<br />Image 6<br />Image 7<br />Image 10<br />variance<br />Image Number<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  38. 38. Focus Detection<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  39. 39. Outline<br /><ul><li>Introduction
  40. 40. Focus
  41. 41. Focus Detection
  42. 42. Depth-From-Focus
  43. 43. Extended Focused Imaging
  44. 44. Pointwise Approach
  45. 45. Neighbourhood Approach
  46. 46. Results
  47. 47. Conclusion</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  48. 48. What is Depth-From-Focus?<br /> Depth-From-Focus is an image processing technique which is used to determine the depth of a scene or a region within a scene through processing images taken at different focal depths.<br />Why is this applicable to digital holography?<br />Digital Holograms can be numerically reconstructed at an arbitrary depth. <br />These numerical reconstructions are each at a different focal plane, which make them a good input to a Depth-From-Focus algorithm.<br />What do we get from Depth-From-Focus?<br />We can then create depth maps of the scene, segment the scene and create extended focused images of the scene.<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  49. 49. What is Depth-From-Focus?<br /> Depth-From-Focus is an image processing technique which is used to determine the depth of a scene or a region within a scene through processing images taken at different focal depths.<br />Why is this applicable to digital holography?<br />Digital Holograms can be numerically reconstructed at an arbitrary depth. <br />These numerical reconstructions are each at a different focal plane, which make them a good input to a Depth-From-Focus algorithm.<br />What do we get from Depth-From-Focus?<br />We can then create depth maps of the scene, segment the scene and create extended focused images of the scene.<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  50. 50. What is Depth-From-Focus?<br /> Depth-From-Focus is an image processing technique which is used to determine the depth of a scene or a region within a scene through processing images taken at different focal depths.<br />Why is this applicable to digital holography?<br />Digital Holograms can be numerically reconstructed at an arbitrary depth. <br />These numerical reconstructions are each at a different focal plane, which make them a good input to a Depth-From-Focus algorithm.<br />What do we get from Depth-From-Focus?<br />We can then create depth maps of the scene, segment the scene and create extended focused images of the scene.<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  51. 51. n<br />n<br />How to compute a depth map<br />To compute a depth map we first take a reconstruction and a block size of [n x n]. <br />We then calculate our focus measure on the first block in the top left corner of the reconstruction <br />We then process every block in the reconstruction by raster scanning the reconstruction and processing every block with our focus measure. <br />We store the output value from each block in its corresponding position in a focus map.<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  52. 52. How to compute a depth map<br />Step 1:<br />Step 2: <br />Step 3: <br />zmin<br />345 mm<br />Find maximum <br />variance and <br />corresponding <br />depth<br />355 mm<br />365 mm<br />zmax<br />375 mm<br />Vz(k,l)‏<br />DMap(k,l)‏<br />Iz(k,l)‏<br /><ul><li>Limiting factors:
  53. 53. Block size used
  54. 54. Distance between successive reconstructions</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  55. 55. Block Size<br /><ul><li> To determine the depth of a block in an image using a focus measure there needs to be enough object information in the block.
  56. 56. Larger block sizes: low error but fine object features lost.
  57. 57. Smaller block sizes: finer object features but high error in the estimate of the general shape.</li></ul>Object<br />7x7<br />43x43<br />81x81<br />121x121<br />151x151<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  58. 58. Distance between successive reconstructions<br /><ul><li> It is possible to calculate the depth-of-focus of a reconstruction (or reconstruction set) when the distance to the reconstruction plane, the wavelength of the light, the number of pixels in the camera and the camera pixel size is known.
  59. 59. We intend to extend our algorithm to automatically determine what depth resolution to use in the experiment (the distance between successive reconstructions).</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  60. 60. Outline<br /><ul><li>Introduction
  61. 61. Focus
  62. 62. Focus Detection
  63. 63. Depth-From-Focus
  64. 64. Extended Focused Imaging
  65. 65. Pointwise Approach
  66. 66. Neighbourhood Approach
  67. 67. Results
  68. 68. Conclusion</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  69. 69. What is an Extended Focused Image?<br />A disadvantage of holographic reconstructions is the limited depth of field. For a reconstruction at depth d only object points that are located at distance d from the camera are in focus.<br />Why do we want to create an extended focused image?<br />This means that reconstructions can contain large blurry regions. Using our depth maps and the volume of reconstructions used to create them we can create an extended focused image.<br />=<br />+<br />Volume of Reconstructions<br />Extended Focused Image<br />Depth Map<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  70. 70. Outline <br /><ul><li>Introduction
  71. 71. Focus
  72. 72. Focus Detection
  73. 73. Depth-From-Focus
  74. 74. Extended Focused Imaging
  75. 75. Pointwise Approach
  76. 76. Neighbourhood Approach
  77. 77. Results
  78. 78. Conclusion</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  79. 79. Pointwise Approach<br />Animation<br />Animation<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  80. 80. Outline<br /><ul><li>Introduction
  81. 81. Focus
  82. 82. Focus Detection
  83. 83. Depth-From-Focus
  84. 84. Extended Focused Imaging
  85. 85. Pointwise Approach
  86. 86. Neighbourhood Approach
  87. 87. Results
  88. 88. Conclusion</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  89. 89. Neighbourhood Approach<br />Our algorithm computes one depth value for every [n x n] pixel block in a reconstruction.<br />We have developed a second Extended Focused Image technique which can reduce the error in the EFI.<br />In this technique instead of taking one pixel out of our reconstruction at the estimated depth, we take the [n x n] pixel block that was used to calculate the depth value. In this way we average pixel intensities based on the depth value with the aim of smoothing error regions.<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  90. 90. Outline<br /><ul><li>Introduction
  91. 91. Focus
  92. 92. Focus Detection
  93. 93. Depth-From-Focus
  94. 94. Extended Focused Imaging
  95. 95. Pointwise Approach
  96. 96. Neighbourhood Approach
  97. 97. Results
  98. 98. Conclusion</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  99. 99. Results<br />Front Focal Plane<br />Back Focal Plane<br />EFI- Pointwise Approach<br />EFI – Neighborhood Approach<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  100. 100. Results<br />Front Focal Plane<br />Back Focal Plane<br />EFI- Pointwise Approach<br />EFI – Neighborhood Approach<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  101. 101. Outline<br /><ul><li>Introduction
  102. 102. Focus
  103. 103. Focus Detection
  104. 104. Depth-From-Focus
  105. 105. Extended Focused Imaging
  106. 106. Pointwise Approach
  107. 107. Neighbourhood Approach
  108. 108. Results
  109. 109. Conclusion</li></ul>DH and Three-Dimensional Imaging -- 18th March 2008<br />
  110. 110. Conclusion<br />We have demonstrated and discussed the process for creating a depth map from a set of reconstructions from a digital hologram. <br />We have also demonstrated the first EFI's for digital holograms containing macroscopic objects.<br />We have discussed the selection of block size and step size in our depth-from-focus algorithm.<br />Our implementation is currently limited by the lengthy computation time our algorithm requires on serial machines, we are in the process of addressing this and expect to have reasonable computation times on a single machine.<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />
  111. 111. Questions<br />Front Focal Plane<br />Back Focal Plane<br />EFI- Pointwise Approach<br />EFI – Neighborhood Approach<br />DH and Three-Dimensional Imaging -- 18th March 2008<br />

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