1) The document describes algorithms for creating extended focused images from digital holograms of 3D objects. It involves using focus measures and depth from focus techniques on multiple hologram reconstructions to generate a depth map and then composite the reconstructions into a single in-focus image. 2) Two approaches for the extended focused image are presented - a pointwise approach that selects pixels from individual reconstructions, and a neighborhood approach that averages blocks of pixels. 3) Preliminary results demonstrate extended focused images generated with both approaches, though the neighborhood method produces smoother results by reducing errors.

1. Focused Image Creation Algorithms for Digital Holograms of Macroscopic Three-Dimensional Objects Conor Mc Elhinney, Bryan M. Hennelly, Thomas J. Naughton Tuesday 18th March DH and Three-Dimensional Imaging -- 18th March 2008

3. Focus

4. Focus Detection

5. Depth-From-Focus

6. Extended Focused Imaging

7. Pointwise Approach

8. Neighbourhood Approach

9. Results

10. ConclusionDH and Three-Dimensional Imaging -- 18th March 2008

12. Focus

13. Focus Detection

14. Depth-From-Focus

15. Extended Focused Imaging

16. Pointwise Approach

17. Neighbourhood Approach

18. Results

19. ConclusionDH and Three-Dimensional Imaging -- 18th March 2008

20. Why digital holography? 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. Reconstructions Why do we need image processing? 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. Image Processing Depth Map DH and Three-Dimensional Imaging -- 18th March 2008

21. Why not 2D Image Processsing? 2D Standard 2D image processing techniques can be applied to individual digital holographic reconstructions with varying success. 2D Image Processing 3D Digital Holographic Image Processing 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. Using this information we can develop techniques which are more accurate than standard 2D approaches. Reconstructions DH and Three-Dimensional Imaging -- 18th March 2008

22. Reconstructing with digital holography Digital Hologram Digital Reconstruction Discrete Fresnel Transform Distance d DH and Three-Dimensional Imaging -- 18th March 2008

23. Reconstructing with digital holography Digital Hologram Digital Reconstruction d1 Discrete Fresnel Transform d2 d3 d4 d5 d6 Set of distances {d1,d2,d3,d4,d5,d6} DH and Three-Dimensional Imaging -- 18th March 2008

24. Numerical focusing of digital holograms Holograms can be numerically reconstructed at an arbitrary depth away from the camera. DH and Three-Dimensional Imaging -- 18th March 2008

26. Focus

27. Focus Detection

28. Depth-From-Focus

29. Extended Focused Imaging

30. Pointwise Approach

31. Neighbourhood Approach

32. Results

33. ConclusionDH and Three-Dimensional Imaging -- 18th March 2008

36. One function which has been shown to be both a sound focus measure and successfully applicable to reconstructions from digital holograms is variance: DH and Three-Dimensional Imaging -- 18th March 2008

37. Focus Detection Image 2 Image 4 Image 6 Image 7 Image 10 variance Image Number DH and Three-Dimensional Imaging -- 18th March 2008

38. Focus Detection DH and Three-Dimensional Imaging -- 18th March 2008

40. Focus

41. Focus Detection

42. Depth-From-Focus

43. Extended Focused Imaging

44. Pointwise Approach

45. Neighbourhood Approach

46. Results

47. ConclusionDH and Three-Dimensional Imaging -- 18th March 2008

48. What is Depth-From-Focus? 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. Why is this applicable to digital holography? Digital Holograms can be numerically reconstructed at an arbitrary depth. These numerical reconstructions are each at a different focal plane, which make them a good input to a Depth-From-Focus algorithm. What do we get from Depth-From-Focus? We can then create depth maps of the scene, segment the scene and create extended focused images of the scene. DH and Three-Dimensional Imaging -- 18th March 2008

49. What is Depth-From-Focus? 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. Why is this applicable to digital holography? Digital Holograms can be numerically reconstructed at an arbitrary depth. These numerical reconstructions are each at a different focal plane, which make them a good input to a Depth-From-Focus algorithm. What do we get from Depth-From-Focus? We can then create depth maps of the scene, segment the scene and create extended focused images of the scene. DH and Three-Dimensional Imaging -- 18th March 2008

50. What is Depth-From-Focus? 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. Why is this applicable to digital holography? Digital Holograms can be numerically reconstructed at an arbitrary depth. These numerical reconstructions are each at a different focal plane, which make them a good input to a Depth-From-Focus algorithm. What do we get from Depth-From-Focus? We can then create depth maps of the scene, segment the scene and create extended focused images of the scene. DH and Three-Dimensional Imaging -- 18th March 2008

51. n n How to compute a depth map To compute a depth map we first take a reconstruction and a block size of [n x n]. We then calculate our focus measure on the first block in the top left corner of the reconstruction We then process every block in the reconstruction by raster scanning the reconstruction and processing every block with our focus measure. We store the output value from each block in its corresponding position in a focus map. DH and Three-Dimensional Imaging -- 18th March 2008

53. Block size used

54. Distance between successive reconstructionsDH and Three-Dimensional Imaging -- 18th March 2008

56. Larger block sizes: low error but fine object features lost.

57. Smaller block sizes: finer object features but high error in the estimate of the general shape.Object 7x7 43x43 81x81 121x121 151x151 DH and Three-Dimensional Imaging -- 18th March 2008

59. We intend to extend our algorithm to automatically determine what depth resolution to use in the experiment (the distance between successive reconstructions).DH and Three-Dimensional Imaging -- 18th March 2008

61. Focus

62. Focus Detection

63. Depth-From-Focus

64. Extended Focused Imaging

65. Pointwise Approach

66. Neighbourhood Approach

67. Results

68. ConclusionDH and Three-Dimensional Imaging -- 18th March 2008

69. What is an Extended Focused Image? 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. Why do we want to create an extended focused image? 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. = + Volume of Reconstructions Extended Focused Image Depth Map DH and Three-Dimensional Imaging -- 18th March 2008

71. Focus

72. Focus Detection

73. Depth-From-Focus

74. Extended Focused Imaging

75. Pointwise Approach

76. Neighbourhood Approach

77. Results

78. ConclusionDH and Three-Dimensional Imaging -- 18th March 2008

79. Pointwise Approach Animation Animation DH and Three-Dimensional Imaging -- 18th March 2008

81. Focus

82. Focus Detection

83. Depth-From-Focus

84. Extended Focused Imaging

85. Pointwise Approach

86. Neighbourhood Approach

87. Results

88. ConclusionDH and Three-Dimensional Imaging -- 18th March 2008

89. Neighbourhood Approach Our algorithm computes one depth value for every [n x n] pixel block in a reconstruction. We have developed a second Extended Focused Image technique which can reduce the error in the EFI. 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. DH and Three-Dimensional Imaging -- 18th March 2008

91. Focus

92. Focus Detection

93. Depth-From-Focus

94. Extended Focused Imaging

95. Pointwise Approach

96. Neighbourhood Approach

97. Results

98. ConclusionDH and Three-Dimensional Imaging -- 18th March 2008

99. Results Front Focal Plane Back Focal Plane EFI- Pointwise Approach EFI – Neighborhood Approach DH and Three-Dimensional Imaging -- 18th March 2008

100. Results Front Focal Plane Back Focal Plane EFI- Pointwise Approach EFI – Neighborhood Approach DH and Three-Dimensional Imaging -- 18th March 2008

102. Focus

103. Focus Detection

104. Depth-From-Focus

105. Extended Focused Imaging

106. Pointwise Approach

107. Neighbourhood Approach

108. Results

109. ConclusionDH and Three-Dimensional Imaging -- 18th March 2008

110. Conclusion We have demonstrated and discussed the process for creating a depth map from a set of reconstructions from a digital hologram. We have also demonstrated the first EFI's for digital holograms containing macroscopic objects. We have discussed the selection of block size and step size in our depth-from-focus algorithm. 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. DH and Three-Dimensional Imaging -- 18th March 2008

111. Questions Front Focal Plane Back Focal Plane EFI- Pointwise Approach EFI – Neighborhood Approach DH and Three-Dimensional Imaging -- 18th March 2008