List of Figures

  1. The downhill-simplex method.
  2. Contour plot of the Rosenbrock banana function.
  3. Illustration of the downhill simplex method.
  4. Illustration of the gradient descent method.
  5. Illustration of Newton's method.
  6. Illustration of the Gauss-Newton method.
  7. Graphical interpretation of the normal equations.
  8. Illustration of the Levenberg-Marquardt method.
  9. Illustration of the golden section search algorithm.
  10. An historical spline.
  11. Examples of spline functions.
  12. Influence of coincident knots on a B-spline basis function.
  13. Some interesting properties of the B-splines.
  14. A possible graphical representation of B-spline weights.
  15. B-spline with coincident boundary knots.
  16. Basis functions of uniform cubic B-splines.
  17. Anatomy of a B-spline basis function of UCBS.
  18. A vector-valued B-splines.
  19. Construction of a bivariate B-spline basis function.
  20. Bivariate B-spline built using the tensor product.
  21. A 3-vector-valued tensor-product B-spline.
  22. Basis functions of tensor product B-spline.
  23. Influence of the weights of a NURBS.
  24. NURBS and perspective projection.
  25. Rational basis functions and partition of unity.
  26. Continuity conditions with a NURBS of degree 3.
  27. Exact representation of a circle with a NURBS of degree 2.
  28. Some classical radial basis functions.
  29. Probability density function of the normal distribution.
  30. Having values that deviate significantly from the mean of a normal distribution is extremely unlikely.
  31. Some common M-estimators.
  32. Noisy data to fit with a polynomial.
  33. Fitted polynomials for different hyperparameters.
  34. Illustration of the main concepts related to data fitting and hyperparameters.
  35. An example of range surface.
  36. An example of range data points.
  37. Illustration of Shape-from-Stereo.
  38. Illustration of Shape-from-Shading.
  39. Illustration of Shape-from-Texture.
  40. Basic principles of 3D reconstruction using structured light.
  41. Basic principle of LADAR.
  42. Basic principle of ToF cameras.
  43. Example of range data representing Puy Pariou.
  44. Ordinary cross-validation score function.
  45. Final results for our example of range surface fitting.
  46. Sparsity structure of the bending matrix of bi-variate B-splines.
  47. An example of L-curve that has the typical shape of the letter L.
  48. An example of pathological case for the L-curve criterion.
  49. Example of the L-Tangent Norm criterion.
  50. An example of the LTN criterion presenting two meaningful minima.
  51. Examples of randomly generated surfaces.
  52. Real range data used in the experiments.
  53. Timings for computing the criteria.
  54. Computation time needed to optimize the L-tangent norm and the cross-validation.
  55. Computation time needed to reconstruct the whole surfaces.
  56. Comparison of the regularization parameters obtained with the LTN and with the ones obtained with cross-validation.
  57. Integral relative errors for 200 randomly generated surfaces.
  58. Relative error maps for the surfaces reconstructed using the LTN criterion.
  59. Illustration of our algorithm to fit a B-spline to range data with discontinuities and heteroskedastic noise.
  60. Illustration of the performance gain obtained when using a grid approach.
  61. Example of surface fitted on range data with heteroskedastic noise.
  62. Discrepancy between ground truth range images and the ones predicted with the fitted surface using our algorithm.
  63. General principle of image registration.
  64. Illustration of the inverse and forward warping.
  65. Principle of the SSD term for direct image registration.
  66. Introductory example of the proposed approach to direct image registration.
  67. Profile of the cost functions of the adaptive ROI approach.
  68. Profile of the data term for rectangular ROI with margins of various sizes.
  69. Pixels out of the field of view can be considered as usual outliers.
  70. Synthetic data generation.
  71. Failure rates.
  72. Influence of several factors on the the number of iterations.
  73. Influence of several factors on the geometric error.
  74. Influence of several factors on the photometric error.
  75. Examples of registration results for different algorithms.
  76. Panorama calculated wit RectN, RectL, Adap, and MaxC.
  77. Example of deformable mosaic.
  78. Pattern tracking in a video sequence.
  79. Illustration of how some typical hyperparameters influence image registration.
  80. Comparison of the Cauchy distribution and of the actual errors in keypoint locations.
  81. Illustration of the generation of synthetic data.
  82. Relative geometric errors for several criteria used to determine hyperparameters.
  83. Scale parameter of the Cauchy's M-estimator retrieved using several criteria.
  84. Evolution of the relative geometric error in function of the noise.
  85. Images registered with various approaches for determining the hyperparameters.
  86. Images registered with various approaches for determining the hyperparameters.
  87. BS-Warp and affine imaging conditions.
  88. Bad behavior of the BS-Warp in the presence of perspective effects.
  89. NURBS-Warps and perspective imaging conditions.
  90. Simulated threedimensional surfaces.
  91. Influence of the amount of noise.
  92. Influence of the amount of bending.
  93. Influence of the amount of perspective.
  94. Comparison of the BS-warps and the NURBS-warps.
  95. Warps estimated for a rigid surface.
  96. Warps estimated for a deformable scene.
  97. Inextensible object deformation.
  98. Example of randomly generated piece of paper.
  99. Comparison of the reconstruction errors for different algorithms.
  100. Plot of the length of deformed paths against the length they should have.
  101. Monocular reconstruction algorithms in the presence of a self-occlusions.
  102. Results with several monocular reconstruction algorithms.
  103. Illustration of the Feature-Driven parameterization
  104. The Feature-Driven warp threading process.
  105. Examples for the warp threading process.
  106. The Feature-Driven warp reversion process.
  107. Illustration of the warp reversion process on three examples.
  108. The three steps of the Compositional Feature-Driven registration.
  109. Generating training data with a Feature-Driven warp.
  110. Illustration of the FFD basis functions.
  111. Standard and extended basis functions.
  112. Examples of extrapolating FFD in the monodimensional case.
  113. Examples of extrapolating FFD warp.
  114. Comparison of the fitting error of the TPS and FFD warps.
  115. Error between the TPS and FFD warps (1).
  116. Error between the TPS and FFD warps (2).
  117. Comparison of the TPS and the FFD warps for the same driving features.
  118. Example of simulated data.
  119. Comparison of the four algorithms in terms of convergence frequency.
  120. Comparison of the four algorithms in terms of accuracy.
  121. Comparison of the four algorithms in terms of convergence rate.
  122. Registration results for FC-LE on the first T-shirt sequence.
  123. Illustration of our algorithms.
  124. Registration results for FC-LE on the rug sequence.
  125. Registration results for FC-LE on the second T-shirt sequence.
  126. Distribution of the intensity error magnitude.
  127. Comparison of the five piecewise linear relationships in terms of convergence frequency.
  128. Comparison of the five piecewise linear relationships in terms of convergence rate.

Contributions to Parametric Image Registration and 3D Surface Reconstruction (Ph.D. dissertation, November 2010) - Florent Brunet
Webpage generated on July 2011
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