- The downhill-simplex method.
- Contour plot of the Rosenbrock banana function.
- Illustration of the downhill simplex method.
- Illustration of the gradient descent method.
- Illustration of Newton's method.
- Illustration of the Gauss-Newton method.
- Graphical interpretation of the normal equations.
- Illustration of the Levenberg-Marquardt method.
- Illustration of the golden section search algorithm.
- An historical spline.
- Examples of spline functions.
- Influence of coincident knots on a B-spline basis function.
- Some interesting properties of the B-splines.
- A possible graphical representation of B-spline weights.
- B-spline with coincident boundary knots.
- Basis functions of uniform cubic B-splines.
- Anatomy of a B-spline basis function of UCBS.
- A vector-valued B-splines.
- Construction of a bivariate B-spline basis function.
- Bivariate B-spline built using the tensor product.
- A 3-vector-valued tensor-product B-spline.
- Basis functions of tensor product B-spline.
- Influence of the weights of a NURBS.
- NURBS and perspective projection.
- Rational basis functions and partition of unity.
- Continuity conditions with a NURBS of degree 3.
- Exact representation of a circle with a NURBS of degree 2.
- Some classical radial basis functions.
- Probability density function of the normal distribution.
- Having values that deviate significantly from the mean of a normal distribution is extremely unlikely.
- Some common M-estimators.
- Noisy data to fit with a polynomial.
- Fitted polynomials for different hyperparameters.
- Illustration of the main concepts related to data fitting and hyperparameters.
- An example of range surface.
- An example of range data points.
- Illustration of Shape-from-Stereo.
- Illustration of Shape-from-Shading.
- Illustration of Shape-from-Texture.
- Basic principles of 3D reconstruction using structured light.
- Basic principle of LADAR.
- Basic principle of ToF cameras.
- Example of range data representing
*Puy Pariou*. - Ordinary cross-validation score function.
- Final results for our example of range surface fitting.
- Sparsity structure of the bending matrix of bi-variate B-splines.
- An example of L-curve that has the typical shape of the letter L.
- An example of pathological case for the L-curve criterion.
- Example of the L-Tangent Norm criterion.
- An example of the LTN criterion presenting two meaningful minima.
- Examples of randomly generated surfaces.
- Real range data used in the experiments.
- Timings for computing the criteria.
- Computation time needed to optimize the L-tangent norm and the cross-validation.
- Computation time needed to reconstruct the whole surfaces.
- Comparison of the regularization parameters obtained with the LTN and with the ones obtained with cross-validation.
- Integral relative errors for 200 randomly generated surfaces.
- Relative error maps for the surfaces reconstructed using the LTN criterion.
- Illustration of our algorithm to fit a B-spline to range data with discontinuities and heteroskedastic noise.
- Illustration of the performance gain obtained when using a grid approach.
- Example of surface fitted on range data with heteroskedastic noise.
- Discrepancy between ground truth range images and the ones predicted with the fitted surface using our algorithm.
- General principle of image registration.
- Illustration of the inverse and forward warping.
- Principle of the SSD term for direct image registration.
- Introductory example of the proposed approach to direct image registration.
- Profile of the cost functions of the adaptive ROI approach.
- Profile of the data term for rectangular ROI with margins of various sizes.
- Pixels out of the field of view can be considered as usual outliers.
- Synthetic data generation.
- Failure rates.
- Influence of several factors on the the number of iterations.
- Influence of several factors on the geometric error.
- Influence of several factors on the photometric error.
- Examples of registration results for different algorithms.
- Panorama calculated wit RectN, RectL, Adap, and MaxC.
- Example of deformable mosaic.
- Pattern tracking in a video sequence.
- Illustration of how some typical hyperparameters influence image registration.
- Comparison of the Cauchy distribution and of the actual errors in keypoint locations.
- Illustration of the generation of synthetic data.
- Relative geometric errors for several criteria used to determine hyperparameters.
- Scale parameter of the Cauchy's M-estimator retrieved using several criteria.
- Evolution of the relative geometric error in function of the noise.
- Images registered with various approaches for determining the hyperparameters.
- Images registered with various approaches for determining the hyperparameters.
- BS-Warp and affine imaging conditions.
- Bad behavior of the BS-Warp in the presence of perspective effects.
- NURBS-Warps and perspective imaging conditions.
- Simulated threedimensional surfaces.
- Influence of the amount of noise.
- Influence of the amount of bending.
- Influence of the amount of perspective.
- Comparison of the BS-warps and the NURBS-warps.
- Warps estimated for a rigid surface.
- Warps estimated for a deformable scene.
- Inextensible object deformation.
- Example of randomly generated piece of paper.
- Comparison of the reconstruction errors for different algorithms.
- Plot of the length of deformed paths against the length they should have.
- Monocular reconstruction algorithms in the presence of a self-occlusions.
- Results with several monocular reconstruction algorithms.
- Illustration of the Feature-Driven parameterization
- The Feature-Driven warp threading process.
- Examples for the warp threading process.
- The Feature-Driven warp reversion process.
- Illustration of the warp reversion process on three examples.
- The three steps of the Compositional Feature-Driven registration.
- Generating training data with a Feature-Driven warp.
- Illustration of the FFD basis functions.
- Standard and extended basis functions.
- Examples of extrapolating FFD in the monodimensional case.
- Examples of extrapolating FFD warp.
- Comparison of the fitting error of the TPS and FFD warps.
- Error between the TPS and FFD warps (1).
- Error between the TPS and FFD warps (2).
- Comparison of the TPS and the FFD warps for the same driving features.
- Example of simulated data.
- Comparison of the four algorithms in terms of convergence frequency.
- Comparison of the four algorithms in terms of accuracy.
- Comparison of the four algorithms in terms of convergence rate.
- Registration results for FC-LE on the first T-shirt sequence.
- Illustration of our algorithms.
- Registration results for FC-LE on the rug sequence.
- Registration results for FC-LE on the second T-shirt sequence.
- Distribution of the intensity error magnitude.
- Comparison of the five piecewise linear relationships in terms of convergence frequency.
- 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

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