To the Graduate Council: I am submitting herewith a dissertation ...

Figures1.1. General flowchart of our 3D multimodal modeling system. ...................................62.1. Tensor voting for non-oriented points. ..................................................................203.1. The ellipsoid describing orientation uncertainty and the associated eigendecomposition...............................................................................................................243.3. The co-planarity constraint implies that the two rays m 1and m2pointing from twocameras optical centers toward the world point M lie on the same plane with the baselineTvectort = ( tx, ty, tz) . ....................................................................................................273.4. The search for a match for the point in the left (a) image is limited by the epipolarconstraints to a line search ............................................................................................303.5. The degradation of the structure reconstructed from the images of Fig. 3.4 (from. (a)to (d)) as we move away from the correct pose parameters. ........................................303.6. Applying tensor voting and removing non-salient feature-points (v-a to v-d) from thereconstructed point-sets (a to b) for different pose parameters.....................................333.8. Voting for feature saliency in 3D using plate tensors, the accumulated votes aredescribed by the ellipsoid bounding the two plates. .....................................................363.9. Given the local nature of Tensor Voting the two datasets will have little interaction atthe unregistered position (a)..........................................................................................383.10. Tensor voting in the case of smooth curves.........................................................404.1. Illustration of the discrete combinatorial criterion.................................................464.2. Mollification converts the discrete combinatorial criterion into a smooth sum ofGaussians (a).................................................................................................................474.3. Profiles of the Gaussian energy function for a displacement around the registeredposition of the datasets shown in (a).............................................................................494.4. The global optimization strategy that strikes a balance between the width of theregion of convergence and the accuracy of registration is based on adapting the parameterσ, starting form a large value and reducing σ until convergence..................................594.5. In the global strategy we should be careful to avoid being trapped in a localmaximum as seen in (a) ................................................................................................605.1. Fast Gauss Transform and the different clustering schemes, sources are representedwith crosses (+) and targets with circles (○).................................................................695.2. Result of applying the farthest point clustering algorithm to the 3D model (a). ...755.3. Plot showing the CPU time (Pentium IV, 2.3 GHz) required for the evaluation of theGaussian criterion for a given number of points in the datasets...................................78