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

5.2.3 Limitations of the FGT method ............................................................705.3 Improved Fast Gauss Transform...................................................................715.3.1 The multivariate Taylor expansion .......................................................715.3.2 Space subdivision..................................................................................745.3.2 IFGT and its workloads ........................................................................766 RESULTS 796.1 Three Dimensional Analysis, Objectives, and Methodology .......................796.2 3D Synthetic Experiments ............................................................................826.2.1 Noise effects..........................................................................................826.2.2 Local descriptors and fusion .................................................................856.2.3 Local neighborhood size and features...................................................876.2.4 Amount of overlap ................................................................................876.2.5 Surface complexity ...............................................................................896.3 Experiments with 3D Real Datasets .............................................................916.3.1 Plots around the ground truth..............................................................1016.3.2 Effects of varying sigma .....................................................................1036.3.3 Basins of convergence and comparison with ICP...............................1086.3.4 Mean Squared Error, Bias and Variance, and Comparison with ICP.1196.4.4 Sampling effects..................................................................................1256.4 Multimodal Image Registration and Integration for Modeling and Recognition1296.4.1 2D Matching under non-rigid transformations ...................................1296.4.2 IR-Color alignment .............................................................................1306.4.3 Integrating range and color imagery...................................................1336.4.4 Multimodal 3D face reconstruction ....................................................1367 CONCLUSIONS AND FUTURE WORK 1387.1 Dissertation Key Points...............................................................................1387.2 New Questions, Other Applications, and Future Research.........................141BIBLIOGRAPHY 143VITA...........................................................................................................................157