Automatic Reconstruction of Textured 3D Models

Three dimensional modeling and visualization of environments is an increasingly important problem. This work addresses the problem of automatic 3D reconstruction and we present a system for unsupervised reconstruction of textured 3D models in the context of modeling indoor environments. We present solutions to all aspects of the modeling process and an integrated system for the automatic creation of large scale 3D models

Automatic Reconstruction of Textured 3D Models

Three dimensional modeling and visualization of environments is an increasingly important problem. This work addresses the problem of automatic 3D reconstruction and we present a system for unsupervised reconstruction of textured 3D models in the context of modeling indoor environments. We present solutions to all aspects of the modeling process and an integrated system for the automatic creation of large scale 3D models

Geometric Structures arising from Partial Differential Equations

We study several geometric problems arising from partial differential equations: (1) the geometry of Laplacian Eigenfunctions on smooth, compact manifolds without boundary (2) the energy landscape of the conservation laws of the defocusing generalized Korteweg de Vries equation (3) level sets of harmonic functions in the unit disc (4) periodic solutions of ODEs in Banach spaces and (5) packing problems related to nodal domain estimates for Laplacian eigenfunctions in the plane in the style of Pleijel