UBC Theses and Dissertations
Viewpoint invariant surface reconstruction from gradient data King, Yossarian Y.
Surface reconstruction recovers complete and coherent surfaces from scattered, noisy data. Viewpoint invariant reconstruction allows seamless combination of multiple views, recognition of objects in arbitrary poses, and consistent quantitative measurements. Viewpoint invariant reconstruction from gradient data is studied in a variational framework. An invariant smoothing functional based on the bending energy of a thin plate is derived. The functional is nonconvex, and three convex approximations are presented. An invariant but nonconvex metric for measuring fit to gradient data is given, based on the angle between unit surface normals. A convex constraint metric is obtained from the second order Taylor series approximation. The chief goal of this thesis is to evaluate and compare the different functionals, with viewpoint invariance the prime evaluation criterion. The approximately invariant regularizing functionals are discretized on a regular grid using a finite difference method. Reconstruction from gradient data proceeds in three stages: interpolation of the initial data; smoothing of the gradient map; and recovery of height from gradient. Data were generated for multiple views of a synthetic surface. Each reconstruction method is applied to recover a surface for each view. The viewpoint invariance of the reconstruction is evaluated by measuring, qualitatively and quantitatively, how well the surfaces from different views match up. Experiments are performed with real data from photometric stereo in the context of building 3D object models by fitting together surfaces reconstructed from multiple views. Viewpoint invariance is important in order for the different surfaces to fit together. Multiple views of a simple ellipsoid of known shape allows accurate evaluation of the results, while data gathered from a doll's face provides more of a challenge to the reconstruction techniques.
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