Vector space methods for surface reconstruction from one or more images acquired from the same view with application to scanning electron microscopy images.

摘要

This dissertation develops novel methods to reconstruct a three-dimensional surface together with a characterization of the surface composition given one or more images obtained from the same viewing direction. First, a vector space method to reconstruct a surface given a gradient field is developed using the linear relationship between a surface and its gradient field in discrete surface domains. The developed gradient field representation is generalized to alleviate the common assumption of uniform integrability in gradient fields to partial integrability, allowing adequate reconstruction of surfaces with non-integrable gradient fields. In addition, the developed technique is further explored for gradient field noise reduction, by embedding multi-scale properties providing sparse gradient field representations. Next, the ambiguity in possible surface gradients obtained by a two-image photometric stereo analysis is resolved using a cyclic projections algorithm based on the set of possible gradient fields and the previously developed gradient field representation. An algorithm that provides accurate surface reconstructions and surface type characterizations given two images of an unknown composite surface is established. We then apply this algorithm to Scanning Electron Microscopy (SEM) images to extract specimen surface topography and material type information from a pair of Secondary Electron (SE) and Back-scattered Electron (BSE) images. We then use a similar cyclic projections algorithm to reconstruct a surface from a single image. The simulation results indicate that the developed algorithm solves this classical shape-from-shading problem in a robust and accurate manner for varying illumination conditions. Finally, we establish a unified surface reconstruction framework using previously developed techniques on a photometric stereo image triplet containing shadows. We categorize the surface pixels as those illuminated in all three images, only two images and only one image. We then establish through simulation results that the developed method uses the surface gradient information obtained from the brightness images efficiently and effectively, and provides an accurate surface reconstruction.