Methods for Volumetric Reconstruction of Visual Scenes

In this paper, we present methods for 3D volumetric reconstruction of visual scenes photographed by multiple calibrated cameras placed at arbitrary viewpoints. Our goal is to generate a 3D model that can be rendered to synthesize new photo-realistic views of the scene. We improve upon existing voxel coloring/space carving approaches by introducing new ways to compute visibility and photo-consistency, as well as model infinitely large scenes. In particular, we describe a visibility approach that uses all possible color information from the photographs during reconstruction, photo-consistency measures that are more robust and/or require less manual intervention, and a volumetric warping method for application of these reconstruction methods to large-scale scenes

Graphene formation on SiC substrates

Graphene layers were created on both C and Si faces of semi-insulating, on-axis, 4H- and 6H-SiC substrates. The process was performed under high vacuum (<10-4 mbar) in a commercial chemical vapor deposition SiC reactor. A method for H2 etching the on-axis sub-strates was developed to produce surface steps with heights of 0.5 nm on the Si-face and 1.0 to 1.5 nm on the C-face for each polytype. A process was developed to form graphene on the substrates immediately after H2 etching and Raman spectroscopy of these samples confirmed the formation of graphene. The morphology of the graphene is described. For both faces, the underlying substrate morphology was significantly modified during graphene formation; sur-face steps were up to 15 nm high and the uniform step morphology was sometimes lost. Mo-bilities and sheet carrier concentrations derived from Hall Effect measurements on large area (16 mm square) and small area (2 and 10 um square) samples are presented and shown to compare favorably to recent reports.Comment: European Conference on Silicon Carbide and Related Materials 2008 (ECSCRM '08), 4 pages, 4 figure

A categorical foundation for Bayesian probability

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\mu: 1 \rightarrow D$, a posterior probability $\widehat{P_H}= I \circ \mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additional measurement. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the setting of Polish spaces. This less stringent setting then allows for non-trivial decision rules (Eilenberg--Moore algebras) on finite (as well as non finite) spaces, and also provides for a common framework for decision theory and Bayesian probability.Comment: 15 pages; revised setting to more clearly explain how to incorporate perfect measures and the Giry monad; to appear in Applied Categorical Structure