We study the space of Killing fields on the four dimensional AdS spacetime AdS 3,1 . Two subsets S and O are identified: S (the spinor Killing fields) is constructed from imaginary Killing spinors, and O (the observer Killing fields) consists of all hypersurface orthogonal, future timelike unit Killing fields. When the cosmology constant vanishes, or in the Minkowski spacetime case, these two subsets have the same convex hull in the space of Killing fields. In presence of the cosmology constant, the convex hull of O is properly contained in that of S . This leads to two different notions of energy for an asymptotically AdS spacetime, the spinor energy and the observer energy. In [10], Chru\'sciel, Maerten and Tod proved the positivity of the spinor energy and derived important consequences among the related conserved quantities. We show that the positivity of the observer energy follows from the positivity of the spinor energy. A new notion called the "rest mass" of an asymptotically AdS spacetime is then defined by minimizing the observer energy, and is shown to be evaluated in terms of the adjoint representation of the Lie algebra of Killing fields. It is proved that the rest mass has the desirable rigidity property that characterizes the AdS spacetime.

This work presents Sketch2Scene, a framework that automatically turns a freehand sketch drawing inferring multiple scene objects to semantically valid, well arranged scenes of 3D models. Unlike the existing works on sketch-based search and composition of 3D models, which typically process individual sketched objects one by one, our technique performs co-retrieval and co-placement of 3D relevant models by jointly processing the sketched objects. This is enabled by summarizing functional and spatial relationships among models in a large collection of 3D scenes as structural groups. Our technique greatly reduces the amount of user intervention needed for sketch-based modeling of 3D scenes and fits well into the traditional production pipeline involving concept design followed by 3D modeling. A pilot study indicates that the 3D scenes automatically synthesized by our technique in seconds are comparable to those manually created by an artist in hours in terms of visual aesthetics.

No abstract uploaded!

A multilevel quality-guided phase unwrapping algorithm for real-time 3D shape measurement is presented. The quality map is generated from the gradient of the phase map. Multilevel thresholds are used to unwrap the phase level by level. Within the data points in each level, a fast scan-line algorithm is employed. The processing time of this algorithm is approximately 18.3 ms for an image size of 640480 pixels in an ordinary computer. We demonstrate that this algorithm can be implemented into our real-time 3D shape measurement system for real-time 3D reconstruction. Experiments show that this algorithm improves the previous scan-line phase unwrapping algorithm significantly although it reduces its processing speed slightly.

Let n be an integer such that 25≤n≤51. We construct a smooth metric g on Sn with the property that the set of constant scalar curvature metrics in the conformal class of g is not compact.