YDULDWLRQDO FODVVLILFDWLRQFigure 1: A surface extracted from 3D ultrasound data (left) vs. a surface displayed after variational opacity classification (right). AbstractWe present a new technique for visualizing surfaces from 3D ultrasound data. 3D ultrasound datasets are typically fuzzy, contain a substantial amount of noise and speckle, and suffer from several other problems that make extraction of continuous and smooth surfaces extremely difficult. We propose a novel opacity classification algorithm for 3D ultrasound datasets, based on the variational principle. More specifically, we compute a volumetric opacity function that optimally satisfies a set of simultaneous requirements. One requirement makes the function attain nonzero values only in the vicinity of a user-specified value, resulting in soft shells of finite, approximately constant thickness around isosurfaces in the volume. Other requirements are designed to make the function smoother and less sensitive to noise and speckle. The computed opacity function lends itself well to explicit geometric surface extraction, as well as to direct volume rendering at interactive rates. We also describe a new splatting algorithm that is particularly well suited for displaying soft opacity shells. Several examples and comparisons are included to illustrate our approach and demonstrate its effectiveness on real 3D ultrasound datasets.

Polarization correlation in a linear basis, but not entanglement, is observed between the biexciton and single-exciton photons emitted by a single InAs quantum dot in a two-photon cascade. The results are well described quantitatively by a probabilistic model that includes two decay paths for a biexciton through a nondegenerate pair of one-exciton states, with the polarization of the emitted photons depending on the decay path. The results show that spin nondegeneracy due to quantum-dot asymmetry is a significant obstacle to the realization of an entangled-photon generation device.