We consider the volumetric barrier for semide2nite programming, or “generalized” volumetric barrier, as introduced by Nesterov and Nemirovskii. We extend several fundamental properties of the volumetric barrier for a polyhedral set to the semide2nite case. Our analysis facilitates a simpli2ed proof of self-concordance for the semide2nite volumetric barrier, as well as for the combined volumetri...

With the dramatic increase of 3D imaging techniques, there is a great demand for new approaches in texture analysis of volumetric data. In this paper, we present a new approach for volumetric texture analysis using a runlength encoding matrix and its texture descriptors. We experiment with our approach on the volumetric data generated from two normal Computed Tomography (CT) studies of the ches...

We consider the volumetric barrier for semideenite programming, or \generalized" volumetric barrier, as introduced by Nesterov and Nemirovskii. We extend several fundamental properties of the volumetric barrier for a polyhedral set to the semideenite case. Our analysis facilitates a simpliied proof of self-concordancy for the semideenite volu-metric barrier, as well as for the combined volumetr...