Fast stereo matching by iterated dynamic programming and quadtree subregioning

The application of energy minimisation methods for stereo matching has been demonstrated to produce high quality disparity maps. However the majority of these methods are known to be computationally expensive, requiring minutes or even hours of computation. We propose a fast minimisation scheme that produces strongly competitive results for significantly reduced computation, requiring only a few seconds of computation. In this paper, we present our iterated dynamic programming algorithm along with a quadtree subregioning process for fast stereo matching.

Measurement-based teleportation along quantum spin chains

We examine the teleportation of an unknown spin-1/2 quantum state along a quantum spin chain with an even number of sites. Our protocol, using a sequence of Bell measurements, may be viewed as an iterated version of the 2-qubit protocol of C. H. Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)]. A decomposition of the Hilbert space of the spin chain into 4 vector spaces, called Bell subspaces, is given. It is established that any state from a Bell subspace may be used as a channel to perform unit fidelity teleportation. The space of all spin-0 many-body states, which includes the ground states of many known antiferromagnetic systems, belongs to a common Bell subspace. A channel-dependent teleportation parameter O is introduced, and a bound on the teleportation fidelity is given in terms of O.

Anisotropic viscous models of large-deformation Mohr-Coulomb failure

We have developed a way to represent Mohr-Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. We also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems.

Dynamic breast MRI: Image registration and its impact on enhancement curve estimation

A novel algorithm for performing registration of dynamic contrast-enhanced (DCE) MRI data of the breast is presented. It is based on an algorithm known as iterated dynamic programming originally devised to solve the stereo matching problem. Using artificially distorted DCE-MRI breast images it is shown that the proposed algorithm is able to correct for movement and distortions over a larger range than is likely to occur during routine clinical examination. In addition, using a clinical DCE-MRI data set with an expertly labeled suspicious region, it is shown that the proposed algorithm significantly reduces the variability of the enhancement curves at the pixel level yielding more pronounced uptake and washout phases.

Programs as paths: An approach to timing constraint analysis

A program can be decomposed into a set of possible execution paths. These can be described in terms of primitives such as assignments, assumptions and coercions, and composition operators such as sequential composition and nondeterministic choice as well as finitely or infinitely iterated sequential composition. Some of these paths cannot possibly be followed (they are dead or infeasible), and they may or may not terminate. Decomposing programs into paths provides a foundation for analyzing properties of programs. Our motivation is timing constraint analysis of real-time programs, but the same techniques can be applied in other areas such as program testing. In general the set of execution paths for a program is infinite. For timing analysis we would like to decompose a program into a finite set of subpaths that covers all possible execution paths, in the sense that we only have to analyze the subpaths in order to determine suitable timing constraints that cover all execution paths.

An anisotropic viscous representation of Mohr-Coulomb failure for use is modelling coupled mantle-continent dynamics

In mantle convection models it has become common to make use of a modified (pressure sensitive, Boussinesq) von Mises yield criterion to limit the maximum stress the lithosphere can support. This approach allows the viscous, cool thermal boundary layer to deform in a relatively plate-like mode even in a fully Eulerian representation. In large-scale models with embedded continental crust where the mobile boundary layer represents the oceanic lithosphere, the von Mises yield criterion for the oceans ensures that the continents experience a realistic broad-scale stress regime. In detailed models of crustal deformation it is, however, more appropriate to choose a Mohr-Coulomb yield criterion based upon the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favorably oriented with respect to the stress field. As coupled crust/mantle models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantle convection problems coupled to large-scale crustal deformation. Our approach uses an orthotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation - neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane which is formally equivalent in any symmetric formulation. It is also important to allow strain-weakening of the material. The material should remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-Integration-point finite element code and will show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion, and comparisons between mantle convection models using the von Mises versus the Mohr-Coulomb yield criteria. The formulation itself is general and applies to 2D and 3D problems, although it is somewhat more complicated to identify the slip plane in 3D.