Deriving a function that maps one image on to another similar image is a useful method in medical imaging. The modelling of this deformation function in terms of a functional basis leads to numerical methods of obtaining a good deformation. It is advantageous to be able to represent a wide class commonly observed deformations economically, i.e. where most coeecients are zero. We proposed a wave...

In this work, we propose a method to interactively deform high-resolution volumetric datasets, such as those obtained through medical imaging. Interactive deformation enables the visualization of these datasets in full detail using state-of-the-art volume rendering techniques as they are dynamically modified. Our approach relies on resampling the original dataset to a target regular grid, follo...

This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form F + ∑i=1Gi, where F has a Lipschitzcontinuous gradient and the Gi’s are simple in the sense that their Moreau proximity operators are easy to compute. While the forward-backward algorithm cannot deal with more than n = 1 non-smooth function, our method generalizes it to the cas...

This paper presents a new method for real-time modelling soft tissue deformation. It improves the traditional mass-spring model with conical springs to deal with nonlinear mechanical behaviours of soft tissues. A conical spring model is developed to predict soft tissue deformation with reference to deformation patterns. The model parameters are formulated according to tissue deformation pattern...

Scanning the deformation behavior of real objects is a useful technique to acquire physically realistic behavior. It has been shown previously how to acquire physically realistic object behavior for small deformation and how to render the behavior at interactive rates. This paper introduces a novel method to extend previous work to handle large scale deformation. We model large scale deformatio...

We discuss a leading-edge model used in the computation of the run-out length of dry-flowing avalanches. The model has the form of a singular initial value problem for a scalar ordinary differential equation describing the avalanche dynamics. Existence, uniqueness and smoothness properties of the analytical solution are shown. We also prove the existence of a unique root of the solution. Moreov...

A nonlinear degenerate convection-diffusion initial boundary value problem is studied in a bounded domain. A dynamical boundary condition (containing the time derivative of a solution) is prescribed on the one part of the boundary. This models a non-perfect contact on the boundary. Existence and uniqueness of a weak solution in corresponding function spaces is proved using the backward Euler me...

This paper provides an introduction to Monte Carlo algorithms for pricing American options written on multiple assets, with special emphasis on methods that can be applied in a multi-dimensional setting. Simulated paths can be used to estimate by nonparametric regression the continuation value of the option or the optimal exercise policy and the value functions can then be computed by backward ...

Numerical approximations to the solution of a linear singularly perturbed parabolic problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh for a convectiondiffusion problem. A proof is given to show first order convergence of these numerical approximations in appropriately weighted C-norm. Numerical re...