Johan Lie's Publications List

Simulating Two Phase Navier-Stokes Flow by a Discontinuous Galerkin Finite Element Level Set Approach

2010-01-05T11:19:50Z

We develop a two-phase incompressible uid ow simulator based on the Navier-Stokes equations. The interface between the two uids is modelled by a level set approach. The Navier-Stokes equations are solved by a standard splitting algorithm. We use a combined continuous and discontinuous Galerkin approach for the dierent subproblems of the splitting algorithm.We study various phenomena r...

Johan Lie and Roland Kaufmann (2009) (Preprint)

Shape-Adaptive DCT for Denoising of Tensor Valued 3D Images

2009-05-11T08:02:42Z

Ørjan Bergmann, Oddvar Christiansen, Johan Lie, Arvid Lundervold (2009) Journal of Digital Imaging 22: 3

An Operator Algebraic Inverse Scale Space Method for Symmetric Matrix Valued Images

2009-03-23T12:25:26Z

Johan Lie, Bernhard Burgeth, Oddvar Christiansen ( 2009) :

Inverse Scale Spaces for Nonlinear Regularization

2007-12-15T13:32:36Z

Johan Lie, Jan M Nordbotten (2007) Journal of Mathematical Imaging and Vision 27: 1 41-50

Mathematical Imaging with Applications to MRI and Diffusion Tensor MRI

2009-03-23T13:02:06Z

Johan Lie (2007)

A Dual Operator Algebraic Method for Regularization of Matrix Valued Images

2007-12-14T23:49:54Z

Oddvar Christiansen, Johan Lie, Bernhard Burgeth (2007) (Preprint) :

Total Variation Regularization of Matrix Valued Images

2009-03-23T10:55:58Z

In this work we generalize the total variation restoration model, introduced by Rudin, Osher and Fatemi in 1992, to matrix valued data. In particular to Diffusion Tensor Images (DTI). Our model is a natural extension of the color total variation model proposed by Blomgren and Chan in 1996. We treat the diffusion matrix D implicitly as the product D = LL^T, and work with the elements of L as variab...

Oddvar Christiansen, Tin-Man Lee, Johan Lie, Usha Sinha, Tony F Chan (2007) International Journal of Biomedical Imaging. Special issue on Mathematics in Biomedical Imaging Vol. 2007:

A Binary Level Set Model and some Applications to Mumford-Shah Image Segmentation

2009-03-23T10:57:49Z

In this work we propose a PDE based level set method. Traditionally interfaces are represented by the zero level set of continuous level set functions. We instead let the interfaces be represented by discontinuities of piecewise constant level set functions. Each level set function can at convergence only take two values, i.e.\ it can only be 1 or -1, thus our method is related to phase-field meth...

Johan Lie, Marius Lysaker, Xue-Cheng Tai (2006) IEEE Transactions on Image Processing 15: 5 1171-1181

A Variant of the Level Set Method and Applications to Image Segmentation

2009-03-23T12:11:31Z

In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of $n$ level set functions are utilized to identify up to $2^n$ phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If $2^n$ phase...

Johan Lie, Marius Lysaker, Xue-Cheng Tai (2006) AMS Mathematics of Computation 75: 1155-1174

A piecewise constant level set framework

2009-03-23T12:17:54Z

Johan Lie, Marius Lysaker and Xue-Cheng Tai (2005) International Journal of Numerical Analysis and Modeling 2: 4 422-438

Piecewise Constant Level Set Methods and Image Segmentation

2007-12-14T23:49:54Z

In this work we discuss variants of a PDE based level set method. Traditionally interfaces are represented by the zero level set of continuous level set functions. We instead use piecewise constant level set functions, and let interfaces be represented by discontinuities. Some of the properties of the standard level set function are preserved in the proposed method. Using the methods for interface...

Johan Lie, Marius Lysaker, Xue-Cheng Tai (2005) Scale Space and PDE Methods in Computer Vision : 5th International Conference, Scale-Space 2005 http://dx.doi.org/10.1007/11408031_49 3459: