A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology

This work deals with the numerical solution of the monodomain and bidomain models of electrical activity of myocardial tissue. The bidomain model is a system consisting of a possibly degenerate parabolic PDE coupled with an elliptic PDE for the transmembrane and extracellular potentials, respectively. This system of two scalar PDEs is supplemented by a time-dependent ODE modeling the evolution of the so-called gating variable. In the simpler sub-case of the monodomain model, the elliptic PDE reduces to an algebraic equation. Two simple models for the membrane and ionic currents are considered, the Mitchell-Schaeffer model and the simpler FitzHugh-Nagumo model. Since typical solutions of the bidomain and monodomain models exhibit wavefronts with steep gradients, we propose a finite volume scheme enriched by a fully adaptive multiresolution method, whose basic purpose is to concentrate computational effort on zones of strong variation of the solution. Time adaptivity is achieved by two alternative devices, namely locally varying time stepping and a Runge-Kutta-Fehlberg-type adaptive time integration. A series of numerical examples demonstrates thatthese methods are efficient and sufficiently accurate to simulate the electrical activity in myocardial tissue with affordable effort. In addition, an optimalthreshold for discarding non-significant information in the multiresolution representation of the solution is derived, and the numerical efficiency and accuracy of the method is measured in terms of CPU time speed-up, memory compression, and errors in different norms.Comment: 25 pages, 41 figure

A hybrid representation for modeling, interactive editing, and real-time visualization of terrains with volumetric features

Cataloged from PDF version of article.Terrain rendering is a crucial part of many real-time applications. The easiest way to process and visualize terrain data in real time is to constrain the terrain model in several ways. This decreases the amount of data to be processed and the amount of processing power needed, but at the cost of expressivity and the ability to create complex terrains. The most popular terrain representation is a regular 2D grid, where the vertices are displaced in a third dimension by a displacement map, called a heightmap. This is the simplest way to represent terrain, and although it allows fast processing, it cannot model terrains with volumetric features. Volumetric approaches sample the 3D space by subdividing it into a 3D grid and represent the terrain as occupied voxels. They can represent volumetric features but they require computationally intensive algorithms for rendering, and their memory requirements are high. We propose a novel representation that combines the voxel and heightmap approaches, and is expressive enough to allow creating terrains with caves, overhangs, cliffs, and arches, and efficient enough to allow terrain editing, deformations, and rendering in real time

Retrieval of 3D polygonal objects based on multiresolution signatures

In this paper we present a method for retrieving 3D polygonal objects by using two sets of multiresolution signatures. Both sets are based on the progressive elimination of object's details by iterative processing of the 3D meshes. The first set, with five parameters, is based on mesh smoothing. This mainly affects an object's surface. The second set, with three parameters, is based on difference volumes after successive mesh erosions and dilations. Characteristic feature vectors are constructed by combining the features at three mesh resolutions of each object. In addition to being invariant to mesh resolution, the feature vectors are invariant to translation, rotation and size of the objects. The method was tested on a set of 40 complex objects with mesh resolutions different from those used in constructing the feature vectors. By using all eight features, the average ranking rate obtained was 1.075: 37 objects were ranked first and only 3 objects were ranked second. Additional tests were carried out to determine the significance of individual features and all combinations. The same ranking rate of 1.075 can be obtained by using some combinations of only three features. © 2011 Springer-Verlag

Planet-Sized Batched Dynamic Adaptive Meshes (P-BDAM)

This paper describes an efficient technique for out-of-core management and interactive rendering of planet sized textured terrain surfaces. The technique, called planet-sized batched dynamic adaptive meshes (P-BDAM), extends the BDAM approach by using as basic primitive a general triangulation of points on a displaced triangle. The proposed framework introduces several advances with respect to the state of the art: thanks to a batched host-to-graphics communication model, we outperform current adaptive tessellation solutions in terms of rendering speed; we guarantee overall geometric continuity, exploiting programmable graphics hardware to cope with the accuracy issues introduced by single precision floating points; we exploit a compressed out of core representation and speculative prefetching for hiding disk latency during rendering of out-of-core data; we efficiently construct high quality simplified representations with a novel distributed out of core simplification algorithm working on a standard PC network.147-15

2D and 3D surface image processing algorithms and their applications

This doctoral dissertation work aims to develop algorithms for 2D image segmentation application of solar filament disappearance detection, 3D mesh simplification, and 3D image warping in pre-surgery simulation. Filament area detection in solar images is an image segmentation problem. A thresholding and region growing combined method is proposed and applied in this application. Based on the filament area detection results, filament disappearances are reported in real time. The solar images in 1999 are processed with this proposed system and three statistical results of filaments are presented. 3D images can be obtained by passive and active range sensing. An image registration process finds the transformation between each pair of range views. To model an object, a common reference frame in which all views can be transformed must be defined. After the registration, the range views should be integrated into a non-redundant model. Optimization is necessary to obtain a complete 3D model. One single surface representation can better fit to the data. It may be further simplified for rendering, storing and transmitting efficiently, or the representation can be converted to some other formats. This work proposes an efficient algorithm for solving the mesh simplification problem, approximating an arbitrary mesh by a simplified mesh. The algorithm uses Root Mean Square distance error metric to decide the facet curvature. Two vertices of one edge and the surrounding vertices decide the average plane. The simplification results are excellent and the computation speed is fast. The algorithm is compared with six other major simplification algorithms. Image morphing is used for all methods that gradually and continuously deform a source image into a target image, while producing the in-between models. Image warping is a continuous deformation of a: graphical object. A morphing process is usually composed of warping and interpolation. This work develops a direct-manipulation-of-free-form-deformation-based method and application for pre-surgical planning. The developed user interface provides a friendly interactive tool in the plastic surgery. Nose augmentation surgery is presented as an example. Displacement vector and lattices resulting in different resolution are used to obtain various deformation results. During the deformation, the volume change of the model is also considered based on a simplified skin-muscle model

Wavelet representation of contour sets

Journal ArticleWe present a new wavelet compression and multiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contours and compactly stores this parametrization rather than function values sampled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of coefficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the corresponding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to volumetric domains, time-varying contours, and level sets of vector fields

Adaptive Resolution for Topology Modifications in Physically-based Animation

This paper shows the interest of basing a mechanical mesh upon an efficient topological model in order to give any simulation the ability to refine this mesh locally and apply topological modifications such as cutting, tear and matter destruction.Refinement and modifications can indeed be combined in order to get a more precise result.The powerful combinatorial map model provides the mathematical background which ensures that the quasi-manifold property is guaranteed for the mesh after any topological modification.The obtained results offer the versatility and time efficiency that are expected in applications such as surgical simulation

GIFTed Demons: deformable image registration with local structure-preserving regularization using supervoxels for liver applications.

Deformable image registration, a key component of motion correction in medical imaging, needs to be efficient and provides plausible spatial transformations that reliably approximate biological aspects of complex human organ motion. Standard approaches, such as Demons registration, mostly use Gaussian regularization for organ motion, which, though computationally efficient, rule out their application to intrinsically more complex organ motions, such as sliding interfaces. We propose regularization of motion based on supervoxels, which provides an integrated discontinuity preserving prior for motions, such as sliding. More precisely, we replace Gaussian smoothing by fast, structure-preserving, guided filtering to provide efficient, locally adaptive regularization of the estimated displacement field. We illustrate the approach by applying it to estimate sliding motions at lung and liver interfaces on challenging four-dimensional computed tomography (CT) and dynamic contrast-enhanced magnetic resonance imaging datasets. The results show that guided filter-based regularization improves the accuracy of lung and liver motion correction as compared to Gaussian smoothing. Furthermore, our framework achieves state-of-the-art results on a publicly available CT liver dataset