Fast Marching and Fast Sweeping are the two most commonly used methods for solving the Eikonal equation. Each of these methods performs best on a different set of problems. Fast Sweeping, for example, will outperform Fast Marching on problems where the characteristics are largely straight lines. Fast Marching, on the other hand, is usually more efficient than Fast Sweeping on problems where cha...

In this work, a new family of time marching procedures based on Green’s function matrices is presented. The formulation is based on the development of new recurrence relationships, which employ time integral terms to treat initial condition values. These integral terms are numerically evaluated taking into account Newton-Cotes formulas. The Green’s matrices of the model are also numerically com...

This paper presents a method for identifying image loci that can be used as a basis for object segmentation and image registration. The focus is on 1D and 2D shape loci in 3D images. This method, called marching ridges, uses generalized height ridges, oriented medialness measures and a marching cubes like algorithm to extract optimal scale-orientation cores. This algorithm can can also be used ...

Image processing in machine vision is a challenging task because often real-time requirements have to be met in these systems. To accelerate the processing tasks in machine vision and to reduce data transfer latencies, new architectures for embedded systems in intelligent cameras are required. Furthermore, innovative processing approaches are necessary to realize these architectures efficiently...

The Centered Cubic Lattice method is used for an iso-surface extraction. This paper focuses on its comparison with other fundamental methods (Marching Cubes, Marching Tetrahedra) that are also used to extract an iso-surface from regular volume data. Iso-surfaces that are generated using above mentioned methods and mathematical data are compared due to area and volume approximation. The Hausdorf...

Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the fast marching method is presented. This augmented fast marching method will calculate the signed distance function and up to the secondorder derivatives of the ...

Three dimensional datasets representing scalar fields are frequently rendered using isosurfaces. For datasets arranged as a cubic lattice, the marching cubes algorithm is the most used isosurface extraction method. However, the marching cubes algorithm produces some ambiguities which have been solved using different approaches that normally imply a more complex process. One of them is to tessel...

We propose a novel method, slice marching 1, for segmenting opacified vessels tree in 3D images (volume data), from multislice computed tomography (MSCT) scans. The method uses fast marching with freezing of boundaries to advance inside the vessel, slice per slice. Large scale features, such as vessel section and curvature, are evaluated for each slice. These features can then be used to influe...