Igor Sazonov

Geometrically Induced Force Interaction for Three-Dimensional Deformable Models

In this paper, we propose a novel 3-D deformable model that is based upon a geometrically induced external force field which can be conveniently generalized to arbitrary dimensions. This external force field is based upon hypothesized interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient. The evolution of the deformable model is solved using the level set method so that topological changes are handled automatically. The relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves. The geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and it gives the deformable model a high invariancy in initialization configurations. The voxel interactions across the whole image domain provide a global view of the object boundary representation, giving the external force a long attraction range. The bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross-boundary initializations, and facilitates the handling of weak edges and broken boundaries. In addition, we show that by enhancing the geometrical interaction field with a nonlocal edge-preserving algorithm, the new deformable model can effectively overcome image noise. We provide a comparative study on the segmentation of various geometries with different topologies from both synthetic and real images, and show that the proposed method achieves significant improvements against existing image gradient techniques.

An improved baseline model for a human arterial network to study the impact of aneurysms on pressure‐flow waveforms

In this study, an improved and robust one-dimensional human arterial network model is presented. The one-dimensional blood flow equations are solved using the Taylor-locally conservative Galerkin finite element method. The model improvements are carried out by adopting parts of the physical models from different authors to establish an accurate baseline model. The predicted pressure-flow waveforms at various monitoring positions are compared against in vivo measurements from published works. The results obtained show that wave shapes predicted are similar to that of the experimental data and exhibit a good overall agreement with measured waveforms. Finally, computational studies on the influence of an abdominal aortic aneurysm are presented. The presence of aneurysms results in a significant change in the waveforms throughout the network.

Shape prior model for media-adventitia border segmentation in IVUS using graph cut

We present a shape prior based graph cut method which does not require user initialisation. The shape prior is generalised from multiple training shapes, rather than using singular templates as priors. Weighted directed graph construction is used to impose geometrical and smooth constraints learned from priors. The proposed cost function is built upon combining selective feature extractors. A SVM classifier is used to determine an optimal combination of features in presence of calcification, fibrotic tissues, soft plaques, and metallic stent, each of which has its own characteristics in ultrasound images. Comparative analysis on manually labelled ground-truth shows superior performance of the proposed method compared to conventional graph cut methods.

Geometric Potential Force for the Deformable Model

We propose a new external force field for deformable models which can be conveniently generalized to high dimensions. The external force field is based on hypothesized interactions between the relative geometries of the deformable model and image gradients. The evolution of the deformable model is solved using the level set method. The dynamic interaction forces between the geometries can greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and in dealing with weak image edges. The new deformable model can handle arbitrary cross-boundary initializations. Here, we show that the proposed method achieve significant improvements when compared against existing state-of-the-art techniques.

Segmentation of biomedical images using active contour model with robust image feature and shape prior

In this article, a new level set model is proposed for the segmentation of biomedical images. The image energy of the proposed model is derived from a robust image gradient feature which gives the active contour a global representation of the geometric configuration, making it more robust in dealing with image noise, weak edges, and initial configurations. Statistical shape information is incorporated using nonparametric shape density distribution, which allows the shape model to handle relatively large shape variations. The segmentation of various shapes from both synthetic and real images depict the robustness and efficiency of the proposed method.

Automatic IVUS media-adventitia border extraction using double interface graph cut segmentation

We present a fully automatic segmentation method to extract media-adventitia border in IVUS images. Segmentation in IVUS has shown to be an intricate process due to relatively low contrast and various forms of interferences and artifacts caused by, for example, calcification and acoustic shadow. Graph cut based methods often require careful manual initialization and produces in consistent tracing of the border. We use a double interface automatic graph cut technique to prevent the extraction of media-adventitia border from being distracted by those image features. Novel cost functions are derived from using a combination of complementary texture features. Comparative studies on manual labeled data show promising performance of the proposed method.

Smooth Delaunay-Voronoï Dual Meshes for Co-Volume Integration Schemes

Yee’s scheme for the solution of the Maxwell equations [1] and the MAC algorithm for the solution of the Navier–Stokes equations [2] are examples of co-volume solution techniques. Co-volume methods, which are staggered in both time and space, exhibit a high degree of computationally efficiency, in terms of both CPU and memory requirements compared to, for example, a finite element time domain method (FETD). The co-volume method for electromagnetic (EM) waves has the additional advantage of preserving the energy and, hence, maintaining the amplitude of plane waves. It also better approximates the field near sharp edges, vertices and wire structures, without the need to reduce the element size. Initially proposed for structured grids, Yee’s scheme can be generalized for unstructured meshes and this will enable its application to industrially complex geometries [3]. Despite the fact that real progress has been achieved in unstructured mesh generation methods since late 80s, co-volume schemes have not generally proved to be effective for simulations involving domains of complex shape. This is due to the difficulties encountered when attempting to generate the high quality meshes that satisfying the mesh requirements necessary for co-volume methods. In this work, we concentrate on EM wave scattering simulations and identify the necessary mesh criteria required for a co-volume scheme. We also describe several approaches for generating two-dimensional and three-dimensional meshes satisfying these criteria. Numerical examples on the scattering of EM waves show the efficiency and accuracy that can be achieved with a co-volume method utilising the proposed meshing scheme.

Generating the Voronoi-Delaunay Dual Diagram for Co-Volume Integration Schemes

Advantages of co-volume methods (based on the use of a high quality Voronoi diagram and the dual Delaunay mesh) for two- and three-dimensional computational electromagnetics are well known. The co-volume method is faster than traditional methods for an unstructured mesh and needs less memory. The co-volume integration scheme preserves energy, i.e. gives high accuracy of wave amplitude. It also gives better accuracy if the scattering objects has sharp corners or vertices. However, the co-volume method requires use of high quality unstructured dual Voronoi-Delaunay diagrams which cannot be created by classical mesh generation methods. For two-dimensional problems, a stitching method gives the best mesh quality for a wide variety of domains. Generation of a three-dimensional dual mesh appropriate for the use of a co-volume scheme is a much more difficult issue. Here, an approach is being developed where the main ideas of the stitching method are exploited. Some examples of three-dimensional meshes generated by this new method, as well as the results of the integration of Maxwells equations on those meshes, are presented.

Level set segmentation with robust image gradient energy and statistical shape prior

We propose a new level set segmentation method with statistical shape prior using a variational approach. The image energy is derived from a robust image gradient feature. This gives the active contour a global representation of the geometric configuration, making it more robust to image noise, weak edges and initial configurations. Statistical shape information is incorporated using nonparametric shape density distribution, which allows the model to handle relatively large shape variations. Comparative examples using both synthetic and real images show the robustness and efficiency of the proposed method.

Travelling waves in a network of SIR epidemic nodes with an approximation of weak coupling

A 1D lattice of coupled susceptible/infected/removed (SIR) epidemic centres is considered numerically and analytically. We describe a mechanism for the interaction between nodes in an SIR network, i.e. for the migration process of individuals between epidemic centres with a finite-characteristic time. More specifically, we study a model for a weakly coupled population distributed between the interacting centres with a diffusion-type migration process. A 1D lattice of SIR nodes is studied numerically. Travelling wave-like solutions preserving their shape and speed are found over a wide parameter range. For weak coupling, the main part of the travelling wave is well approximated by the limiting SIR solution. Explicit formulae are found for the speed of the travelling waves and compared with the results of numerical simulation.