We propose a novel iterative method to adapt a a graph to d-dimensional image data. The method drives the nodes of the graph towards image features. The adaptation process naturally lends itself to a measure of feature saliency which can then be used to retain meaningful nodes and edges in the graph. From the adapted graph, we also propose the computation of a dual graph, which inherits the saliency measure from the adapted graph, and whose edges run along image features, hence producing an oversegmenting graph. The proposed method is computationally efficient and fully parallelisable. We propose two distance measures to find image saliency along graph edges, and evaluate the performance on synthetic images and on natural images from publicly available databases. In both cases, the most salient nodes of the graph achieve average boundary recall over 90 . We also apply our method to image classification on the MNIST hand-written digit dataset, using a recently proposed Deep Geometric Learning architecture, and achieving state-of-the-art classification accuracy, for a graph-based method, of 97.86 .
Finite element (FE) modelling based on data from three-dimensional high-resolution computed tomography (CT) imaging systems provides a non-invasive method to assess structural mechanics. Automated mesh generation from these voxel based image data can be achieved by direct conversion to hexahedron elements, however these model representations have jagged edges. This paper proposes an automated method to generate smoothed FE meshes from voxel-based image data. Mesh fairing processes are utilized that allow constraints that control the smoothing process, and are computationally efficient. Surfaces of the mesh on the exterior, as well as interfaces between two tissues, can be smoothed by varying fairing parameters and constraint criteria. The method was tested on a variety of real and simulated three-dimensional data sets, resulting in both hexahedron and tetrahedron meshes. It was shown that the fairing process is linearly related to the number of smoothing iterations, and that peak stresses are reduced in FE simulations of the smoothed models. Although developed for micro-CT data sets, this fast and reliable mesh smoothing method could be applied to any three-dimensional image data where node and element connectivity have been defined. TetGen is a Cpp program for generating good quality tetrahedral meshes aimed to support numerical methods and scientific computing. The problem of quality tetrahedral mesh generation is challenged by many theoretical and practical issues. TetGen uses Delaunay-based algorithms which have theoretical guarantee of correctness. It can robustly handle arbitrary complex 3D geometries and is fast in practice. The source code of TetGen is freely available. This article presents the essential algorithms and techniques used to develop TetGen. The intended audience are researchers or developers in mesh generation or other related areas. It describes the key software components of TetGen, including an efficient tetrahedral mesh data structure, a set of enhanced local mesh operations (combination of flips and edge removal), and filtered exact geometric predicates. The essential algorithms include incremental Delaunay algorithms for inserting vertices, constrained Delaunay algorithms for inserting constraints (edges and triangles), a new edge recovery algorithm for recovering constraints, and a new constrained Delaunay refinement algorithm for adaptive quality tetrahedral mesh generation. Experimental examples as well as comparisons with other softwares are presented. In medical simulations involving tissue deformation, the finite element method (FEM) is a widely used technique, where the size, shape, and placement of the elements in a model are important factors that affect the interpolation and numerical errors of a solution. Conventional model generation schemes for FEM consist of a segmentation step delineating the anatomy followed by a meshing step generating elements conforming to this segmentation. In this paper, a single-step model generation technique is proposed based on optimization. Starting from an initial mesh covering the domain of interest, the mesh nodes are adjusted to minimize an objective function which penalizes intra-element intensity variations and poor element geometry for the entire mesh. Trade-offs between mesh geometry quality and intra-element variance are achieved by adjusting the relative weights of the geometric and intensity variation components of the cost function. This meshing approach enables a more accurate rendering of shapes with fewer elements and provides more accurate models for deformation simulation, especially when the image intensities represent a mechanical feature of the tissue such as the elastic modulus. The use of the proposed mesh optimization is demonstrated in 2-D and 3-D on synthetic phantoms, MR images of the brain, and CT images of the kidney. A comparison with previous meshing techniques that do not account for image intensity is also provided demonstrating the benefits of our approach.