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 .
Image meshing consists on extracting an (ideally) uniform triangular mesh from an image, so that image contours are aligned with triangle edges, normally in the aim of using the resulting mesh as a discretized domain for computational modelling using the Finite Element Method (FEM) @cite_31 @cite_25 , for example to simulate flow, mechanics, or other physical phenomena. This meshing process is normally carried out in two steps, a first segmentation step in which the domain of interest is extracted from the image, followed by a meshing step, in which a binary image of the extracted domain is meshed. A method to carry out the image meshing in one step, called was recently proposed @cite_20 . This method adapts a triangular mesh to image data directly, by defining an objective function related to the goodness-of-fit of the mesh to the image data and searching for the optimum of such function.
@cite_31 @cite_25 @cite_20
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This article proposes a variational multi-view stereo vision method based on meshes for recovering 3D scenes (shape and radiance) from images. Our method is based on generative models and minimizes the reprojection error (difference between the observed images and the images synthesized from the reconstruction). Our contributions are twofold. 1) For the first time, we rigorously compute the gradient of the reprojection error for non smooth surfaces defined by discrete triangular meshes. The gradient correctly takes into account the visibility changes that occur when a surface moves; this forces the contours generated by the reconstructed surface to perfectly match with the apparent contours in the input images. 2) We propose an original modification of the Lambertian model to take into account deviations from the constant brightness assumption without explicitly modelling the reflectance properties of the scene or other photometric phenomena involved by the camera model. Our method is thus able to recover the shape and the diffuse radiance of non Lambertian scenes. 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. This paper describes an algorithm to extract adaptive and quality quadrilateral hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad hex mesh, which is decomposed into finer quads hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, a relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations. We present a new volumetric method for reconstructing watertight triangle meshes from arbitrary, unoriented point clouds. While previous techniques usually reconstruct surfaces as the zero level-set of a signed distance function, our method uses an unsigned distance function and hence does not require any information about the local surface orientation. Our algorithm estimates local surface confidence values within a dilated crust around the input samples. The surface which maximizes the global confidence is then extracted by computing the minimum cut of a weighted spatial graph structure. We present an algorithm, which efficiently converts this cut into a closed, manifold triangle mesh with a minimal number of vertices. The use of an unsigned distance function avoids the topological noise artifacts caused by misalignment of 3D scans, which are common to most volumetric reconstruction techniques. Due to a hierarchical approach our method efficiently produces solid models of low genus even for noisy and highly irregular data containing large holes, without loosing fine details in densely sampled regions. We show several examples for different application settings such as model generation from raw laser-scanned data, image-based 3D reconstruction, and mesh repair.