Search

A 3D image I is well-composed if it does not contain critical edges or vertices (where the boundary of I is non-manifold). The process of transforming an image into a well composed one is called repairing. We propose to repair 3D images by associating the face-centered cubic grid (FCC grid) with the cubic grid. We show that the polyhedral complex in the FCC grid, obtained by our repairing algorithm, is well-composed and homotopy equivalent to the complex naturally associated with the given image I with edge-adjacency (18-adjacency). We illustrate an application on two tasks related to the repaired image: boundary reconstruction and computation of its Euler characteristic. [ABSTRACT FROM AUTHOR]

Abstract: An ocean general circulation model (OGCM) on a non-orthogonal cubic grid originally proposed by Purser and Rančić [Purser, R.J., Rančić, M.A., 1998. Smooth quasi-homogeneous gridding of the sphere, Q.J.R. Meteorol. Soc., 124, 637–647] is developed. The grid size is very homogeneous with the ratio of the minimum to the maximum grid intervals being about 0.7. Hence this OGCM is free from severe time step limitation which the traditional latitude–longitude grid based OGCMs are subjected. In other aspects, the OGCM is similar to OGCMs used for climate research: Boussinesq and hydrostatic approximations, Arakawa B-grid and level coordinates. Since the grid is non-orthogonal, we formulated and discretized the equations on a general curvilinear coordinate system by careful treatment of non-orthogonality including variation of the directions of the local basis vectors. The performance of the model was evaluated by two tests. First the results of the long-term global integration of the cubic grid OGCM are compared with those of a latitude–longitude grid model. Except for small differences that could be attributed to the different representation of the bottom topography and coastline, the two results agree quite well. Thus the fidelity of the cubic grid OGCM has been shown to be equally good as the latitude–longitude OGCM. Next, we investigated the resolution dependence of the maximum allowable time step in linear and realistic situations. In the linear situations, the maximum allowable time step agrees with the analytical values. In the realistic situations, though the baroclinic time step is shorter than that derived from analytical estimation, it is still long enough to retain the advantage compared with latitude–longitude models. By measurements of computational costs, we confirmed that the cubic grid model is roughly five times faster than a corresponding latitude–longitude model which has nearly the same resolution and covers a ±85° latitude range by the relocation of the North and South Poles on continents. [Copyright &y& Elsevier]

Abstract: In this paper we compute distances with neighbourhood sequences in the cubic and in the triangular grids. First we give a formula which computes the distance with arbitrary neighbourhood sequence in the three-dimensional digital space. After this, using the injection of the triangular grid to the cubic grid, we modify the formula for to the triangular plane. The distances in the triangular grid have some properties which are not present on the square and cubic grids. It may be non-symmetric, and it is possible that the distance depends on the ordering of elements of the initial part of the neighbourhood sequence. The distance depends on the ordering of the initial part (up to the kth element) of the neighbourhood sequence if and only if there is a permutation of these elements such that the distance (up to value k) is non-symmetric using the elements in this new order. This dependence means somehow more flexibility of the distances based on neighbourhood sequences on the triangular grid than in . [Copyright &y& Elsevier]