多元函数中值定理“中间点”的渐近性

讨论了矩形域上的二元函数微分中值定理“中间点”当矩形域的某个顶点沿对角线方向趋向于另一个顶点时的渐近性．     

Contrast enhancement in atherosclerosis development in a mouse model: in vivo results at 2 Tesla

To develop an MRI method for the evaluation of contrast enhancement in early atherosclerotic plaque development in the abdominal aorta of a mouse model. Male apoE^–/– mice from three groups, respectively 4 (n = 6), 8 (n = 11) and 16 (n = 4) weeks were included. Axial T1 spin echo images of the abdominal aorta were obtained above and below the renal arteries (90 m spatial resolution) before and over 1 h after the injection of a macromolecular contrast agent. Signal enhancement was measured in the vessel wall and compared to histological features. Maximal arterial wall signal enhancement was obtained from 16 to 32 min post injection. During this time, the signal-to-noise ratio increased by a factor up to 1.7 in 16 week mice and 2.7 and 2.4 in 8 and 4 weeks mice, respectively. The enhancement of the arterial wall appeared less pronounced in the oldest mice, 16 weeks old, exhibiting more advanced lesions. Using a macromolecular gadolinium agent, contrast uptake in atherogenesis varies with lesion stage and may be related to vessel-wall permeability. Dynamic contrast-enhanced MRI may be useful to evaluate the atherosclerotic plaque activity in mice.     

Medial axis computation for planar free-form shapes

We present a simple, efficient, and stable method for computing—with any desired precision—the medial axis of simply connected planar domains. The domain boundaries are assumed to be given as polynomial spline curves. Our approach combines known results from the field of geometric approximation theory with a new algorithm from the field of computational geometry. Challenging steps are (1) the approximation of the boundary spline such that the medial axis is geometrically stable, and (2) the efficient decomposition of the domain into base cases where the medial axis can be computed directly and exactly. We solve these problems via spiral biarc approximation and a randomized divide & conquer algorithm.     

Skeletonization based on error reduction

The accuracy of a non-pixel-based skeletonization method is largely dependent on the contour information chosen as input. When using a Constrained Delaunay Triangulation to construct an object's skeleton, a number of contour pixels must be chosen as a basis for triangulation. This paper presents a new method of selecting these contour pixels. A new method for measuring skeletonization error is proposed, which quantifies the deviation of a skeleton segment from the true medial axis of a stroke in an image. The goal of the proposed algorithm is to reduce this error to an acceptable level, whilst retaining the superior efficiencies of previous non-pixel-based techniques. Experimental results show that the proposed method is adept at following the medial axis of an image, and is capable of producing a skeleton that is confirmed by a human's perception of the image. It is also computationally efficient and robust against noise.     

Robust skeletonization using the discrete λ-medial axis

Medial axes and skeletons are notoriously sensitive to contour irregularities. This lack of stability is a serious problem for applications in e.g. shape analysis and recognition. In 2005, Chazal and Lieutier introduced the λ-medial axis as a new concept for computing the medial axis of a shape subject to single parameter filtering. The λ-medial axis is stable under small shape perturbations, as proved by these authors. In this article, a discrete λ-medial axis (DLMA) is introduced and compared with the recently introduced integer medial axis (GIMA). We show that DLMA provides measurably better results than GIMA, with regard to stability and sensibility to rotations. We give efficient algorithms to compute the DLMA, and we also introduce a variant of the DLMA which may be computed in linear-time.     

Calculating the medial axis of a CAD model by multi-CPU based parallel computation

Computational efficiency is still a great challenge for the generation of the Medial Axis (MA) for complicated CAD models. Current research mainly focuses on CPU-based MA generation methods. However, most of the methods emphasize using a single CPU. The highly-efficient methods based on parallel computing are still missing. In this study, a parallel method based on multi-CPU is proposed for the efficient MA generation of CAD models using distance dilation. By dividing the whole model into several parts for which MAs are calculated in parallel and then combined, computational efficiency can be greatly improved in theory and the computation time can be reduced nearly K times if K CPUs are used. Firstly, an adaptive division method is proposed to divide the voxelized model into blocks which have nearly the same number of voxels to balance the computational burden. Secondly, the local Euclidean Distance Transform (EDT) is calculated for each block based on the existing distance dilation method. Thirdly, the complete inter-dilation method is proposed to compute the influence between different blocks to get a global EDT for each block. Finally, each block generates a sub-MA separately and then all the generated MAs are combined to obtain the final MA. The last three processes can be efficiently conducted in parallel by using multiple CPUs. Several groups of experiments are conducted which demonstrate the good performance of the proposed methods in terms of efficiency.     

New reduced discrete Euclidean nD medial axis with optimal algorithm

Skeletons have been playing an important role in shape analysis since the introduction of the medial axis in the sixties. The original medial axis definition is in the continuous Euclidean space. It is a skeleton with the following characteristics: centered, thin, homotopic (it has the same topology as the object), and reversible (sufficient for the reconstruction of the object). The discrete version of the Euclidean medial axis (MA) is also reversible and centered, but no longer homotopic nor thin. The combination of the MA with homotopic thinning algorithms can result in a topology preserving, reversible skeleton. However, such combination may generate thicker skeletons, and the choice of the thinning algorithm is not obvious. A robust and well defined framework for fast homotopic thinning available in the literature is defined in the domain of abstract complexes. Since the abstract complexes are represented in a doubled resolution grid, some authors have extended the MA to a doubled resolution grid and defined the discrete Euclidean medial axis in higher resolution (HMA). The HMA can be combined with the thinning framework defined on abstract complexes. Other authors have given an alternative definition of medial axis, which is a subset of the MA, called reduced discrete medial axis (RDMA). The RDMA is reversible, thinner than the MA, and it can be computed in optimal time. In this paper, we extend the RDMA to the doubled resolution grid and we define the high-resolution RDMA (HRDMA). We provide an optimal algorithm to compute the HRDMA. The HRDMA can be combined with the thinning framework defined on abstract complexes. The skeleton obtained by such combination is provided with strong characteristics, not found in the literature.     

Flexible bones for the haptic prototyping of deformable objects

Accurate modelling of the compliance characteristics of solid models is an important rendering task for increasing the realism of virtual environments. The ability to feel the force and moment stress resultants that cause the bending, twisting, shearing and/or fracture of physically-based models is useful for a large number of application areas including medical training, CAD environments, computer animation and games. An important element of compliance rendering is the mechanics engine that solves the equations governing the deformations and stresses in solid models. The development of such engines has to carefully balance the needs for haptic (not just graphical) realism with the needs for real time processing at rates in the range of 500-1000 Hz. In this paper we describe methods and techniques we have developed for such an engine, and demonstrate their characteristics in a number of applications including design of compliant mechanisms, animation and solid modelling.     

基于模糊控制的自适应有限元网格自动剖分

本文采用模糊控制策略，对有限元网格划分过程中难以控制的因素－网格密度作出自适应控制。同时借鉴先验自适应的思想，在后验控制过程中综合考虑了边界属性的影响，避免了较多层次的网格局部细化与退化，采用此方法，不仅保证了计算精度，而且可以提高运算效率。