基于双法线跟踪的形状中轴并行提取算法

为准确而高效地提取出形状的中轴,提出一种利用双法线跟踪算法来并行计算形状中轴的方法。通过离散化将形状的边界离散为由若干样本点连接成的多边形,分别对样本点以及样本点连接成的边界边进行两次的法线跟踪,通过多次的迭代与并行计算后,得到所有样本点对应的中轴点,根据样本点的拓扑联通性连接相应中轴点,生成形状的中轴。通过多次实验,该方法可以快速准确得到形状的中轴,验证了其精确性和高效性。     

小波轮廓描述符及在图像查询中的应用

该文提出一种基于小波变换方法对目标形状的描述方法．在给出小波轮廓描述符数学定义的基础上,详细分析和实验验证了描述符的各个性质,并讨论了描述符的实际计算问题．另外结合基于内容的图像查询对小波轮廓描述符与傅里叶轮廓描述符的描述和检索性能进行了比较,证实了小波轮廓描述符的优越性．     

A new method for analyzing local shape in three-dimensional images based on medial axis transformation

In this paper, we propose a new approach based on three-dimensional (3-D) medial axis transformation for describing geometrical shapes in three-dimensional images. For 3-D-images, the medial axis, which is composed of both curves and medial surfaces, provides a simplified and reversible representation of structures. The purpose of this new method is to classify each voxel of the three-dimensional images in four classes: boundary, branching, regular and arc points. The classification is first performed on the voxels of the medial axis. It relies on the topological properties of a local region of interest around each voxel. The size of this region of interest is chosen as a function of the local thickness of the structure. Then, the reversibility of the medial axis is used to deduce a labeling of the whole object. The proposed method is evaluated on simulated images. Finally, we present an application of the method to the identification of bone structures from 3-D very high-resolution tomographic images.     

On the intrinsic reconstruction of shape from its symmetries

The main question we address is: What is the minimal information required to generate closed, nonintersecting planar boundaries? For this paper, we restrict "shape" to this meaning. More precisely, we examine whether the medial axis, together with dynamics, can serve as a language to design shapes and to effect shape changes. We represent the medial axis together with a direction of flow along the axis as the shock graph and examine the reconstruction of shape along each of the three types of medial axis points, A/sub 1//sup 2/, A/sub 1//sup 3/, A/sub 3/, and the associated six types of shock points. First, we show that the tangent and curvature of the medial axis and the speed and acceleration of the shock with respect to time of propagation are sufficient to determine the boundary tangent and curvature at corresponding points of the boundary. This implies that a rather coarse sampling of the symmetry axis, its tangent, curvature, speed, and acceleration is sufficient to regenerate accurately a local neighborhood of shape at regular axis points (A/sub 1//sup 2/). Second, we examine the reconstruction of shape at branch points (A/sub 1//sup 3/) where three regular branches are joined. We show that the three pairs of geometry (that is, curvature) and dynamics (that is, acceleration) must satisfy certain constraints. Finally, we derive similar results for the end points of shock branches (A/sub 3/ points). These formulas completely specify the local reconstruction of a shape from its shock-graph or medial axis and the conditions required to form a coherent shape from the medial axis.     

Isogeometric analysis and shape optimization via boundary integral

In this paper, we present a boundary integral based approach to isogeometric analysis and shape optimization.For analysis, it uses the same basis, Non-Uniform Rational B-Spline (NURBS) basis, for both representing object boundary and for approximating physical fields in analysis via a Boundary-Integral-Equation Method (BIEM). We propose the use of boundary points corresponding to Greville abscissae as collocation points. We conducted h-, p- and k-refinement study for linear elasticity and heat conduction problems. Our numerical experiments show that collocation at Greville abscissae leads to overall better convergence and robustness. Replacing rational B-splines with the linear B-Splines as shape functions for approximating solution space in analysis does not yield significant difference in convergence.For shape optimization, it uses NURBS control points to parameterize the boundary shape. A gradient based optimization approach is adopted where analytical sensitivities of how control points affect objective and constraint functions are derived. Two 3D shape optimization examples are demonstrated.Our study finds that the boundary integral based isogeometric analysis and optimization have the following advantages: (1) the NURBS based boundary integral exhibits superior computational advantages over the usual Lagrange polynomials based BIEM on a per degree-of-freedom basis; (2) it bypasses the need for domain parameterization, a bottleneck in current NURBS based volumetric isogeometric analysis and shape optimization; (3) it offers tighter integration of CAD and analysis since both the geometric models for both analysis and optimization are the same NURBS geometry.     

Hyperbolic Hausdorff Distance for Medial Axis Transform

Although the Hausdorff distance is a popular device to measure the differences between sets, it is not natural for some specific classes of sets, especially for the medial axis transform which is defined as the set of all pairs of the centers and the radii of the maximal balls contained in another set. In spite of its many advantages and possible applications, the medial axis transform has one great weakness, namely its instability under the Hausdorff distance when the boundary of the original set is perturbed. Though many attempts have been made for the resolution of this phenomenon, most of them are heuristic in nature and lack precise error analysis. In this paper, we show that this instability can be remedied by introducing a new metric called the hyperbolic Hausdorff distance, which is most natural for measuring the differences between medial axis transforms. Using the hyperbolic Hausdorff distance, we obtain error bounds, which make the operation of medial axis transform almost an isometry. By various examples, we also show that the bounds obtained are sharp. In doing so, we show that bounding both the Hausdorff distance between domains and the Hausdorff distance between their boundaries is necessary and sufficient for bounding the hyperbolic Hausdorff distance between their medial axis transforms. These results drastically improve the previous results and open a new way to practically control the Hausdorff distance error of the domains under its medial axis transform error, and vice versa.     

Image Thinning by Neural Networks

An image thinning technique using a neural network is proposed. Using different activation functions at different layers, the proposed neural network removes the boundary pixels from four directions in such a manner that the general configuration of the input pattern is unaltered and the connectivity is preserved. The resulting object, called a skeleton, provides an abstraction of the global shape of the object. The skeleton is often useful for geometrical and structural analysis of the object. The output skeleton here satisfies the basic properties of a skeleton, namely connectivity and unit thickness. The proposed method is experimentally found to be more efficient in terms of better medial axis representation and robustness to boundary noise over a few existing algorithms. ID="A1" Correspondence and offprint requests to: Dr A. Datta, Indian Statistical Institute, 203 B. T. Road, Calcutta – 700 108, India. Email: amitava@isical.ac.in     

Medial axis transformation of a planar shape

The medial axis transformation is a means first proposed by Blum to describe a shape. In this paper we present a 0(n log n) algorithm for computing the medial axis of a planar shape represented by an n-edge simple polygon. The algorithm is an improvement over most previously known results interms of both efficiency and exactness and has been implemented in Fortran. Some computer-plotted output of the program are also shown in the paper.