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一种基于MQ 拟插值的自适应边缘检测方法

  

  1. 1. 大连外国语大学经济与管理学院，辽宁 大连 116044;
    2. 大连医科大学公共卫生学院，辽宁 大连 116044;
    3. 大连交通大学理学院，辽宁 大连 116044
  • 出版日期:2017-06-30 发布日期:2017-07-06
  • 基金资助:

    国家自然科学基金项目(11501006)；辽宁省教育厅一般项目(L2013434)；大连外国语大学校级青年项目(2014XJQN11)

Adaptive Boundary Detection Method Based on Multi-Quadric Quasi-Interpolation

  1. 1. School of Economics & Management, Dalian University of Foreign Languages, Dalian Liaoning 116044, China;
    2. Department of Health Statistics, Dalian Medical University, Dalian Liaoning 116044, China;
    3. School of Science, Dalian Jiaotong University, Dalian Liaoning 116044, China
  • Online:2017-06-30 Published:2017-07-06

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摘要： MQ 拟插值方法在进行微分方程数值解时具有精度高、稳定性好且节点移动灵活等
特点。基于此提出一种使用MQ 拟插值模拟几何活动轮廓模型(GAC)的自适应算法。将几何流表
示为参数形式，首先在空间方向用MQ 拟插值及其导数来逼近函数及其空间导数, 然后通过节点
移动方程移动节点使得节点几乎均匀分布在轮廓线上，最后在时间方向用向前差分法离散得到下
一个时间层的函数逼近。该算法可使用较少的点达到较好的拟合效果，节省计算量，在进行具有
大曲率大变化图像的边缘检测时更加精确、高效。最后给出几个实例，说明了该方法的有效性。

关键词: 边缘检测, 自适应方法, 几何活动轮廓模型, MQ 拟插值

Abstract: This paper proposes an adaptive method for simulating one kind of geometric active contours
(GAC) applying multiquadric (MQ) quasi-interpolation. The geometric flow is presented in its
parametric form. Then the numerical scheme is obtained: Firstly the spatial derivatives of each variable
are approximated applying the MQ quasi-interpolation; secondly the knots are moved according to the
moving knots equation to pull the knots to concentrate in regions with large variations. Thirdly the
forward difference methods are applied to approximate the temporal derivative of each variable. The
resulting scheme is simple, efficient and easy to implement. Also images with complex boundaries can
be simulated more efficiently on the basis of the good properties of the adaptive MQ method. Several
examples of applications are shown in the paper.

Key words: boundary detection, adaptive method, geometric active contours, MQ quasi-interpolation