DEVELOPMENT OF A GENERAL METHOD FOR DETECTING A SPECIFIED FAMILY OF CURVES IN A DIGITAL IMAGE

检测黑白图像中包含的所有数字线分量是模式识别中最基本的问题之一。在这项研究中，我们开发了有效的算法来检测所有的数字线分量。我们还开发了用于检测所有数字曲线分量的空间高效算法。这是第一个用于检测曲线分量的线性空间算法，也是第一个使用尽可能少的参数定义一组数字曲线的算法。更具体地说，关键思想是点与线之间的对偶变换和线排列中的高效搜索。该算法与现有算法的一个不同之处在于，它可以检测出满足条件的所有可能的直线和曲线分量，而不会遗漏任何一个。我们还分析了问题本身和算法的计算复杂度，以确定所提出算法的最优性。实验结果表明了该方法的实用性和有效性。

The problem of detecting all digital line components contained in a black-white image is one of the most fundamental problems in pattern recognition. In this study we have developed efficient algorithms for detecting all of digital line components. We also developed space-efficient algorithms for detecting all of digital curve components. This is the first linear-space algorithm for the purpose for detecting curve components and in addition the first to define a family of digital curves using least possible number of parameters. More concretely, key ideas are duality transform between points and lines and efficient search in an arrangment of lines. One advantage of the proposed algorithms to be distinguished from the existing ones is that they can detect all possible line and curve components satisfying the conditions without missing one. We also analyzed the computational complexity of the problem itself and algorithms to establish the optimality of the proposed algorithms. Experimental results show the practical usefullness and effectiveness of the proposed methods.