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边界跟踪

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二值图像的边界跟踪Boundary tracing,也称 轮廓跟踪contour tracing)可以被认为是一种识别数字区域边界像素的图像分割技术。边界跟踪是分析区域的第一步操作。

算法

边界跟踪的算法有:[1]

  • Square跟踪算法[2]
  • Moore邻域跟踪算法
  • 径向扫描 (radical sweep)[3]
  • Theo Pavlidis算法 [4]
  • 一种使用向量几何的泛化的算法:[5]
  • 一种分割区域为开、闭子区域的算法:[6]

Square 跟踪算法

Square跟踪算法简单但有效。它的行为完全基于格子是白格还是黑格(假设白格是形状的一部分)。首先,从左上到右上逐行扫描。进入第一个白格后,算法的核心部分就开始了。它主要包括两个规则:

  • 如果在白格,左转
  • 如果在黑格,右转

需要记录进入当前格的过程,这样才能定义左和右方向。

public void GetBoundary(byte[,] image)
{
    for (int j = 0; j < image.GetLength(1); j++)
        for (int i = 0; i < image.GetLength(0); i++)
            if (image[i, j] == 255)               // Found first white pixel
                SquareTrace(new Point(i, j));
}

public void SquareTrace(Point start)
{
    HashSet<Point> boundaryPoints = new HashSet<Point>();  // Use a HashSet to prevent double occurrences
    // We found at least one pixel
    boundaryPoints.Add(start);

    // The first pixel you encounter is a white one by definition, so we go left. 
    // Our initial direction was going from left to right, hence (1, 0)
    Point nextStep = GoLeft(new Point(1, 0));               
    Point next = start + nextStep;
    while (next != start)
    {
        // We found a black cell, so we go right and don't add this cell to our HashSet
        if (image[next.x, next.y] == 0)
        {
            next = next - nextStep
            nextStep = GoRight(nextStep);
            next = next + nextStep;
        }
        // Alternatively we found a white cell, we do add this to our HashSet
        else
        {
            boundaryPoints.Add(next);
            nextStep = GoLeft(nextStep);
            next = next + nextStep;
        }
    }
}

private Point GoLeft(Point p) => new Point(p.y, -p.x);
private Point GoRight(Point p) => new Point(-p.y, p.x);

参见

参考资料

  1. ^ Contour Tracing Algorithms. [2021-12-28]. (原始内容存档于2022-07-04). 
  2. ^ Abeer George Ghuneim: square tracing algorithm. [2021-12-28]. (原始内容存档于2022-03-25). 
  3. ^ Abeer George Ghuneim: The Radial Sweep algorithm. [2021-12-28]. (原始内容存档于2021-12-28). 
  4. ^ Abeer George Ghuneim: Theo Pavlidis' Algorithm. [2021-12-28]. (原始内容存档于2021-12-28). 
  5. ^ Vector Algebra Based Tracing of External and Internal Boundary of an Object in Binary Images, Journal of Advances in Engineering Science Volume 3 Issue 1, January–June 2010, PP 57–70 [1]页面存档备份,存于互联网档案馆
  6. ^ Graph theory based segmentation of traced boundary into open and closed sub-sections, Computer Vision and Image Understanding, Volume 115, Issue 11, November 2011, pages 1552–1558 [2]页面存档备份,存于互联网档案馆