如何获得目标连接组件的边界椭圆 [英] How to obtain the bounding ellipse of a target connect component

问题描述

假设我们有图像中的连接组件如下图所示：

我的问题是如何计算的连接组件的边界椭圆（红色椭圆形的形象）。我已经检查了MATLAB函数 regionprops 和理解MATLAB能怎么办那。我还注意到，OpenCV的类似功能做到这一点 CBlob :: GetEllipse（）。不过，虽然我知道他们是如何通过阅读code获得的结果，其背后的基本理论仍然不清楚我。因此，我想知道是否有一定的标准算法来完成这项工作。谢谢！

编辑：

根据该意见

，我重组我的问题：在图像一刻维基百科中的计算公式最长的轴的角度为

然而，在MATLAB函数 regionprops 时，所述codeS如下：

 ％计算方向。
    如果（uyy＆GT; UXX）
        NUM = uyy  -  UXX +开方（（uyy  -  UXX）^ 2 + 4 * UXY ^ 2）;
        书房= 2 * UXY;
    其他
        NUM = 2 * UXY;
        书房= UXX  -  uyy +开方（（UXX  -  uyy）^ 2 + 4 * UXY ^ 2）;
    结束
 

此实现是与式Wikipedia中不一致。我想知道哪一个是正确的。

解决方案

我试图找出什么是它背后的算法，以及让我可以写我自己的实现它。我发现它在MathWorks公司的博客文章。在意见之一，作者说：

  

regionprops计算所讨论的对象的第二次矩，然后返回椭圆的测量结果与相同第二次矩

和后来的后来：

  

给出的公式是由Haralick和夏皮罗，计算机和机器人视觉体积。 1，附录A，艾迪生韦斯利1992年我做了一个全面的检查通过构建包含与长轴长度为100和短轴长度= 50，和regionprops椭圆图像返回正确的测量结果。

我没有这方面的书，但看来我需要得到它的副本。

Suppose we have a connected component in the image as the following image illustrates:.

My question is how can calculate the bounding ellipse of the connected components (the red ellipse in the image). I have checked MATLAB function regionprops, and understand how MATLAB can do that. I also notice that Opencv has similar function to do that CBlob::GetEllipse(). However, although I understand how they obtain the result by reading the code, the fundamental theory behind it is still unclear to me. I am therefore wondering whether there are some standard algorithms to do the job. Thanks!

EDIT:

Based on the comments, I reorganized my question: in image moment Wikipedia the calculation formula of the longest axis angle is

However, in the MATLAB function regionprops, the codes are as follows:

    % Calculate orientation.
    if (uyy > uxx)
        num = uyy - uxx + sqrt((uyy - uxx)^2 + 4*uxy^2);
        den = 2*uxy;
    else
        num = 2*uxy;
        den = uxx - uyy + sqrt((uxx - uyy)^2 + 4*uxy^2);
    end

This implementation is inconsistent with the formula in Wikipedia. I was wondering which one is correct.

解决方案

I was trying to find out what's the algorithm behind it as well so I could write my own implementation of it. I found it on a blog post of mathworks. In one of the comments, the author says:

regionprops calculates the 2nd-order moments of the object in question and then returns measurements of the ellipse with the same 2nd-order moments.

and later later:

The equations used are from Haralick and Shapiro, Computer and Robot Vision vol. 1, Appendix A, Addison-Wesley 1992. I did a sanity check by constructing an image containing an ellipse with major axis length = 100 and minor axis length = 50, and regionprops returned the correct measurements.

I don't have that book but seems I'll need to get a copy of it.

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