OpenCV中minEnclosingCircle的意外结果 [英] Unexpected results of minEnclosingCircle in OpenCV

问题描述

我最近使用了OpenCV(2.4.2)的minEnclosingCircle函数，因为我需要测量一点的直径.

I have recently used the function minEnclosingCircle of OpenCV (2.4.2) because I needed to measure the diameters of a blob of points.

过了一会儿，我意识到结果不正确，所以我决定编写一个小的例程来计算一组非常小的点的直径.

After a while I realized that the results were not correct, so I decided to write a small routine that calculates the diameters of a really small set of points.

我针对以下功能测试了该功能:

I tested the function against:

• 1个单点点
• 连续2-4点
• 仅由4个角点组成的不同大小的正方形

在下表中，您可以看到我的测试结果:

In the table below you can see the results of my tests:

Note         Diameter           Center                                         Points
1x1             2.000       (1.0, 1.0)                                       [[1, 1]]
2x1             2.000       (1.0, 1.5)                               [[1, 1], [1, 2]]
3x1             2.060       (1.0, 2.0)                       [[1, 1], [1, 2], [1, 3]]
4x1             3.090       (1.0, 2.5)               [[1, 1], [1, 2], [1, 3], [1, 4]]
2x2             2.000       (1.5, 1.5)               [[1, 1], [1, 2], [2, 1], [2, 2]]
3x3             2.913       (2.0, 2.0)               [[1, 1], [1, 3], [3, 1], [3, 3]]
4x4             4.370       (2.5, 2.5)               [[1, 1], [1, 4], [4, 1], [4, 4]]
6x6             7.283       (3.5, 3.5)               [[1, 1], [1, 6], [6, 1], [6, 6]]
8x8            10.196       (4.5, 4.5)               [[1, 1], [1, 8], [8, 1], [8, 8]]
9x9            11.653       (5.0, 5.0)               [[1, 1], [1, 9], [9, 1], [9, 9]]
16x16          21.850       (8.5, 8.5)           [[1, 1], [1, 16], [16, 1], [16, 16]]
10x10          13.110       (5.5, 5.5)           [[1, 1], [1, 10], [10, 1], [10, 10]]
100x100       144.207     (50.5, 50.5)       [[1, 1], [1, 100], [100, 1], [100, 100]]
1000x1000    1455.183   (500.5, 500.5)   [[1, 1], [1, 1000], [1000, 1], [1000, 1000]]

我已经看到该函数不会返回小于1的半径，因此我得到的最小直径为2.0.

I have already seen that the function does not return a radius smaller than 1, so the minimum diameter I get is 2.0.

除此之外，该函数总是返回比我期望的半径大的半径. 例如，10x10正方形的半径大约为12.726，而不是13.110. 误差随着正方形的大小而增加:对于1000x1000的正方形，我期望的是1412.5而不是1455.

Apart from that, the function is always returning a radius bigger than I would expect. For instance the 10x10 square would have a radius of about 12.726 instead of 13.110. The error increases with the size of the square: for a square of 1000x1000 I would expect 1412.5 instead of 1455.

实际上，我意识到相对误差始终约为3％.

Actually, I realized that the relative error is always about 3%.

我该如何解释这种奇怪的行为?

How can I explain this strange behavior?

推荐答案

我尝试使用另一个名为

I tried to solve the same problem using another library called Miniball.

用迷你球获得的结果是正确的.在这一点上，我猜想minEnclosingCircle中使用的算法包含一些错误.

The results obtained with Miniball are correct. At this point I guess that the algorithm used in minEnclosingCircle contains some error.

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