How to determine curve points in OpenCV contours

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Hello everyone,

For my image processing project i need to find curve points in a contour.

In the example image shown below, detected contour is shown in Red. Now i need to find the curve points/coordinates (indicated with blue arrows) on horizontal and/or vertical axis.

http://imageshack.com/a/img540/7162/3NEzhC.jpg[^]

The curves may not necessarily be perfect ellipses.

Can anyone please let me know a good approach to do so.
Some reference code block would be much appreciated but an explanation alone would also be helpful.

Posted 2-Aug-15 1:15am

Abhishrek

Updated 3-Aug-15 2:51am

v4

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Comments

Afzaal Ahmad Zeeshan 2-Aug-15 7:29am

That is even algorithm-less problem. Only the algorithm that generates the shape would be able to find a solution. Do you have that?

Sergey Alexandrovich Kryukov 2-Aug-15 8:06am

Exactly. The inquirer has to show us the code sample performing the recognition, as simple as possible.
—SA

Abhishrek 2-Aug-15 7:35am

Thanks for the comment, but no algorithm is generating is the shape. Contours are extracted from life time images.
And, there can be some algorithms to do so. One lousy trick can be to use GetConvexityDefacts() then using "defect.StartPoint" & "defect.EndPoint".

Sergey Alexandrovich Kryukov 2-Aug-15 8:09am

This is nonsense. "are extracted" means there is an algorithm. And it follows some model used to represent the recognition result, such as "convex hull". But your example is different. Is it just the set of overlapping ellipsis? But then the problem simply does not exist, you already have all you need. Doesn't it look like you only look at the resulting rendering image, not the data returned by the algorithm?
—SA

Abhishrek 2-Aug-15 8:48am

How i extracted the contour is irrelevant to this question.
The question is related to post processing of contour.
But if you still want to know, i did the regular 3 step contour extracting process.
Color filter -> Threshold Binarization -> Extract contour

Sergey Alexandrovich Kryukov 2-Aug-15 8:54am

What is totally relevant is the resulting data structure.
—SA

Abhishrek 2-Aug-15 9:12am

Resultant DS (of contour) is simply a List of Point. (using emguCV)

Abhishrek 5-Aug-15 6:44am

Hello Mr. Sergey, I have posted a solution, i would be happy if you could you please give some feedback.

Abhishrek 2-Aug-15 8:53am

As i am saying in the question, the contour may not necessarily be of perfect elipses. For example, the image can be of spilled juice, or a pile of tomatoes etc.

Sergey Alexandrovich Kryukov 2-Aug-15 8:56am

Of course, but it could be presented as the union of ellipses. Or some other way...
—SA

Abhishrek 2-Aug-15 8:59am

Approximation in ellipses won't help me. I need exact coordinates. :(

Sergey Alexandrovich Kryukov 2-Aug-15 9:22am

Of what..?
Anyway, do you really need to pull the information from you piece by piece? You are the only one who is interested in some solution.
—SA

Abhishrek 2-Aug-15 9:29am

I am so sorry for not explaining the question properly.
As shown in the pic given in question, i need local maxima and minima (of the graph, i.e. contour) kind of thing.

Sergey Alexandrovich Kryukov 2-Aug-15 15:15pm

If your structure is a list of ellipses, you get it from each ellipse and then select the value from the list, if you want global width/height...
—SA

Kornfeld Eliyahu Peter 2-Aug-15 9:24am

It is possible that even the best fitting curve will not cross event a single point of your contour!

Kornfeld Eliyahu Peter 2-Aug-15 8:20am

How do you extract the contours from images?

Abhishrek 2-Aug-15 8:50am

I did the regular 3 step contour extracting process.
Color filter -> Threshold Binarization -> Detect contour

Kornfeld Eliyahu Peter 2-Aug-15 9:21am

So now you have an array of points for each contour identified by the functions...
And now you want to assign a curve to each contour? Something like this: https://en.wikipedia.org/wiki/Curve_fitting?

Abhishrek 2-Aug-15 9:26am

hmm, thanks. perhaps curve fitting might help.
my question in other words, is to find out local maxima and local minima from a graph (contour) represented as a List of Points.

Kornfeld Eliyahu Peter 2-Aug-15 9:55am

A list of point (contour) is not a graph (in the sense of mathematical equation)! Curve fitting is a process to find a equation that produces a curve where all the points of the contour is at the minimal possible distance from the curve...However it is possible that none of the original points of the curve will be actually on the final curve!!!

Abhishrek 5-Aug-15 6:36am

Hello Mr. Peter, I have posted a solution, could you please give some feedback.

Kornfeld Eliyahu Peter 2-Aug-15 8:00am

How the contours are presented?

Abhishrek 2-Aug-15 9:19am

Contour is presented as a List of Point. of C#

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Abhishrek · Accepted Answer · 2015-08-05T00:33:00

Hello Everyone

I studied a bit and found that taking the first order derivative of the contour (for x and for y separately) can solve this problem.

The first order derivative is used to find Local Maxima and Minima. On the curve points the value of the first order derivative changes from positive to negative (for a peak) and from negative to positive (for a valley).

A basic definition of the first-order derivative of a one-dimensional function f(x) is the difference

df/dx = f(x + 1) - f(x)

To determine valley and peaks (curve points on horizontal axis), only Y value of the contour points is required. Similarly to determine curve points on vertical axis, only X value of the contour points is required.

I am putting here a small part of code used to determine only valleys (Minima) in a contour.

Any suggestion to improve the approach or the code is very much welcome.

C#

int posCntr = 0;
int negCntr = 0;
var diffY = new List<List<int>>();
var diff2Y = new List<List<int>>();
var diffSeq = new List<List<int>>();
// Process each detected contour
for (int n = 0; n < validContours.Count; n++)
{
    posCntr = 0;
    negCntr = 0;
    diffY.Add(new List<int>());
    diffSeq.Add(new List<int>());
    for (int i = 0; i < validContours[n].Total - 1; i++)
    {
        // Taking first derivative of contour
        // df/dy = f(y+1) - f(y);
        diffY[n].Add(validContours[n][i + 1].Y - validContours[n][i].Y);
        // count continuous positive and negative values and add them to a list
        // list will have consecutive positives, negatives, positives, negatives, ...
        if (diffY[n][i] >= 0)
        {
            posCntr++;
            if (negCntr != 0)
            {
                diffSeq[n].Add(negCntr);
                negCntr = 0;
            }
        }
        else //if (diffY[n][i] < 0)
        {
            negCntr++;
            if (posCntr != 0)
            {
                diffSeq[n].Add(posCntr);
                posCntr = 0;
            }
        }
    }
    if (negCntr != 0)
    {
        diffSeq[n].Add(negCntr);
        negCntr = 0;
    }
    else if (posCntr != 0)
    {
        diffSeq[n].Add(posCntr);
        posCntr = 0;
    }
}
int cntr;
for (int n = 0; n < validContours.Count; n++)
{
    cntr = 0;
    for (int i = 0; i < diffSeq[n].Count - 1; i = i + 2)
    {
        // Check if the consequtive pos, neg seq counts are above a threshold level
        // if they are, means we have found a Minima
        if (diffSeq[n][i]     >= Constants.CURVE_SZ && 
            diffSeq[n][i + 1] >= Constants.CURVE_SZ)
            Console.WriteLine(validContours[n][cntr + diffSeq[n][i]].ToString());
        cntr += diffSeq[n][i] + diffSeq[n][i+1];
    }
}