How to find the length of ellipse portion?

I plotted an ellipse interactively by using imellipse function. After that I select two points on the ellipse interactively by mouse ginput. Is there any method to find out the shortest length along ellipse boundary between these two selected points. Thank You

[Image Analyst]

Analytically with the theoretical equation of arc length along the ellipse, or numerically with a digital image?

[John BG]

don't you need at least 3 points? because even if you say 'shortest length' since the 2 points you choose are random they define a set of ellipses, not just one ellipse

[Image Analyst]

I think he still has the coordinates of the ellipse, and just needs to identify which of those points are closest to the two points chosen by ginput. Like:

imshow('cameraman.tif');
% User draws curve on image here.
hEllipse = imellipse();
% Get the xy coordinates of where they drew.
xyWidthheight = hEllipse.getPosition
% Create a binary image ("mask") from the ROI object.
binaryImage = hEllipse.createMask();
boundaries = bwboundaries(binaryImage);
x = boundaries{1}(:,2);
y = boundaries{1}(:,1);
hold on;
plot(x, y, 'r-', 'LineWidth', 2);
xyPoints = ginput(2)
distances1 = sqrt((x - xyPoints(1,1)).^2 + (y - xyPoints(1,2)).^2)
distances2 = sqrt((x - xyPoints(2,1)).^2 + (y - xyPoints(2,2)).^2)
[dist1, index1] = min(distances1)
[dist2, index2] = min(distances2)

[John D'Errico]

It sounds to me as if given an ellipse, and two points on the ellipse, you need to know the distance between those points along the ellipse. Of course, you can go either way around. So, this just seems a problem of computing the arclength of the corresponding elliptical arcs in each direction, then take the shorter arc.

Or, maybe the issue is, given a pair of selections by mouse clicks, to first find those points on the ellipse. I'm not totally sure about your goals.

Or, do you not actually have the equations of the ellipse. It looks like imellipse does not return the parameters of the created ellipse. Sorry, but IMHO, thats a bad idea. High quality code SHOULD always return information like that as a return argument! (Sigh. Yes, I'm insane in that respect.) Oh well, maybe in the next release it will.

[Image Analyst]

The getPosition returns the left, top, width, and height, from which you can get the analytical formula if you want it. Using bwboundaries(), you can get the boundary coordinates on a digital image and then use the Pythagorean theorem to run along the boundary from one point to the other, summing up distances as you go. Maybe that's good enough. It would be good to know the whole picture -- the larger context of why this is thought to be needed.

[rupam baruah]

numericaly with the digital image.

[rupam baruah]

@image analyst

By using the above code given by you, how can we calculate the arclength between the two ginput points. And how can we get the analytical formula of the ellipse from getPosition return value of the ellipse.

Thanks