How to extract boundaries and calculate curvatures in biological data without doing it manually?

I need to calculate the curvature of a fluorescently labeled membrane for all points on its periphery. (Please take a look at the image below).
I found Kappa plugin in Fiji that may meet this purpose but I have a problem using it.
I imported my ND2 image-series data and selected my region of interest manually, and the spline curve appeared on what I drew manually, while I expected it to detect the boundaries of membrane inside that region.
Does this plugin capable of doing so?
If not, I have the boundaries of my data from my costume-made Matlab code; Can I import the boundaries from matlab, then implement Kappa algorithm on it?

Does anyone have any suggestions?
Thanks in advance for any help you cab provide. :pray:

pic(2)|500x500

PS. I guess it may help to mention @hadim (through wandering into the forum! :grinning:).

You may have a look at the ImageJ-plugin Contour_Curvature.

From this binarized version of your sample image
binObject.tif (69.6 KB)
and with the default parameters of the plugin, I get the curvature plot:

(The smoothed contour appears overlayed to the binary image.)

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Thank you @notQRV. I tried it, it sounds cool!
The only problem is how to calculate the error. I think I should minimize the error by varying the two parameters that Contour_Curvature plugin uses. Do you have any idea about it?
Maybe one way is to import a circle of a certain radius, with the same resolution as this image, and see how different would be the curvature from its absolute value.

By the way, your binary image looks different from what I made in Matlab and ImageJ. Would you please let me know what you have done to obtain that binary image?
Thanks very much again for your help. :slight_smile:

I have no idea what you mean by error.
Do you mean that without smoothing there should be no error?
If so, apply no smoothing.

Generally, the degree of contour smoothing should be defined. In the present case your requirements are not defined. Consequently, this question is to be answered by you. The smoothing depends on the choice of the first parameter and the mechanism is explained in the ReadMe document.
(The second parameter has nothing to do with the smoothing. Please try to understand the documented description.)

You could do it but I have no idea how it would help you with the real data (your images).

The sample image was thresholded using the default thresholding scheme of ImageJ.