There's an easy way to encircle the points you want, with a high degree of accuracy.
The areas of the image you want to spot are inflection points with change of derivative sign: geometric vertices.
If we look for high degree of Curvature only, it has to do with the radius only, and very small circles would give false detections.
You are precisely asking for a sudden change of sign of the direction of the trace.
I tried with your original image, that includes a grey trace, but it complicates the processing.
Allow me to show a solution for black traces only:
clear all;clc;close all
do not apply imbinarize here, it removes the grey line
The 2D variance of the images points straight to the areas of interest
ax.DataAspectRatio=[50 50 1];
ax.CameraPosition= [cp1(1) cp1(2) -cp1(3)];
Now with Natan's function FastPeakFind
the coordinates of a 2D surface are readily available, note that the supplied coordinates are interleaved.
[idx,C] = kmeans(pxy,4);
hold all;viscircles(ax1, flip(uint32(C),2),10*ones(1,4),'Color','green')
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