# Estimating the perimeter of irregular shape

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SAMUEL AYINDE on 22 Sep 2018
Commented: Image Analyst on 22 Sep 2018
Please, how can I estimate the perimeter of the shape in this picture, given the x and y coordinates of all the grid points of the geometry. I need a matlab code that will give me a good estimation of the perimeter. Thank you so much.

Nicole Peltier on 22 Sep 2018
My answer assumes that the starting point is the first and last item in the x and y vectors, so if that's not your case, you'll have to add the first point to the end.
x_diff = diff(x);
y_diff = diff(y);
segment_lengths = sqrt(x_diff.^2+y_diff.^2);
perimeter = sum(segment_lengths);
This could be cut down to one line of code, but I wrote it out so you can see each step. You calculate the differences in x and y between each point. The length of each line segment can be calculated according to the Pythagorean theorem (x_diff^2 + y_diff^2 = segment_length^2). The perimeter is the sum of the line segment lengths.
If you're curious, this is how the same code would look when condensed to one line:
perimeter = sum(sqrt(diff(x).^2+diff(y).^2));
Hope this helps!
Image Analyst on 22 Sep 2018
If you also want to include the length from the last point to the first point, you'll need to tack that on:
x2 = [x, x(1)];
y2 = [y, y(1)];
x_diff = diff(x2);
y_diff = diff(y2);