Estimating the perimeter of irregular shape

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.

Answer 1

[Nicole Peltier]

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]

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);