List of points in the shape of rectangles - which point is the corner?

I have thousands of points (x,y,z) that make up 4 distinct rectangles. How can I find the 4 corners of each rectangle?

i.e. x=[]; y=[]; z=[]; & scatter3(x,y,z) shows a couple rectangles (randomly oriented) densely made of points. I want to know the x,y,z of the corners. I attached a screenshot of the graph and the M-File.

These rectangles are not touching, and we don't know what points belong to what rectangle.

Answer 1

[Image Analyst]

Do the rectangles overlap?

Do you know which rectangle each point belongs to? Or do we have to figure that out, like via kmeans() or some other clustering method?

You forgot to attach your data file, code to read it in, and a screenshot. Can you do so, to make it easier for people to help you?

Once you know which rectangle the points belong to, then you can John D'Errico's minboundrect() to find the corner points. http://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects

[Brandon]

I have edited my question to answer these questions, and also attached files. I will read up on these methods you've pointed out. Much appreciated!!

[Image Analyst]

The .fig file can't be viewed in the browser. I ran the m-file and created a screenshot and added it to your original post.

Another question. The points along z show that the points are not all in a plane for a specific rectangle. They're in a 3-D cloud/cluster. Can we assume you want the bounding x,y coordinates, like we pretend all the z values are the same for a given rectangle? This is fairly easy. If we need to assume that the rectangle could be oriented at any crazy bizarre angle in 3-D then it gets a lot harder.

[Image Analyst]

See my shape recognition demo, attached. It shows you how you can get the vertices of shapes. I'd do something along those lines. You can do it with points - it doesn't have to be an image - just do the same concept.

[Brandon]

You are right in these are not all in the exact same plane. The z varies throughout the "cloud" as the rectangle is at a slant. The rectangles are all close to what is seen in the example (they are generated from 3D scanning).

It took a day or so but I used kmeans and John D'Errico's minboundrect() to accomplish this is 2D. I have now translated everything into 3D, except for the minboundrect(). I will tackle that next! If this becomes too daunting I will look into your shape recognition demo. Thanks again Image Analyst.