fitting rectangle through data points

Let's say I have the data as shown in OXY plane(Here, I show 2 examples):

How can I fit the rectangle through data:

Answer 1

[darova]

If your data always has V form (look like triangle). Tree corners can be found. Find farthest corners using pdist2()

Use wikipedia formula to find the 3rd corner of a triangle (wiki)

Divide points into 2 groups. If distance point-corner smaller than radius:

Use polyfit() to calculate coeffiecients of line. What if angle between calculated lines is not 90 degree?

[ha ha]

Thanks @darova for good idea.

But I would like to consider for general case( section may have 2 sides, 3sides, or 4sides).

Because in general, I don't know my data contain 2, 3 (as my illustration photo) or full 4 sides of square(rectangle) shape. Do you have any idea for general case?

[Image Analyst]

Do a web search for "Minimum bounding perimeter MATLAB"

[darova]

Use pdist2() to find farthest corners. Draw a line from those points. Find another corners

Divide points into 4 sets using some tolerance distance to lines

Apply polyfit() to each set

It's the best i can

Answer 2

[Image Analyst]

What I would try first is to use principal components analysis ("PCA") to identify the two axes. Use pca() if you have the stats toolbox. Then you can fit lines with polyfit() going through the points along each PC. Use the points at the limits to determine where the lines start and stop. Sorry, no I don't have code that does this already - I'd have to develop it just as you would.

Another method you might also try is RANSAC.

[ha ha]

Thanks @Image Analyst for your kind.

Can you show example code of rectangle fitting using pca? I try to follow your advice but I am not totally understand.