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I have a question that seems simple, but I cannot come up with the right answer.

Suppose you have a square with sides 2 (xrange[-1:1], yrange[-1:1])

Further suppose that there are equal number of vertical, horizontal and diagonal (exactly 45 degrees) lines of various lengths inside the square.

Now draw a square inside with sides 1 (xrange[-0.5:0.5],yrange[-0.5:0.5]).

The goal is to find the overall statistics of line orientation in the bigger square from looking at the line statistics inside smaller square.

I wrote a simple program to count the number of lines inside the square for each type of orientation, and found that there are always slightly more diagonal lines(vertical and horizontal are about the same).

When I change the sample space, lets say to something like a rectangle of width 2 and height 1 (xrange[-1:1] yrange[-0.5:0.5]) I get more vertical counts than horizontal counts with diagonal count in between.

From these results I calculate the average orientation of lines for different sample spaces and get different answers (so it doesn't give me the right average orientation of the lines in the larger square).

What I am currently thinking is adding a component of "weight" in certain directions when calculating the average, so that no matter what shape the sample space is, the weighted average will approximately be the same.

Now my question is, how would you determine this "weight"?

I've tried simple things like the distance from the center to the edge of the sample space but it didn't work.

Anyone have any ideas or experience with this kind of thing?

Thank you so much!

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# Orientation of lines?

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