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I have 2D line segments extracted from an image. So i know end point coordinates of them. also, i have some reference 2d line segments. Both line segments are now in vector form. comparing to reference and extracted lines,I have huge amount of extracted lines segments.

What i want to do is to find conjugate line segment for each reference line from my extraction. that is I want to match line segments. But, to reduce the search area i wish to limit it in such a way that by defining a buffer zone around a reference line segment.

(1) My first question is how can i implement this buffer case with c++ as i am lacking with geometric theories.

Note: I dont want to use a bounding box and looking for a rectangular buffer which orient along the reference line.

(2) my second question is, if i know the rectangular buffer limits, then which type of concept should i use to avoid unnecessary searches of line segments.

Actually, I am looking a geometric base method

please do not think this as home work and i am really struggling because of my poor mathematics. thanks in advance.

Please look at the example. if i take bounding box (blue box) unnecessary lines come, if it is a buffer rectangle (red), which is oriented to main reference line (dark black) few lines come.

black line is - reference line and dashed lines are image based extracted lines

enter image description here

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closed as off topic by joriki, Austin Mohr, rschwieb, Quixotic, amWhy Jan 18 '13 at 2:09

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This belongs on one of the sites for computer science. There's a lot of work on algorithms and data structures for dealing with geometric objects like this so as to reduce the search effort, and people on those sites will likely know a lot more about that than people here. –  joriki Jan 17 '13 at 11:53
    
@joriki: I think it is some math which is needed here, not any special data structures. I don't think this would benefit from migration. –  robjohn Jan 17 '13 at 13:47

1 Answer 1

up vote 2 down vote accepted

Given a reference line $\left(\begin{bmatrix}x_1\\y_1\end{bmatrix},\begin{bmatrix}x_2\\y_2\end{bmatrix}\right)$, note that the matrix $$ M=\begin{bmatrix}x_2-x_1&y_2-y_1\\[9pt]y_1-y_2&x_2-x_1\end{bmatrix} $$ rotates and uniformly scales the reference line to a horizontal line since $$ \begin{bmatrix}x_2-x_1&y_2-y_1\\[9pt]y_1-y_2&x_2-x_1\end{bmatrix}\left(\begin{bmatrix}x_2\\[9pt]y_2\end{bmatrix}-\begin{bmatrix}x_1\\[9pt]y_1\end{bmatrix}\right)=\begin{bmatrix}(x_2-x_1)^2+(y_2-y_1)^2\\[9pt]0\end{bmatrix} $$ Once rotated to a horizontal line, the bounding box would be exactly what you want for the red rectangle above. Matching inside the red rectangle should now be a simple matter of bounds checking. That is, simply apply $M$ to all the image lines and reject those that do not fall within the bounds based on the rotated (horizontal) reference line.

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