Hough Transform – Restricting line lengths

In version 3.2 of the Imaging Whiteboard a Line Detector control has been added. The line detection is performed using a Hough transform https://en.wikipedia.org/wiki/Hough_transform . The lines detected are defined by the shortest distance from the origin to the line, and the angle between the x axis and the line connecting the origin to the closest point on the line. Theoretically the lines are infinitely long.

Since we want to be able to restrict the Hough transform to a specified region we want to display the detected lines in that region. Without line length restriction the display would look like:

With lines restricted to the specified region the display correctly looks like:

How is this performed? Every point on a line is defined by:

where r is the distance from the origin to the closest point on the straight line, and θ is the angle between the x axis and the line connecting the origin with that closest point.

So for each line the start and end points must be trimmed to lay on the region perimeter. Each point must be trimmed horizontally and vertically. Horizontal trimming looks like:

if (point.X < region.Left)
{
point.X = region.Left;
point.Y = _centerH – (int)((radius – Math.Cos(thetaRadians) * (region.Left – _centerW)) /
Math.Sin(thetaRadians));
}

if (point.X > region.Right)
{
point.X = region.Right;
point.Y = _centerH – (int)((radius – Math.Cos(thetaRadians) * (region.Right – _centerW)) /
Math.Sin(thetaRadians));
}

Vertical trimming is similar. The _centerW and _centerH values exist because the origin is in the center of the image, but, pixel 0,0 is in the top left corner; adjustment must be made before and after the calculation.