A good approach for detecting lines in an image?

Question

I've written some code that uses OpenCV libraries to detect white lines painted on grass. I need someone's opinion on the approach I used (as I'm sure there's a much better way than mine). Also, the results I'm getting are not as good as I expected because slight variations in the image require tweaking the parameters (and I need to operate on fixed parameters).

My approach so far:

1. Grab image from webcam (and turn into grayscale obviously)
2. Run it through a threshold filter (using THRESH_TO_ZERO mode, where it zeros out any pixels BELOW the threshold value).
3. blur the image
4. run it through an erosion filter
5. run it through a Canny edge detector
6. finally, take this processed image and find the lines using Probabilistic Hough Transform HoughLinesP

Should I change the sequence of the filters?

P.S. I'm not too concerned about processing power; I'm running the HoughLinesP on the GPU B-)

Also, here is a sample image:

The results I'm getting: with canny WITHOUT canny (slightly tweaked parameters)

Any help or guidance would be appreciated! I just have no idea what to do to improve it!

UPDATE After using a really quick skeleton implementation (with TONS of blur) as per the chosen answer, I got this:

Answer 1

I would try to use a skeleton representation of the image. The problem with your canny, here, is that it basically results in two lines because of the width of the line.

Then I would apply the Hough transform on it.

Answer 2

One possible solution is to take all the edge points that you obtain from the canny edge detection and fit a line using linear least sqaures (maybe iterative) on these points. This way you always get a single line that "best fits" the edge points. There is virtually no parametrisation involved with this method.