Detect edges between the walls and the floor only

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I'm trying to process the following images from a maze. My Question is about how to process the edges. I'm using OpenCV 2.4 with c++. I'd like to know if there is any way to discriminate the edges between the floor and the wall from the lines painted in the floor?

The floor is black, the walls are white and the lines painted in the floor are white too.

I'm using Canny and HoughLinesP functions to detect and save the lines. But as you can see in the images the program doesn't separate the lines from the edges.