Detect quadrangle from grayscale image

Question

I am looking for a way to detect a four-sided image based on grayscale images.

The actual solution I made is based on HoughLines and has two problems:

• Since this is a parametric method, small changes in the input image give me two different rectangles.
• The outputs are not accurate because the borders of the rectangle in the input image are thick.

Can you recommend me another way to do this? I am really looking at this article , but it seems to be a slow method.