I\'m trying to write a ridge detection algorithm, and all of the sources I\'ve found seem to conflate edge detection with ridge detection. Right now, I\'ve implemented the Canny
Maybe you need to think in terms of cleaning up the line you already have, rather than a Canny-like edge detection. It feels like you should be able to do something with image morphology, in particular I'm thinking of the skeletonize and ultimate eroded points type operations. Used appropriately these should remove from your image any features which are not 'lines' - I believe they're implemented in Intel's OpenCV library.
You can recover a single line from your double line generated using the Canny filter using one dilate operation followed by 3 erodes (I tried it out in ImageJ) - this should also remove any edges.