Does "detecting the edges" mean "detecting the approach"?

Not detecting the edges in this case means detecting the outline of a possible threat by detecting the visual edges of the object of concern from the visual background.

I don't think so. It sounds like they are describing the automatic process that our brains use to take raw light data provided by our eyes and transform it into an understanding of what is in front of us.

I think "detecting the edges" is intended literally. Some part of the brain determines that all of the incoming photons from a certain area represent one single object (later to be identified as a tiger), and that the incoming photons from elsewhere do not represent that same object.

Preventing the brain from recognizing the outline of a disguised object is a big part of how camouflage works.