I found that we can use shader programs even with wire frame fill mode; I am not sure whether or not it can be faster than solid fill mode. Therefore I could implement shaders that generate a derivative image directly with rendering wire-frame model.
I like to show some of screen shots.
The first image is the scene from light perspective:Then, the depth map is generated. The depth values are stored at Red and Green channels.
Note that the leg parts of the elephant looks like blurred. It hasn't been blurred but because their derivative values are small. Thus I can expect that contact points between the disk and the elephant will have sharp shadow.
It fetches five times at quarter resolution and I didn't see any false-positive edges. Since the derivative values are 8bit data, they can be retrieved by linear filter.