How to layer movie clips with black backgrounds in compositor? I am using Blender 2.76.  

I want to layer this movie clip:


over this one:


So far this is what I have:


using this set of nodes:


I set "Dilate/Erode" to -100 to achieve this effect.  The compositor takes about two minutes to create the image.  I would prefer the top image be completely opaque rather than slightly translucent.  

I am wondering, is there a better way to achieve the effect I am looking for?  Is there a method that will not require two minutes to composite one frame?

Thank you! 

Edit:

This set of nodes solved the problem, thanks to Troy_S:
 

Edit #2:

I tried the "Math" version but it did not work properly.  I am hoping Troy_S will let me know how to correct my error:
Two ways spring immediately to mind, assuming zero emission backgrounds:


Take the output of the image and roll it through a node to get the maximum value.
Set Alpha on the image from the result from 1.1.
Use a generic alpha over and done.


For a more abstract glowy vibe:


Take the output of the image and roll it through a colour to BW node.
Set Alpha on the image from result from 1.1
Use a generic alpha over and done.


The former is a generic alpha over on imagery with zero emission background. The latter is a generic alpha over, but will result in some values being semi-additive akin to fire / candle flames.