Heroku typically uses small virtual machine instances, so depending on just how heavy your processing is, it may not be the best choice of architecture. However, if you do use it I would do this:
Use a background task gem to do your processing. Have this running on a separate process (called a worker rather than a dyno in Heroku terminology). Delayed Job is a tried and tested solution for background tasks with a wealth of online information relating to integrating it into Heroku, but there are newer ones like Sidekiq which use the new threading system in modern versions of Ruby. They would allow everything to be done in the dyno, but I would say that it would be useful to keep all background processing away from the webserver dynos, so Delayed Job (or similar) would be fine.
As for integrating C/C++, I haven't needed to do this as yet. However, I know it is possible to create gems that integrate C or C++ code and compile natively. As long as you're using ruby rather than JRuby, I don't think Heroku should have a problem with them. There are other ways of accomplishing this, look at SO questions specifically about this topic, such as
How can I call C++ functions from within ruby
It seems that you need to create an extension, then create a gem to contain it. These links may or may not help.
http://www.rubyinside.com/how-to-create-a-ruby-extension-in-c-in-under-5-minutes-100.html
http://guides.rubygems.org/gems-with-extensions/
I recommend making a gem as I think it may be difficult to otherwise get libraries or executables on to a Heroku instance. You can store the gem in your vendor directory if you don't want to make it public.
Overall I would have the webserver upload to S3 or wherever you're storing the images (this can be done directly in the browser without using the webserver as a stepping stone with the AWS JS API. Have a look for gems to help.)
Then the webserver can request a background task to process the image.
If you're not storing them, things become a little more interesting... You'll need a database if you're using background tasks, so you could pass the image data over to the worker as a blob in the database perhaps.
I really wouldn't do all the processing just in the webserver dyno, unless you're really only hitting this thing very occasionally. With multiple users you'd hit a bottleneck very quickly.
The background process can set a flag on the image table row so the webserver can let the user know when processing is complete. (You can poll for information using JS on the upload complete screen using AJAX)
Of course, there are many other ways of accomplishing this, depending on a number of factors.
Apologies that the answer is vague, but the question is quite open-ended.
Good luck.
