It can be done using an external module called lscallproftree

This article explains how: CherryPy - CacheGrind

With my resulting code looking like so:

...
if profile:
    import cProfile
    import lsprofcalltree

    profileFileName = 'Profiles/pythonray_' + time.strftime('%Y%m%d_%H%M%S') + '.profile'

    profile = cProfile.Profile()
    profile.run('pilImage = camera.render(scene, samplePattern)')

    kProfile = lsprofcalltree.KCacheGrind(profile)

    kFile = open (profileFileName, 'w+')
    kProfile.output(kFile)
    kFile.close()

    profile.print_stats()    
else:            
    pilImage = camera.render(scene, samplePattern)
...

If anyone knows a way to do this that doesn't require an external (ie. not shipped with Python) module, I'd still be very interested to hear about it.

3 differents ways to profile your code and visualizing results in KCachegrind/Qcachegrind:

I - CPROFILE

1 - Profile myfunc() from ipython

import cProfile
filename = 'filename.prof'
cProfile.run('myfunc()', filename)

2 - Convert your file to a usable kcachegrind file in your shell

sudo pip install pyprof2calltree
pyprof2calltree -i filename.prof -o callgrind.filename.prof

3 - Open callgrind.filename.prof in kcachegrind

II - EMBEDDED CPROFILE

1 - Profile few lines in your code.

import cProfile
filename = 'filename.prof'
pr = cProfile.Profile()
pr.enable()
# ... lines to profile ...
pr.disable()
pr.dump_stats(filename)

2 - Convert your file to a usable kcachegrind file in your shell

sudo pip install pyprof2calltree
pyprof2calltree -i filename.prof -o callgrind.filename.prof

3 - Open callgrind.filename.prof in kcachegrind

III - YAPPI

1 - Profile myfunc() from ipython or from your code

import yappi
filename = 'callgrind.filename.prof'
yappi.set_clock_type('cpu')
yappi.start(builtins=True)
myfunc()
stats = yappi.get_func_stats()
stats.save(filename, type='callgrind')

2 - Open callgrind.filename.prof in kcachegrind

If what you're actually trying to do is see what parts of your code could be optimized for speed, and you can randomly pause it in the debugger, this method works. It may be surprising, but you don't need very many stackshots.