(a) We merged the photon map with a ray tracer. Can you think of how to merge it with a path tracer instead?
(b) The photon mapper stops pushing around photons after some maximum depth; that introduces a bias. How? For a photon map that allows only n bounces, construct a scene where the resultant radiance estimate is drastically wrong, no matter how many photons you send into the scene.
(c) Can you take the idea from the path tracer-"just continue tracing until things stop"-and use it in the propagation of photons? Will it solve the problem with the scene you constructed in part (b)?