Comment by logicallee | Hacker News Reader

Comment by logicallee | Hacker News Reader

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could you elaborate on where the symmetry breaks down?

From your comment and another one here, it seems to be the case that actually some of the photons that don't hit the sensor still affect the image (either that, or you can't get back to the source starting at the sensor for some of the photons). In other words, if a light source emits a trillion photons everywhere in the room, and your sensor (the idealized camera) catches ten million photons, then it's not strictly equivalent to trace back the ten million maths to the light source, and ignore the ones that didn't make it to the idealized camera.

If it were equivalent, you wouldn't need "photon tracing and ray tracing" or bidirectionality.

But I'm struggling at where the symmetry breaks down, since it seems that tracing a path back from the sensor along the same angles should produce the same result as tracing it forward from the light source - for the photons that directly or indirectly (after a certain number of bounces or passing through the materials) make it to the idealized camera.

But the ones that don't make it to the idealized camera - how can they still affect the frame? Or (equivalently), when is it the case that you can trace it forward to the camera but not backward from the camera?

Why do you need bidirectionality? Where does the symmetry break down?

When you do photon tracing, you begin with beams of known intensity, wavelength, direction because you are aware of the light source. That combines with everything else that hits the sensor to give the image.

When you do ray tracing, you don't immediately know if 10 million photons were captured. You know how many rays you are going to send based on the resolution of the image. This also means there's issues with say light coming from narrow apertures because you limit yourself to a finite number of rays.

If you use photon tracing and a light source sends 10 million photons and 70,000 are absorbed that's 70,000 data points to define the image which may be plotted on a 200x200 canvas. If you use ray tracing with a 200x200 canvas you will have the same size of image, but only get 40,000 samples. Even if you expand the size of the canvas, there may be some photons which can reach the camera but whose path the ray tracer can't reach.

For instance, say some photons hit the camera at pixel x-coordinates 10.0003 to 10.0005 through a fine aperture.

This will illuminate the camera in a photon tracing simulation. The ray tracer will not capture that photon unless its resolution were 10,000 times higher. The ray tracer will trace back from 10, 11. It can't do every intermediary step. The photon tracer can account for those circumstances.

A simple case: the sun illuminating a large white room through a small window. The light creeps all over the room, not just at the direct illuminated spot, as you'd expect If you were to do a simple camera-trace.

The issue at hand is: we don't experience it, but light behaves in a thermodynamic (dynamic) equilibrium way. You don't see the transients, because the equilibrium takes nanoseconds to converge, but when you turn on a light all your room is exchanging photons until it settles at a rate where everywhere is receiving as much as it's irradiating plus what's wasted as heat, and the total heat is equal to the energy coming through the light sources. Finding those values is solving the so called light transport equation -- and this clearly requires probing geometrical information from all over the place.

In the sunlit room case, all that light is a) heating the room and b) going outside. Now let me try to build a physical model based on your intuition: this equilibrium dynamic depends on the rate of absorption/reflection of each surface. If you have experience with EE, the room is essentially a resonator, where walls are reflecting some and absorbing some until it's absorbing as much as there is light coming in. The less absorbing the walls are, the greater the Q factor of the resonator is: the light is going to bounce a lot and build intensity before it gets absorbed. This is why dark walled rooms are so dramatically, well, darker than white rooms -- the Q factor is not bounded. If your walls were perfect mirrors the intensity would build up with time to +inf.

With bi-directional path tracing it works something like this:

  * trace a photon from the light source with x bounces
  * trace a ray from the camera with x bounces

Now the end points of those traces are not connected but you can calculate the probability that they can 'see' each other. You can use this calculation for the light transport from the light source (photon) to the camera (pixel).

Edit: maybe this image will make it clear: http://lebedev.as/web_images/historyGlobal/15.png

The 'deterministic step' connects the raydiance from the light to the pixel.

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