In photon mapping, the total flux of an emitter is split into many small flux packets and then these packets are traced. And while packets are gathered for density estimation, total flux of gathered packets are divided by projected area of searching sphere to approximate irradiance assuming local coherence. I guess such projected area is the footprint of mutual visibility of emitter and sensor, but what is the relationship between it and corresponding packets' footprint (area contributes to these packets) on emitter? In the limiting case tracing flux is equivalent to tracing radiance as long as more packets being fired, and such footprint tends to shrink. However, it seems to be counterintuitive since only radiance can be traced due to its invariance through vacuum. Can I regard these packets as bins and the photon map as a histogram so we can do nonparametric density estimation?
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