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Simple Photon Mapping Question

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So I was just reading Jensen's 2004 paper http://portal.acm.org/citation.cfm?id=1103920, A practical guide to global illumination using ray tracing and photon mapping.

My question is how exactly he goes from equation (2.5) to (2.6) on page 25. Equation 2.5 is an integral over the hemisphere, which is approximated using the sum of the photons in the photon map in 2.6.

My question is why is he not dividing by the probability of seeing the photon coming from that direction, in equation 2.6? ie. Why is does he not dividing by p(\omega_p) = 1 / 2Pi?

Equation 2.5:

L_r(x,\omega) = \int_\Omega f_r(x,\omega',\omega) \frac{d^2\Phi_i(x,\omega')}{dA_i}

Equation 2.6:
L_r(x,\omega) \approx \sum_{p=1}^n f_r(x,\omega_p,\omega) \frac{\Delta\Phi_p(x,\omega_p)}{\Delta A}

[Edited by - psastras on July 16, 2010 1:07:04 PM]

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