When we defined the Lambertian BRDF, it was defined as the albedo divided by pi. However, here, we say that the norm of the pseudo-normal is the albedo, which seems to drop the pi term. Can the entire fraction (after dividing by pi) also be considered an albedo or would we also need to multiply rho by pi here to get the actual albedo?
mpotoole
The albedo $\rho$ is defined as the ratio of energy reflected by an object, so technically its value should be between 0 and 1. So a Lambertian BRDF should be defined as the ratio between albedo and $\pi$.
You're right though---we are dropping the $\pi$ constant here, which makes these equations technically incorrect / off by a constant scalar. In practice, this is not that big a deal, because we're usually interested in the relative albedo values across the image (rather than the absolute albedo values).
spethani
Is I supposed to be I_1, I_2, I_2 here, or should the last element be I_3? A little confused on where the second I_2 is coming from.
When we defined the Lambertian BRDF, it was defined as the albedo divided by pi. However, here, we say that the norm of the pseudo-normal is the albedo, which seems to drop the pi term. Can the entire fraction (after dividing by pi) also be considered an albedo or would we also need to multiply rho by pi here to get the actual albedo?
The albedo $\rho$ is defined as the ratio of energy reflected by an object, so technically its value should be between 0 and 1. So a Lambertian BRDF should be defined as the ratio between albedo and $\pi$.
You're right though---we are dropping the $\pi$ constant here, which makes these equations technically incorrect / off by a constant scalar. In practice, this is not that big a deal, because we're usually interested in the relative albedo values across the image (rather than the absolute albedo values).
Is I supposed to be I_1, I_2, I_2 here, or should the last element be I_3? A little confused on where the second I_2 is coming from.
Good catch; it should be $I_1, I_2, I_3$.