VolumeRendering

Pre-Integration

← Ring Artifacts | ● | Preintegration Example →

As so called slab is defined to be the volume enclosed between two neighbouring slices.

Analysis: To account for the ring artifacts, the exact line integral bteween two sampling points on the slab has to be calculated. In particular the self-absorption of the self-emission within the slab needs to be accounted for.

Proposition: Scalar function is assumed to be linear between two sampling points.

$ s_l(x) = s_f + \frac{x}{l}(s_b-s_f) $

Then the ray integral can be written as:

$ I' = I \cdot e^{-\int_0^l \rho(s_l(t)dt} + \int_0^l e^{-\int_0^t \rho(s_l(u)du} \kappa(s_l(t))\rho(s_l(t)) dt $

Observation: The ray integral between two points does only depend on $s_f$, $s_b$ and $l$.

Under the assumption that l=const for a constant slab thickness, the ray integral is a 2D table with coordinates $s_f$ and $s_b$. This table can be precomputed by integrating the TF between $s_f$ and $s_b$. This procedure is called pre-integration (Röttger, Kraus et al. 2000).

← Ring Artifacts | ● | Preintegration Example →

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