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\title{\textbf{Using Photon Maps and Irradiance Cache in Photorealistic Image Synthesis}}
\author{
\textbf{Jaroslav K�iv�nek}\\
\emph{Departement of Computer Science and Engineering,}\\
\emph{Karlovo n\'am. 13, 121 35 Prague, tel.: +420 2 2435 7268}\\
email: \texttt{xkrivanj@fel.cvut.cz}}
\date{}


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\maketitle
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Photorealistic image synthesis involves simulating the transport of
light energy in the scene. At every visible point $\vec{x}$ in the scene, the
value of
\emph{radiance} $L$ reflected to the camera must be evaluated. The equation describing
how reflected radiance depends on the incident radiance is called the
\emph{rendering equation} and has the following form:
\begin{displaymath}
L(\vec{x},\vec{\omega}_r) = L_e(\vec{x},\vec{\omega}_r) +
\int_\Omega L(\vec{x},\vec{\omega})\; f_r(\vec{\omega}_r,\vec{x},\vec{\omega})
\;\cos \theta\; d \vec{\omega}.
\end{displaymath}
It says that the radince $L$ reflected from the point $\vec{x}$ to the
direction $\vec{\omega}_r$ is equal to the self emitted radiance $L_e$ plus
the sum (or integral) of contributions of radiance incoming to the point
$\vec{x}$ from any direction. The interaction of the incoming radiance with
the material is modeled by multiplying its value with the value of the
\emph{bidirectional reflectance distribution function}, denoted $f_r$ in our
formula.

Shortly, the reflected radiance at
a point is expressed by means of the incoming radiance and
material characteristics of the surface being hit by the light ray. The
incoming radiance can be regarded as the radiance reflected from
some other point in the scene. To compute radiance at the other point, the
same method as
for the point directly visible by the camera is used. The same method is used
even for higher order reflections of light.
The recurrence of the rendering equation is apparent and it causes that the
complexity of its solution is very high.

There is a lot of techniques for solving the rendering equation, but the
majority of them is not able to simulate the light interaction with any kind
of surface material (diffuse/glossy/specular/refractive). Nowadays, the most
popular techniques solve the rendering equation using the Monte Carlo
integration. Application of pure Monte Carlo to solve the integral in the
rendering equation is very general --- it can handle any material, but the
problem is the speed of convergence, which is proportional to the square root
of the number of used
samples. Therefore, special techniques are used to simulate particular
kinds of light--material interactions.

The most successful method for photorealistic image synthesis is undoubtfully
the ray tracing, but it ignores multiple diffuse
reflections of light and so called
caustics, which are the patterns of light specularly reflected or refracted and
then seen on the diffuse surface (for example the light focused by the lens).

In our work, we extended existing raytracer with capability of simulating both
effects missed in classical ray tracing. We used \emph{Irradiance Cache}
\cite{Ward88} to simulate multiple diffuse reflections and \emph{Photon Maps}
\cite{Jensen96c} to simulate caustics and full global illumination of the
scene. We combined Photon Maps and Irradiance Cache as advised in
\cite{Jensen96c}. The details on what Irradince cache and Photon Maps are and
how are they used can be found in our work \cite{MojeDiplomka}. The main
advantages of Photon Maps are:
\begin{itemize}
\item[-] They can handle scenes with objects with all combinations of material
properties.
\item[-] Photon Maps are independent from the scene geometry and do
not put any restrictions on the models of the objects.
\item[-] Compared to other methods, they are relatively fast.
\item[-] The implementation of the Photon Maps does not require any changes of
crucial importance in the architecture of existing raytracer.
\item[-] They are easy to parallelize.
\end{itemize}
Photon Maps have of course some drawbacks:
\begin{itemize}
\item[-] A lot of memory (tens of MB) is used in scenes with complex
illumination.
\item[-] The algorithm behaviour depends on many parameters which has to be
tuned for every scene by user.
\end{itemize}

In our work we solved some problems not addressed byt author of
\cite{Jensen96c}. It was the problem of estimating the number of ligh
samples needed to fill the Photon Map with user specified number of photons.
We also presented a novel method for reconstructing the value of radiance
from the photon map which preserves better the real shape of the caustics
than the method used in \cite{Jensen96c}.

To test our algorithms, we also implemented new types of point light sources
(two types of spot lights) and area light sources, that are not easy to
simulate using ray tracing.

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