source: trunk/VUT/doc/SciReport/online.tex @ 243

\chapter{Online Visibility Culling}
%*****************************************************************************

\section{Introduction}

 Visibility culling is one of the major acceleration techniques for
the real-time rendering of complex scenes. The ultimate goal of
visibility culling techniques is to prevent invisible objects from
being sent to the rendering pipeline. A standard visibility-culling
technique is {\em view-frustum culling}, which eliminates objects
outside of the current view frustum. View-frustum culling is a fast
and simple technique, but it does not eliminate objects in the view
frustum that are occluded by other objects. This can lead to significant
{\em overdraw}, i.e., the same image area gets covered more than
once. The overdraw causes a waste of computational effort both in the
pixel and the vertex processing stages of modern graphic hardware.
%that is, we render each pixel in the image several times. For many complex
%scenes with high occlusion, the effort wasted on overdraw cannot simply be
%eliminated by the increasing the raw computational power of the hardware.
%This problem becomes even more apparent on recent graphics hardware with
%programmable vertex and pixel shaders: all complex per-vertex or per-pixel
%computations on object get completely wasted if the object is occluded.
The elimination of occluded objects is addressed by {\em occlusion
culling}. In an optimized rendering pipeline, occlusion culling complements
other rendering acceleration techniques such as levels of detail or
impostors.

 Occlusion culling can either be applied offline or online.  When
applied offline as a preprocess, we compute a potentially visible set
(PVS) for cells of a fixed subdivision of the scene. At runtime, we
can quickly identify a PVS for the given viewpoint. However, this
approach suffers from four major problems: (1) the PVS is  valid only
for the original static scene configuration, (2) for a given
viewpoint, the corresponding cell-based PVS can be overly
conservative, (3) computing all PVSs is computationally expensive, and (4)
an accurate PVS computation is difficult to implement for general
scenes. Online occlusion culling can solve these problems at the cost
of applying extra computations at each frame. To make these additional
computations efficient, most online occlusion culling methods rely on a
number of assumptions about the scene structure and its occlusion
characteristics (e.g. presence of large occluders, occluder
connectivity, occlusion by few closest depth layers).

Recent graphics hardware natively supports an \emph{occlusion query}
to detect the visibility of an object against the current contents of the
z-buffer.  Although the query itself is processed quickly using the
raw power of the graphics processing unit (GPU), its result is not
available immediately due to the delay between issuing the query and
its actual processing in the graphics pipeline. As a result, a naive
application of occlusion queries can even decrease the overall
application performance due the associated CPU stalls and GPU
starvation. In this paper, we present an algorithm that aims to
overcome these problems by reducing the number of issued queries and
eliminating the CPU stalls and GPU starvation. To schedule the
queries, the algorithm makes use of both the spatial and the temporal
coherence of visibility. A major strength of our technique is its
simplicity and versatility: the method can be easily integrated in
existing real-time rendering packages on architectures supporting the
underlying occlusion query.

%Using spatial and assuming temporal coherence

\section{Related Work}

With the demand for rendering scenes of ever increasing size, there
have been a number of visibility culling methods developed in the
last decade.  A comprehensive survey of visibility culling methods
was presented by Cohen-Or et al.~\cite{Cohen:2002:survey}. Another
recent survey of Bittner and Wonka~\cite{bittner03:jep} discusses
visibility culling in a broader context of other visibility problems.

According to the domain of visibility computation, we distinguish
between {\em from-point} and {\em from-region} visibility algorithms.
From-region algorithms compute a PVS and are applied offline in a
preprocessing phase~\cite{Airey90,Teller91a,Leyvand:2003:RSF}.
From-point algorithms are applied online for each particular
viewpoint~\cite{Greene93a,Hudson97,EVL-1997-163,bittner98b,Wonka:1999:OSF,Klosowski:2001:ECV}.
In our further discussion we focus on online occlusion culling methods
that exploit graphics hardware.

A conceptually important online occlusion culling method is the
hierarchical z-buffer introduced by Greene et al.~\cite{Greene93a}. It
organizes the z-buffer as a pyramid, where the standard z-buffer is
the finest level. At all other levels, each z-value is the farthest in
the window corresponding to the adjacent finer level. The hierarchical
z-buffer allows to quickly determine if the geometry in question is
occluded. To a certain extent this idea is used in the current
generation of graphics hardware by applying early z-tests of
fragments in the graphics pipeline (e.g., Hyper-Z technology of ATI or
Z-cull of NVIDIA). However, the geometry still needs to be sent to the
GPU, transformed, and coarsely rasterized even if it is later
determined invisible.

 Zhang~\cite{EVL-1997-163} proposed hierarchical occlusion maps, which
do not rely on the hardware support for the z-pyramid, but instead
make use of hardware texturing. The hierarchical occlusion map is
computed on the GPU by rasterizing and down sampling a given set of
occluders. The occlusion map is used for overlap tests whereas the
depths are compared using a coarse depth estimation buffer. Wonka and
Schmalstieg~\cite{Wonka:1999:OSF} use occluder shadows to compute
from-point visibility in \m25d scenes with the help of the GPU. This
method has been further extended to online computation of from-region
visibility executed on a server~\cite{wonka:01:eg}.

%% In
%% parallel to rendering, the visibility server calculates visibility for
%% the neighborhood of the given viewpoint and sends them back to the
%% display host.

%% A similar method designed by Aila and
%% Miettinen~\cite{aila:00:msc}. The incremental occlusion maps are
%% created on the CPU, which takes the CPU computational time but it does
%% not suffer the problem of slow read-back from the GPU.

%Klosowski:2001:ECV

Bartz et al.~\cite{Bartz98} proposed an OpenGL extension for occlusion
queries along with a discussion concerning a potential realization in
hardware. A first hardware implementation of occlusion queries came
with the VISUALIZE fx graphics hardware~\cite{Scott:1998:OVF}. The
corresponding OpenGL extension is called \hpot{}. A more recent OpenGL
extension, \nvoq{}, was introduced by NVIDIA with the GeForce 3 graphics
card and it is now also available as an official ARB extension.

%Both
%extensions have been used in several several occlusion methods
%algorithms~\cite{Meissner01,Hillesland02,Staneker:2004:OCO}.
%\cite{Meissner01}

 Hillesland et al.~\cite{Hillesland02} have proposed an algorithm
which employs the \nvoq. They subdivide the scene using a uniform
grid. Then the cubes are traversed in slabs roughly perpendicular to
the viewport. The queries are issued for all cubes of a slab at once,
after the visible geometry of this slab has been rendered. The method
can also use nested grids: a cell of the grid contains another grid
that is traversed if the cell is proven visible. This method however
does not exploit temporal and spatial coherence of visibility and it
is restricted to regular subdivision data structures. Our new method
addresses both these problems and provides natural extensions to
balance the accuracy of visibility classification and the associated
computational costs.

 Recently, Staneker et al.~\cite{Staneker:2004:OCO} developed a method
integrating occlusion culling into the OpenSG scene graph
framework. Their technique uses occupancy maps maintained in software
to avoid queries on visible scene graph nodes, and temporal coherence
to reduce the number of occlusion queries. The drawback of the method
is that it performs the queries in a serial fashion and thus it
suffers from the CPU stalls and GPU starvation.

%% The methods proposed in this paper can be used to make use of temporal
%% and spatial coherence in the scope of existing visibility algorithms,
%% that utilise a spatial hierarchy. Examples of these are algorithms
%% based on hierarchical occlusion maps~\cite{Zhang97}, coverage
%% masks~\cite{Greene:1996:HPT}, shadow frusta~\cite{Hudson97}, and
%% occlusion trees~\cite{bittner98b_long}.

On a theoretical level, our paper is related to methods aiming to
exploit the temporal coherence of visibility. Greene et
al.~\cite{Greene93a} used the set of visible objects from one frame to
initialize the z-pyramid in the next frame in order to reduce the
overdraw of the hierarchical z-buffer. The algorithm of Coorg and
Teller~\cite{Coorg96b} restricts the hierarchical traversal to nodes
associated with visual events that were crossed between successive
viewpoint positions. Another method of Coorg and Teller~\cite{Coorg97}
exploits temporal coherence by caching occlusion relationships.
Chrysanthou and Slater have proposed a probabilistic scheme for
view-frustum culling~\cite{Chrysanthou:97}.

The above mentioned methods for exploiting temporal coherence are
tightly interwoven with the particular culling algorithm. On the
contrary, Bittner et al.~\cite{bittner01:jvca} presented a general
acceleration technique for exploiting spatial and temporal coherence
in hierarchical visibility algorithms. The central idea, which is also
vital for this paper, is to avoid repeated visibility tests of
interior nodes of the hierarchy. The problem of direct adoption of
this method is that it is designed for the use with instantaneous CPU
based occlusion queries, whereas hardware occlusion queries exhibit
significant latency. The method presented herein efficiently overcomes
the problem of latency while keeping the benefits of a generality and
simplicity of the original hierarchical technique. As a result we
obtain a simple and efficient occlusion culling algorithm utilizing
hardware occlusion queries.


%In this paper we show how to overcome this problem while
%keeping the benefits of exploiting.


The rest of the paper is organized as follows:
Section~\ref{sec:hwqueries} discusses hardware supported occlusion
queries and a basic application of these queries using a kD-tree.
Section~\ref{sec:hoq} presents our new algorithm and
Section~\ref{sec:optimizations} describes several additional
optimizations. Section~\ref{sec:results} presents results obtained by
experimental evaluation of the method and discusses its
behavior. Finally Section~\ref{sec:conclusion} concludes the paper.




\section{Hardware Occlusion Queries}
\label{sec:hwqueries}


Hardware occlusion queries follow a simple pattern: To test visibility
of an occludee, we send its bounding volume to the GPU. The volume is
rasterized and its fragments are compared to the current contents of
the z-buffer. The GPU then returns the number of visible
fragments. If there is no visible fragment, the occludee is invisible
and it need not be rendered.

\subsection{Advantages of hardware occlusion queries}

There are several advantages of hardware occlusion queries:

\begin{itemize}

\item {\em Generality of occluders.} We can use the original scene geometry
as occluders, since the queries use the current contents of the z-buffer.


\item {\em Occluder fusion.} The occluders are merged in the z-buffer,
so the queries automatically account for occluder fusion. Additionally
this fusion comes for free since we use the intermediate result of the
rendering itself.

\item {\em Generality of occludees.} We can use complex
occludees. Anything that can be rasterized quickly is suitable.

\item {\em Exploiting the GPU power.} The queries take full advantage of
the high fill rates and internal parallelism provided by modern GPUs.

\item {\em Simple use.} Hardware occlusion queries can be easily
integrated into a rendering algorithm. They provide a powerful tool to
minimize the implementation effort, especially when compared to
CPU-based occlusion culling.


\end{itemize}



\subsection{Problems of hardware occlusion queries}

 Currently there are two main hardware supported variants of occlusion
queries: the HP test (\hpot) and the more recent NV query (\nvoq, now
also available as \arboq). The most important difference between the
HP test and the NV query is that multiple NV queries can be
issued before asking for their results, while only one HP test is
allowed at a time, which severely limits its possible algorithmic
usage. Additionally the NV query returns the number of visible pixels
whereas the HP test returns only a binary visibility
classification.

%% Issuing multiple independent NV queries is crucial for
%% the design of algorithms that strive to exploit power of the GPU.

 The main problem of both the HP test and the NV query is the latency
between issuing the query and the availability of the result. The
latency occurs due to the delayed processing of the query in a long
graphics pipeline, the cost of processing the query itself, and the
cost of transferring the result back to the CPU. The latency causes
two major problems: CPU stalls and GPU starvation. After issuing the
query, the CPU waits for its result and does not feed the GPU with new
data. When the result finally becomes available, the GPU pipeline can
already be empty. Thus the GPU needs to wait for the CPU to process
the result of the query and to feed the GPU with new data.

A major challenge when using hardware occlusion queries is to avoid
the CPU stalls by filling the latency time with other tasks, such as
rendering visible scene objects or issuing other, independent
occlusion queries (see Figure~\ref{fig:latency})


\begin{figure}[htb]
  \centerline{
    \includegraphics[width=0.5\textwidth,draft=\DRAFTFIGS]{figs/latency2}
    }

  \caption{(top) Illustration of CPU stalls and GPU starvation.
    Qn, Rn, and Cn denote querying, rendering, and culling of object
    n, respectively. Note that object 5 is found invisible by Q5 and
    thus not rendered. (bottom) More efficient query scheduling. The
    scheduling assumes that objects 4 and 6 will be visible in the
    current frame and renders them without waiting for the result of
    the corresponding queries. }
  \label{fig:latency}
\end{figure}





\subsection{Hierarchical stop-and-wait method}
\label{sec:basic}

Many rendering algorithms rely on hierarchical structures in order to
deal with complex scenes.  In the context of occlusion culling, such a
data structure allows to efficiently cull large scene blocks, and thus
to exploit spatial coherence of visibility and provide a key to
achieving output sensitivity.

This section outlines a naive application of occlusion queries in the
scope of a hierarchical algorithm. We refer to this approach as the
{\em hierarchical stop-and-wait} method. Our discussion is based on
kD-trees, which proved to be efficient for point location, ray
tracing, and visibility
culling~\cite{MacDonald90,Hudson97,Coorg97,bittner01:jvca}. The
concept applies to general hierarchical data structures as well, though.

The hierarchical stop-and-wait method proceeds as follows: Once a
kD-tree node passes view-frustum culling, it is tested for
occlusion by issuing the occlusion query and waiting for its
result. If the node is found visible, we continue by recursively
testing its children in a front-to-back order. If the node is a
leaf, we render its associated objects.

 The problem with this approach is that we can continue the tree
traversal only when the result of the last occlusion query becomes
available. If the result is not available, we have to stall the CPU,
which causes significant performance penalties. As we document in
Section~\ref{sec:results}, these penalties together with the overhead
of the queries themselves can even decrease the overall application
performance compared to pure view-frustum culling. Our new method aims
to eliminate this problem by issuing multiple occlusion queries for
independent scene parts and exploiting temporal coherence of
visibility classifications.


\section{Coherent Hierarchical Culling}

\label{sec:hoq}

 In this section we first present an overview of our new
algorithm. Then we discuss its steps in more detail.

%and present a
%generalization of the method to other spatial data structures.

\subsection{Algorithm Overview}

\label{sec:overview}


Our method is based on exploiting temporal coherence of visibility
classification. In particular, it is centered on the following
three ideas:

\begin{itemize}
 \item We initiate occlusion queries on nodes of the hierarchy where
   the traversal terminated in the last frame. Thus we avoid queries
   on all previously visible interior nodes~\cite{bittner01:jvca}.
 \item We assume that a previously visible leaf node remains visible
   and render the associated geometry without waiting for the result
   of the corresponding occlusion query.
\item Issued occlusion queries are stored in a query queue until they are known to be carried out by the GPU. This allows
  interleaving the queries with the rendering of visible geometry.
\end{itemize}


The algorithm performs a traversal of the hierarchy that is
terminated either at leaf nodes or nodes that are classified as
invisible. Let us call such nodes the {\em termination nodes}, and
interior nodes that have been classified visible the {\em opened
nodes}. We denote sets of termination and opened nodes in the $i$-th
frame $\mathcal{T}_i$ and $\mathcal{ O}_i$, respectively. In the
$i$-th frame, we traverse the kD-tree in a front-to-back order, skip
all nodes of $\mathcal{ O}_{i-1}$ and apply occlusion queries first on
the termination nodes $\mathcal{ T}_{i-1}$. When reaching a
termination node, the algorithm proceeds as follows:

\begin{itemize}
\item For a previously visible node (this must be a leaf), we issue
the occlusion query and store it in the query queue. Then we
immediately render the associated geometry without waiting for the
result of the query.
 \item For a previously invisible node, we issue the query and store
 it in the query queue.
\end{itemize}

\begin{figure}[htb]
{\footnotesize
  \input{code/pseudocode2}
 }
  \caption{Pseudo-code of coherent hierarchical culling.}
  \label{fig:pseudocode}
\end{figure}

When the query queue is not empty, we check if the result of the
oldest query in the queue is already available. If the query result is
not available, we continue by recursively processing other nodes of
the kD-tree as described above. If the query result is available, we
fetch the result and remove the node from the query queue. If the node
is visible, we process its children recursively. Otherwise, the whole
subtree of the node is invisible and thus it is culled.


In order to propagate changes in visibility upwards in the hierarchy,
the visibility classification is \emph{pulled up} according to the
following rule: An interior node is invisible only if all its children
have been classified invisible. Otherwise, it remains visible and thus
opened. The pseudo-code of the complete algorithm is given in
Figure~\ref{fig:pseudocode}. An example of the behavior of the method
on a small kD-tree for two subsequent frames is depicted
Figure~\ref{fig:cut}.

\begin{figure*}[htb]
  \centerline{
    \includegraphics[width=0.73\textwidth,draft=\DRAFTFIGS]{figs/cut} }
  \caption{(left) Visibility classification of a node of the kD-tree and
    the termination nodes. (right) Visibility classification after the
    application of the occlusion test and the new set of termination nodes.
    Nodes on which occlusion queries were applied are depicted with a
    solid outline. Note the pull-up and pull-down due to visibility changes.}
  \label{fig:cut}
\end{figure*}



The sets of opened nodes and termination nodes need not be maintained
explicitly. Instead, these sets can be easily identified by
associating with each node an information about its visibility and an
id of the last frame when it was visited. The node is an opened node
if it is an interior visible node that was visited in the last frame
(line 23 in the pseudocode). Note that in the actual implementation of
the pull up we can set all visited nodes to invisible by default and
then pull up any changes from invisible to visible (lines 25 and line
12 in Figure~\ref{fig:pseudocode}). This modification eliminates
checking children for invisibility during the pull up.



%% \begin{figure*}[htb]
%% \centerline{\includegraphics[width=0.8\textwidth,draft=\DRAFTFIGS]{figs/basic}}
%% \caption{Illustration of the hierarchy traversal. Initially the algorithm
%% starts at the root of the hierarchy (left). In the second frame the
%% opened nodes $\mathcal{ O}_0$ are skipped and the occlusion queries
%% are first applied on the termination nodes $\mathcal{T}_0$. Visibility changes are propagated upwarsds in the hierarchy and a
%% new set of termination nodes $\mathcal{ T}_1$ is established.}
%% \label{fig:basic}
%% \end{figure*}


\subsection{Reduction of the number of queries}

%Skipping the opened nodes and issuing occlusion queries for the
%termination nodes assists in exploiting two main characteristics of
%scene visibility:

%Identifying the set of termination nodes assists in finding a subdivision

Our method reduces the number of visibility queries in two ways:
Firstly, as other hierarchical culling methods we consider only a
subtree of the whole hierarchy (opened nodes + termination
nodes). Secondly, by avoiding queries on opened nodes we eliminate
part of the overhead of identification of this subtree. These
reductions reflect the following coherence properties of scene
visibility:

\begin{itemize}


\item {\em Spatial coherence.} The invisible termination nodes
approximate the occluded part of the scene with the smallest number of
nodes with respect to the given hierarchy, i.e., each invisible
termination node has a visible parent. This induces an adaptive
spatial subdivision that reflects spatial coherence of visibility,
more precisely the coherence of occluded regions. The adaptive nature
of the subdivision allows to minimize the number of subsequent
occlusion queries by applying the queries on the largest spatial
regions that are expected to remain occluded.

%, and visible termination
%nodes correspond to the smallest unoccluded regions (visible
%leafs)

\item {\em Temporal coherence.} If visibility remains constant the set
of termination nodes needs no adaptation. If an occluded node becomes
visible we recursively process its children (pull-down). If a visible
node becomes occluded we propagate the change higher in the hierarchy
(pull-up). A pull-down reflects a spatial growing of visible
regions. Similarly, a pull-up reflects a spatial growing of occluded
regions.


%The first case corresponds to pull-down of the cut, the latter to pull-up.

\end{itemize}

By avoiding queries on the opened nodes, we can save $1/k$ of the queries
for a hierarchy with branching factor $k$ (assuming visibility remains
constant). Thus for the kD-tree, up to half of the queries can be
saved. The actual savings in the total query time are even larger: the
higher we are at the hierarchy, the larger boxes we would have to
check for occlusion. Consequently, the higher is the fill rate that
would have been required to rasterize the boxes. In particular,
assuming that the sum of the screen space projected area for nodes at
each level of the kD-tree is equal and the opened nodes form a
complete binary subtree of depth $d$, the fill rate is reduced $(d+2)$
times.



\subsection{Reduction of CPU stalls and GPU starvation}

\label{sec:latency}

The reduction of CPU stalls and GPU starvation is achieved by
interleaving occlusion queries with the rendering of visible geometry. The
immediate rendering of previously visible termination nodes and the
subsequent issuing of occlusion queries eliminates the requirement of
waiting for the query result during the processing of the initial
depth layers containing previously visible nodes. In an optimal case,
new query results become available in between and thus we completely
eliminate CPU stalls. In a static scenario, we achieve exactly the
same visibility classification as the hierarchical stop-and-wait
method.

If the visibility is changing, the situation can be different: if the
results of the queries arrive too late, it is possible that we
initiated an occlusion query on a previously occluded node $A$ that is
in fact occluded by another previously occluded node $B$ that became
visible. If $B$ is still in the query queue, we do not capture a
possible occlusion of $A$ by $B$ since the geometry associated with
$B$ has not yet been rendered. In Section~\ref{sec:results} we show
that the increase of the number of rendered objects compared to the
stop-and-wait method is usually very small.

%% It is possible that we have already traversed all previously
%% visible nodes and we must stall the CPU by waiting for the result
%% of the oldest occlusion query. A technique completely eliminating
%% CPU stalls at the cost of an increase of the number of rendered
%% objects will be discussed in Section~\ref{sec:full}.

\subsection{Front-to-back scene traversal}

For kD-trees the front-to-back scene traversal can be easily
implemented using a depth first
traversal~\cite{bittner01:jvca}. However, at a modest increase in
computational cost we can also use a more general breadth-first
traversal based on a priority queue. The priority of the node then
corresponds to an inverse of the minimal distance of the viewpoint and
the bounding box associated with the given node of the
kD-tree~\cite{Klosowski:2001:ECV,Staneker:2004:OCO}.

In the context of our culling algorithm, there are two main advantages
of the breadth-first front-to-back traversal :

\begin{itemize}
\item {\em Better query scheduling.} By spreading the traversal of the
scene in a breadth-first manner, we process the scene in depth
layers. Within each layer, the node processing order is practically
independent, which minimizes the problem of occlusion query
dependence. The breadth-first traversal interleaves
occlusion-independent nodes, which can provide a more accurate
visibility classification if visibility changes quickly. In
particular, it reduces the problem of false classifications due to
missed occlusion by nodes waiting in the query queue (discussed in
Section~\ref{sec:latency}).

\item {\em Using other spatial data structures.} By using a
breadth-first traversal, we are no longer restricted to the
kD-tree. Instead we can use an arbitrary spatial data structure
such as a bounding volume hierarchy, octree, grid, hierarchical grid,
etc. Once we compute a distance from a node to the viewpoint, the
node processing order is established by the priority queue.
\end{itemize}

 When using the priority queue, our culling algorithm can also be
applied directly to the scene graph hierarchy, thus avoiding the
construction of any auxiliary data structure for spatial
partitioning. This is especially important for dynamic scenes, in
which maintenance of a spatial classification of moving objects can be
costly.

\subsection{Checking the query result}

  The presented algorithm repeatedly checks if the result of the
 occlusion query is available before fetching any node from the
 traversal stack (line 6 in Figure~\ref{fig:pseudocode}). Our
 practical experiments have proven that the cost of this check is
 negligible and thus it can used frequently without any performance
 penalty. If the cost of this check were significantly higher, we could
 delay asking for the query result by a time established by empirical
 measurements for the particular hardware. This delay should also
 reflect the size of the queried node to match the expected
 availability of the query result as precise as possible.


\section{Further Optimizations}

\label{sec:optimizations}

This section discusses a couple of optimizations of our method that
can further improve the overall rendering performance. In contrast to
the basic algorithm from the previous section, these optimizations
rely on some user specified parameters that should be tuned for a
particular scene and hardware configuration.


\subsection{Conservative visibility testing}

The first optimization addresses the reduction of the number of
visibility tests at the cost of a possible increase in the number of
rendered objects. This optimization is based on the idea of skipping
some occlusion tests of visible nodes. We assume that whenever a node
becomes visible, it remains visible for a number of frames. Within the
given number of frames we avoid issuing occlusion queries and simply
assume the node remains visible~\cite{bittner01:jvca}.

This technique can significantly reduce the number of visibility tests
applied on visible nodes of the hierarchy. Especially in the case of
sparsely occluded scenes, there is a large number of visible nodes
being tested, which does not provide any benefit since most of them
remain visible. On the other hand, we do not immediately capture all
changes from visibility to invisibility, and thus we may render
objects that have already become invisible from the moment when the
last occlusion test was issued.

 In the simplest case, the number of frames a node is assumed visible
can be a predefined constant. In a more complicated scenario this
number should be influenced by the history of the success of occlusion
queries and/or the current speed of camera movement.


 \subsection{Approximate visibility}

 The algorithm as presented computes a conservative visibility
classification with respect to the resolution of the z-buffer. We
can easily modify the algorithm to cull nodes more aggressively in
cases when a small part of the node is visible. We compare the
number of visible pixels returned by the occlusion query with a
user specified constant and cull the node if this number drops
below this constant.


\subsection{Complete elimination of CPU stalls}

\label{sec:full}

 The basic algorithm eliminates CPU stalls unless the traversal stack
is empty. If there is no node to traverse in the traversal stack and
the result of the oldest query in the query queue is still not
available, it stalls the CPU by waiting for the query result. To
completely eliminate the CPU stalls, we can speculatively render some
nodes with undecided visibility. In particular, we select a node from
the query queue and render the geometry associated with the node (or
the whole subtree if it is an interior node). The node is marked as
rendered but the associated occlusion query is kept in the queue to
fetch its result later. If we are unlucky and the node remains
invisible, the effort of rendering the node's geometry is wasted. On
the other hand, if the node has become visible, we have used the time
slot before the next query arrives in an optimal manner.

To avoid the problem of spending more time on rendering invisible
nodes than would be spent by waiting for the result of the query, we
select a node with the lowest estimated rendering cost and compare
this cost with a user specified constant. If the cost is larger than
the constant we conclude that it is too risky to render the node and
wait till the result of the query becomes available.

\section{Results}
\label{sec:results}

We have incorporated our method into an OpenGL-based scene graph
library and tested it on three scenes of different types. All tests
were conducted on a PC with a 3.2GHz P4, 1GB of memory, and a
GeForce FX5950 graphics card.

\subsection{Test scenes}

The three test scenes comprise a synthetic arrangement of 5000
randomly positioned teapots (11.6M polygons); an urban environment (1M
polygons); and the UNC power plant model (13M polygons). The test
scenes are depicted in Figure~\ref{fig:scenes}. All scenes were
partitioned using a kD-tree constructed according to the surface-area
heuristics~\cite{MacDonald90}.


Although the teapot scene would intuitively offer good occlusion, it
is a complicated case to handle for occlusion culling. Firstly, the
teapots consist of small triangles and so only the effect of fused
occlusion due to a large number of visible triangles can bring a
culling benefit. Secondly, there are many thin holes through which it
is possible to see quite far into the arrangement of teapots. Thirdly,
the arrangement is long and thin and so we can see almost
half of the teapots along the longer side of the arrangement.

%Although the teapot scene would intuitively seem to offer good
%occlusion, it is one of the more complicated cases for occlusion
%culling. Due to the high number of very dense objects, a very fine
%kD-tree subdivision was necessary, which in turn leads to higher costs
%for testing many nodes in the hierarchy. Additionally, misclassifying
%a single teapot can lead to a significant increase in frame time due
%to the high polygon density (2,304 polygons per teapot). There are also
%many locations where it is possible to see very far into the block of
%teapots. This can be seen in the kD-tree node classification which is
%shown in the accompanying video.

The complete power plant model is quite challenging even to load into memory,
but on the other hand it offers good
occlusion. This scene is an interesting candidate for testing not only
due to its size, but also due to significant changes in visibility and depth complexity in
its different parts.

%as can also be seen in the
%walkthrough. A relatively coarse subdivision of the model triangles
%into about 4,600 nodes was sufficient to capture most occlusion
%interdependencies.

The city scene is a classical target for occlusion culling
algorithms. Due to the urban structure consisting of buildings and
streets, most of the model is occluded when viewed from the
streets. Note that the scene does not contain any detailed geometry
inside the buildings. See Figure~\ref{fig:city_vis} for a
visualization of the visibility classification of the kD-tree nodes
for the city scene.

%that
%could further



%% However, we still included a section in the walkthrough where the
%% viewpoint is elevated above the building roofs in order to show that
%% the algorithm continues to work without modification, albeit at some
%% expense. It will be an interesting topic of research to automatically
%% recognize such situations and decrease the frequency of visibility
%% queries or turn the occlusion culling algorithm off completely.



\begin{figure}
\centering \includegraphics[width=0.32\textwidth,draft=\DRAFTIMAGES]{images/city_vis}
\caption{Visibility classification of the kD-tree nodes in the city scene.
  The orange nodes were found visible, all the other depicted nodes are invisible.
  Note the increasing size of the occluded nodes with increasing distance from the visible set.}
\label{fig:city_vis}
\end{figure}


\subsection{Basic tests}


We have measured the frame times for rendering with only view-frustum culling
(VFC), the hierarchical stop-and-wait method (S\&W), and our new
coherent hierarchical culling method (CHC). Additionally, we have
evaluated the time for an ``ideal'' algorithm. The ideal algorithm
renders the visible objects found by the S\&W algorithm without
performing any visibility tests. This is an optimal solution with
respect to the given hierarchy, i.e., no occlusion culling algorithm
operating on the same hierarchy can be faster. For the basic tests we
did not apply any of the optimizations discussed in
Section~\ref{sec:optimizations}, which require user specified
parameters.

%% In order to obtain repeatable and comparable timings, the process
%% priority of our application was set to high, timings were obtained
%% using the CPU cycle counter instruction, and the OpenGL {\tt Finish()}
%% instruction was executed before each invocation of the timer at the
%% start and the end of a frame. Furthermore, we did not include clear
%% and buffer swapping times in our results, since they depend strongly
%% on the windowing mode used.

For each test scene, we have constructed a walkthrough which is shown
in full in the accompanying
video. Figures~\ref{fig:teapot_walkthrough},~\ref{fig:city_walkthrough},
and~\ref{fig:plant_walkthrough} depict the frame times measured for
the walkthroughs. Note that Figure~\ref{fig:plant_walkthrough} uses a
logarithmic scale to capture the high variations in frame times during
the power plant walkthrough.
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth,draft=\DRAFTFIGS]{images/teapotgraph1}
\caption{Frame times for the teapot scene.}\label{fig:teapot_walkthrough}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth,draft=\DRAFTFIGS]{images/citygraph1}
\caption{Frame times for the city walkthrough. Note
the spike around frame 1600, where the viewpoint was elevated above the roofs,
practically eliminating any occlusion.}\label{fig:city_walkthrough}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth,draft=\DRAFTFIGS]{images/plantgraph1log}
\caption{Frame times for the power plant walkthrough.
The plot shows the weakness of the S\&W method: when there is not much occlusion it becomes slower than VFC (near frame 2200).
The CHC can keep up even in these situations and in the same time it can exploit occlusion when it appears
(e.g. near frame 3700).}
\label{fig:plant_walkthrough}
\end{figure}
To better demonstrate the behavior of our algorithm, all walkthroughs
contain sections with both restricted and unrestricted visibility. For
the teapots, we viewed the arrangement of teapots along the longer
side of the arrangement (frames 25--90). In the city we elevated the
viewpoint above the roofs and gained sight over most of the city
(frames 1200--1800). The power plant walkthrough contains several
viewpoints from which a large part of the model is visible (spikes in
Figure~\ref{fig:plant_walkthrough} where all algorithms are slow),
viewpoints along the border of the model directed outwards with low depth complexity (holes in
Figure~\ref{fig:plant_walkthrough} where all algorithms are fast), and
viewpoints inside the power plant with high depth complexity where occlusion culling produces a
significant speedup over VFC (e.g. frame 3800).

 As we can see for a number frames in the walkthroughs, the CHC method
can produce a speedup of more than one order of magnitude compared to
VFC. The maximum speedup for the teapots, the city, and the power
plant walkthroughs is 8, 20, and 70, respectively. We can also observe
that CHC maintains a significant gain over S\&W and in many cases it
almost matches the performance of the ideal algorithm. In complicated
scenarios the S\&W method caused a significant slowdown compared to
VFC (e.g. frames 1200--1800 of
Figure~\ref{fig:city_walkthrough}). Even in these cases, the CHC
method maintained a good speedup over VFC except for a small number of
frames.

\begin{table*}
\centering \footnotesize
\begin{tabular}{|c|c|c|c|c|c|c|c|}
 \hline\hline
scene                  & method   & \#queries & wait time [ms] & rendered triangles & frame time [ms]  & speedup \\\hline\hline

Teapots                & VFC      & ---        &  ---     & 11,139,928  & 310.42  & 1.0 \\\hhline{~|-|-|-|-|-|-|-|}
11,520,000 triangles    & S\&W     & 4704     & 83.19  & 2,617,801  & 154.95 & 2.3 \\\hhline{~|-|-|-|-|-|-|-|}
21,639 kD-Tree nodes   & {\bf CHC} &{\bf 2827} & {\bf 1.31}  & {\bf 2,852,514 } & {\bf 81,18 } & {\bf 4.6 } \\\hhline{~|-|-|-|-|-|-|-|}
                       & Ideal    & ---        &  ---     & 2,617,801  & 72.19  & 5.2 \\
                       \hline\hline
City                   & VFC      & ---        &  ---     & 156,521    & 19.79 & 1.0   \\\hhline{~|-|-|-|-|-|-|-|}
1,036,146 triangles    & S\&W     & 663      &  9.49  & 30,594     & 19.9  & 1.5 \\\hhline{~|-|-|-|-|-|-|-|}
33,195 kD-Tree nodes   &{\bf CHC} & {\bf 345} & {\bf 0.18}   & {\bf 31,034}  & {\bf 8.47}  & {\bf 4.0}  \\\hhline{~|-|-|-|-|-|-|-|}
                       & Ideal    & ---        &   ---   & 30,594     & 4.55  & 6.6  \\
                       \hline\hline
Power Plant            & VFC      & ---    &  ---   & 1,556,300 & 138.76 & 1.0 \\\hhline{~|-|-|-|-|-|-|-|}
12,748,510 triangles    & S\&W    & 485   & 16.16  & 392,962  & 52.29 & 3.2 \\\hhline{~|-|-|-|-|-|-|-|}
18,719 kD-Tree nodes    &{\bf CHC} & {\bf 263}  & {\bf 0.70}  & {\bf 397,920} & {\bf 38.73}  & {\bf 4.7} \\\hhline{~|-|-|-|-|-|-|-|}
                       & Ideal    &    ---      &  ---   &   392,962    &  36.34  & 5.8 \\\hline\hline
\end{tabular}
\caption{Statistics for the three test scenes. VFC is rendering with only view-frustum culling, S\&W is the
  hierarchical stop and wait method, CHC is our new method, and Ideal
is a perfect method with respect to the given hierarchy. All values are averages over
all frames (including the speedup).}
\label{tab:averages}
\end{table*}

%VFC     S&W     CHC     Ideal
%(01:50:59) salzrat: 1     3,243823523     4,744645293     5,765981148
%(01:51:04) salzrat: for the powerplant
% for the powerplant
%(01:53:59) salzrat: 1     1,519898136     4,01897468     6,599413211
%(01:54:01) salzrat: for the city
%(01:55:15) salzrat: and
%(01:55:15) salzrat: 1     2,321137905     4,646185621     5,199086993

%salzrat: teapot: 1,977162565     1,128631431
%(02:01:52) salzrat: city: 2,607396227     1,674188137
%(02:02:59) salzrat: powerplant: 1,635036084     1,244446469


 Next, we summarized the scene statistics and the average values per
frame in Table~\ref{tab:averages}. The table shows the number of
issued occlusion queries, the wait time representing the CPU stalls,
the number of rendered triangles, the total frame time, and the
speedup over VFC.


We can see that the CHC method practically eliminates the CPU stalls
(wait time) compared to the S\&W method. This is paid for by a slight
increase in the number of rendered triangles. For the three
walkthroughs, the CHC method produces average speedups of 4.6, 4.0, and
4.7 over view frustum culling and average speedups of 2.0, 2.6, and
1.6 over the S\&W method. CHC is only 1.1, 1.7, and 1.2 times
slower than the ideal occlusion culling algorithm. Concerning the
accuracy, the increase of the average number of rendered triangles for
CHC method compared to S\&W was 9\%, 1.4\%, and 1.3\%. This increase
was always recovered by the reduction of CPU stalls for the tested
walkthroughs.

%% While this number may be very low, the algorithm also incurs a
%% non-negligible overhead which is caused by the graphics card
%% reconfiguration required for the queries and rasterization of the
%% bounding volume geometries.

% triangles
% 9%
% 1.4%
% 1.3%


% speedup over SW
% 1.9
% 2.32
% 1.33

% compare to ideal
% 1.13
% 1.9
% 1.05



\subsection{Optimizations}

First of all we have observed that the technique of complete
elimination of CPU stalls discussed in Section~\ref{sec:full} has a
very limited scope. In fact for all our tests the stalls were almost
completely eliminated by the basic algorithm already (see wait time in
Table~\ref{tab:averages}). We did not find constants that could
produce additional speedup using this technique.

The measurements for the other optimizations discussed in
Section~\ref{sec:optimizations} are summarized in
Table~\ref{tab:assumed}. We have measured the average number of issued queries
and the average frame time in dependence on the number of frames a node is
assumed visible and the pixel threshold of approximate visibility. We
have observed that the effectiveness of the optimizations depends strongly on the scene. If
the hierarchy is deep and the geometry associated with a leaf node is
not too complex, the conservative visibility testing produces a
significant speedup (city and power plant). For the teapot scene the
penalty for false rendering of actually occluded objects became larger
than savings achieved by the reduction of the number of queries. On the other
hand since the teapot scene contains complex visible geometry the
approximate visibility optimization produced a significant
speedup. This is however paid for by introducing errors in the image
proportional to the pixel threshold used.

%Good parameters for these
%optimizations have to be estimated on a scene-by-scene basis.




%% , where we compare the reference frame time and
%% number of queries already shown in the previous table to the
%% approximate visibility optimization using a higher pixel threshold,
%% and to the conservative visibility testing optimization assuming a
%% node remains visible for 2 frames, both for the teapot and the city
%% scene. These tests clearly show that a high visibility threshold
%% improves frame times, albeit at the expense of image quality. The
%% benefit of the conservative visibility optimization, is however
%% limited. While the number of queries can be reduced significantly, the
%% number of misclassified objects rises and increases the frame time
%% again.



%% \begin{table}
%% \centering \footnotesize
%% \begin{tabular}{|l|c|c|}
%%  \hline\hline
%%                 & Teapots & City \\\hline\hline
%%  frame time CHC & 130.42  & 13.91\\\hline
%%  \#queries      & 2267    & 94.04\\\hline\hline
%%  \multicolumn{3}{|l|}{assume 2 frames visible}\\\hline
%%  frame time      & 123.84 & 13.27 \\\hline
%%  \#queries      & 1342    &  42 \\\hline\hline
%%  \multicolumn{3}{|l|}{pixel threshold 50 pixels and assume 2 frames visible}\\\hline
%%  frame time     & 73.22 & 11.47  \\\hline
%%  \#queries      &  1132 &  50 \\\hline\hline
%% \end{tabular}
%% \caption{Influence of optimizations on two test scenes. All values are averages
%% over all frames, frame times are in [ms].}\label{tab:assumed}
%% \end{table}


\begin{table}
\centering \footnotesize
\begin{tabular}{|l|c|c|c|c|}
 \hline\hline
scene                    & t$_{av}$ &  n$_{vp}$ & \#queries & frame time [ms]   \\ \hline\hline
\multirow{3}{*}{Teapots} & 0        &    0         & 2827      & 81.18  \\ \hhline{~----}
                         & 2       &    0         & 1769      &  86.31 \\ \hhline{~----}
                         & 2       &    25         & 1468      & 55.90  \\ \hline\hline
\multirow{3}{*}{City}    & 0        &    0         & 345        & 8.47  \\ \hhline{~----}
                         & 2        &    0         & 192        & 6.70 \\ \hhline{~----}
                         & 2       &    25         & 181       & 6.11  \\ \hline\hline
\multirow{3}{*}{Power Plant}    & 0  &    0        & 263        & 38.73  \\ \hhline{~----}
                         & 2        &    0         & 126        & 31.17 \\ \hhline{~----}
                         & 2       &    25         & 120       & 36.62  \\ \hline\hline
\end{tabular}

\caption{Influence of optimizations on the CHC method.
  $t_{av}$ is the number of assumed visibility frames for conservative
  visibility testing, n$_{vp}$ is the pixel threshold for
  approximate visibility.}\label{tab:assumed}
\end{table}


\subsection{Comparison to PVS-based rendering}

 We also compared the CHC method against precalculated visibility. In
particular, we used the PVS computed by an offline visibility
algorithm~\cite{wonka00}. While the walkthrough using the PVS was
1.26ms faster per frame on average, our method does not require costly
precomputation and can be used at any general 3D position in the
model, not only in a predefined view space.


\section{Conclusion}
\label{sec:conclusion}

 We have presented a method for the optimized scheduling of hardware
 accelerated occlusion queries. The method schedules occlusion queries
 in order to minimize the number of the queries and their latency.
 This is achieved by exploiting spatial and temporal coherence of
 visibility. Our results show that the CPU stalls and GPU starvation
 are almost completely eliminated at the cost of a slight increase in
 the number of rendered objects.

%Additionally it schedules the queries in an order
%minimizing the overhead due to the latency of availability of query
%results.

 Our technique can be used with practically arbitrary scene
 partitioning data structures such as kD-trees, bounding volume
 hierarchies, or hierarchical grids. The implementation of the method
 is straightforward as it uses a simple OpenGL interface to the
 hardware occlusion queries. In particular, the method requires no
 complicated geometrical operations or data structures. The algorithm
 is suitable for application on scenes of arbitrary structure and it
 requires no preprocessing or scene dependent tuning.

 We have experimentally verified that the method is well suited to the
 \nvoq{} supported on current consumer grade graphics hardware. We
 have obtained an average speedup of 4.0--4.7 compared to pure view-frustum
 culling and 1.6--2.6 compared to the hierarchical
 stop-and-wait application of occlusion queries.

  The major potential in improving the method is a better estimation
 of changes in the visibility classification of hierarchy nodes. If
 nodes tend to be mostly visible, we could automatically decrease the
 frequency of occlusion tests and thus better adapt the method to the
 actual occlusion in the scene. Another possibility for improvement is
 better tuning for a particular graphics hardware by means of more
 accurate rendering cost estimation. Skipping occlusion tests for
 simpler geometry  can be faster than issuing comparably expensive
 occlusion queries.



\begin{figure*}[htb]
  \centerline{
     \hfill
     \includegraphics[height=0.2\textwidth,draft=\DRAFTFIGS]{images/teapots}
     \hfill
     \includegraphics[height=0.2\textwidth,draft=\DRAFTFIGS]{images/city}
     \hfill
     \includegraphics[height=0.2\textwidth,draft=\DRAFTFIGS]{images/pplant}
     \hfill
   }
   \caption{The test scenes: the teapots, the city, and the power plant.}
   \label{fig:scenes}
\end{figure*}

%%  \begin{figure}[htb]
%%    \centerline{
%%      \includegraphics[width=0.2\textwidth,draft=\DRAFTFIGS]{images/city}
%%   }
%%   \caption{The the city scene.}
%%   \label{fig:images1}
%% \end{figure}

%%  \begin{figure}[htb]
%%    \centerline{
%%      \includegraphics[width=0.25\textwidth,draft=\DRAFTFIGS]{images/teapots}
%%   }
%%   \caption{The the teapot scene.}
%%   \label{fig:images2}
%% \end{figure}

%%  \begin{figure}[htb]
%%    \centerline{
%%      \includegraphics[width=0.2\textwidth,draft=\DRAFTFIGS]{images/pplant}
%%   }
%%   \caption{The the power plant scene.}
%%   \label{fig:images3}
%% \end{figure}