4 Results
4.1 Test Scenes
There are two test scenes used to show our method and also compared with other
rendering methods. The first one is a general empty Cornell Box. The second scene is a
Cornell Box with two spheres in it, one is made of mirror and the other is made of glass.
The scene has been slightly modified. The right wall of the Cornell box has been changed
to a mirror in order to show the SDS problem. Although the Cornell Box is a simple
scene, it is a classic benchmark for rendering.
4.2 Analysis
In the tests, the resolution of images is 512x512, and we set the maximum length of
paths at 8, which means that we would force the tracing process to stop when it exceeds
the maximum length and shows what it has got. We set the maximum light sub-path
length and eye sub-path length of bidirectional path tracing at 3 and 4 respectively. After
the vertex connection, the whole path length will remain 8 because the extended path is
added to the light sub-path and eye sub-path.
4.2.1 Empty Cornell Box
Figure 4.1 shows empty Cornell Box scene images generated by renderers using 100
iterations. Each image is rendered by a different rendering technique, which are path
tracing, bidirectional path tracing, vertex connection and merging, and our path reuse
method respectively. The rendering time is shown as Table 4.1.
Rendering Technique Time
Path Tracing 55.35 sec
Bidirectional Path Tracing 103.72 sec Vertex Connection and Merging 170.19 sec Our Path Reuse Method 105.57 sec
Table 4.1: Empty Cornell Box.
(a) Path tracing (b) Bidirectional path tracing
(c) Vertex connection and merging (d) Our path reuse method Figure 4.1: Empty Cornell Box.
4.2.2 Cornell Box with Spheres and Mirrors
Figure 4.2 shows the Cornell Box scene with a mirror replacing the right wall. The mirror
sphere is placed on the ground of the box and the glass sphere is floating to generate a
We show the rendering results of path tracing, bidirectional path tracing, vertex
connection and merging, and our path reuse method by using 200 iterations per pixel.
Because we have modified the scene to reveal the SDS problem, we not only record the
rendering times of each technique, but also the amount of failed vertex connection in
bidirectional path tracing.
(a) Path tracing (b) Bidirectional path tracing
(c) Vertex connection and merging (d) Our path reuse method Figure 4.2: Modified Cornell Box.
Rendering Technique Time
Path Tracing 90.22 sec
Bidirectional Path Tracing 136.00 sec Vertex Connection and Merging 234.57 sec Our Path Reuse Method 155.12 sec
Table 4.2: Modified Cornell Box.
4.3 Performance
In the first test scene, according to Figure 4.1 and Table 4.1, the scene generated by path
tracing consumes less time than the others, but we can see obvious noise on the ceiling.
Though the rest methods take more time, noise is hardly seen in the results. Due to no
SDS situation, the path reuse method is not triggered. The time taken by bidirectional
path tracing and our path reuse method are almost the same. Vertex connection and
merging method consumes the most time among the others.
In the second test scene, as shown in Figure 4.2, we just focus on the images rendered
by bidirectional path tracing, vertex connection and merging, and our path reuse method.
Because of the SDS problem, the vertex connection of bidirectional path tracing cannot
work properly. Thus, the reflected caustic cannot be seen in the mirror, and the reflection
on the mirror sphere of the glass sphere is much darker than it should be. The resolution
of the image is 512x512, and we made 200 iterations for each pixel, which means there
are 52,428,800 paths generated, but according to our record, 419,430,400 paths failed in
vertex connection step, which is roughly 12.5% of generated paths. With our path reuse
method, more time is spent, as shown in Table 4.2, but we can render what the scene
should be. It is worth mentioning that the whole path length remains to be 8. Though the
image rendered by vertex connection and merging method looks better than our path
reuse method, the time consumption of it is about 51.22% more than ours.
Chapter 5
Conclusions and Future Work
This thesis has provided an overview of basic concepts related to physically based image
synthesis and some popular sampling techniques. From the way of measuring the energy
of light to the sampling method based on statistics, and then some popular practical
implementations. At last, we introduced an alternative way to deal with the SDS problem
while the bidirectional path tracing method does not work.
Though we have used the MIS to higher the contribution from the light source, it still
fails in some situations. The idea called Light Propagation Volume, which is used by
non-physically based rendering to achieve the global illumination effect, comes to mind.
By using Light Propagation Volume, the space is divided into grids. The information of
light sources is spread into space, just like the first step in photon mapping. The spread
information is compressed and stored in grids by Spherical Harmonics. The energy of
bidirectional path tracing, we can take these grids as a part of samples according to MIS.
It is also convenient to reuse the grids structure to implement some acceleration data
structure, e.g., bounding box and k-d tree.
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