Reducing Computational Complexity of Real-Time Stereoscopic Ray

Tracing with Spatiotemporal Sample Reprojection

Markku M

akitalo, Petrus Kivi, Matias Koskela and Pekka J

askel

ainen

Tampere University, Finland

Keywords:

Computer Graphics, Real-Time Rendering, Ray Tracing, Stereoscopic, Temporal Coherence, Reprojection,

Quality, Metrics.

Abstract:

Sample reprojection is a computationally inexpensive way of increasing the quality of real-time ray tracing,

where the number of samples that can be traced per pixel within the time budget is limited often to just

one. Stereoscopic rendering further doubles the amount of rays to be traced, although it exhibits signiﬁcant

correlation not only temporally between frames, but also spatially between the viewpoints of the two eyes.

We explore various reprojection schemes taking advantage of these correlations, and propose to quantify their

contributions on the improved quality in terms of effective sample per pixel counts. We validate that sample

reprojection is an effective way of reducing the computational complexity of real-time stereoscopic ray tracing,

bringing potential beneﬁts especially to lower-end devices.

1 INTRODUCTION

Real-time ray tracing is currently gaining signiﬁcant

traction, due to modern hardware and state-of-the-art

software beginning to provide a means to achieve it

in practice. However, we are still limited to tracing

about one sample per pixel (1 spp), and rely on so-

phisticated post-processing ﬁlters for reconstructing

an acceptable quality result. With virtual reality and

augmented reality devices also becoming mainstream,

enabling stereoscopic real-time ray tracing is an im-

portant challenge for the near future. However, stere-

oscopy also implies that the computational costs are

roughly doubled, as we need to render a separate im-

age for both eyes.

Image and video data, whether it is natural or com-

puter generated imagery, usually exhibits correlation

between the pixels in both spatial and temporal do-

mains: the scene can contain similar structures in dif-

ferent parts of the same frame (spatial self-similarity),

and successive frames often differ only slightly due to

a small movement of the camera or the movement of

objects in the scene (temporal coherence). In stereo-

scopic data, spatial correlation also manifests itself

between the two eyes, as we are observing the scene

from two different viewpoints at the same time in-

stant.

A common way to reduce the computational com-

plexity of ray tracing, as well as rasterization, is to re-

project already rendered samples into new locations,

based on our knowledge of the movement and other

parameters of the virtual camera. Often we can also

utilize auxiliary data, such as information about the

depth, normals, or world positions of the scene. We

can reproject samples both temporally, i.e., using data

from previous frame(s), and spatially, e.g., from the

viewpoint of one eye to the viewpoint of the other eye.

Some of the challenges of spatiotemporal sample

reprojection include occlusions, non-diffuse shading

(i.e., a pixel whose colour may change in another

viewpoint), and that the reprojection mapping is gen-

erally non-bijective (i.e., many pixels may map onto

a single pixel in another viewpoint, and some pixels

may not have any pixel mapped to them from another

viewpoint) (Walter et al., 1999). Note that the term

”viewpoint” here may indicate either a temporally dif-

ferent frame, or another viewing direction from a dif-

ferent spatial angle at the same time instant (in our

case, the viewpoint of the other eye in a stereoscopic

scene).

We explore both spatial and temporal reprojection,

in an effort to validate their relevance and usefulness

in increasing the quality of stereoscopic real-time ray

tracing. We show that combining reprojection and

sparse ray tracing is an effective way of reducing the

computational complexity, as reprojecting a sample is

a very inexpensive operation compared to tracing a

ray for that sample (typically an order of magnitude

Mäkitalo, M., Kivi, P., Koskela, M. and Jääskeläinen, P.

Reducing Computational Complexity of Real-Time Stereoscopic Ray Tracing with Spatiotemporal Sample Reprojection.

DOI: 10.5220/0007692103670374

In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019), pages 367-374

ISBN: 978-989-758-354-4

367

(a) Stereo

(b) Temporal

Figure 1: Pixels discarded by the reprojection algorithm in

(a) stereoscopically reprojected and (b) temporally blended

ray traced images: green for world position and cyan for

shading normal discards. Pixels reprojected outside of the

frame can be seen as red around the images.

cheaper). Moreover, we advocate a way of quantify-

ing the obtained improvements not only by the per-

centage of samples where ray tracing can be omit-

ted, but also more interestingly by the effective spp

of the result: how many samples per pixel would it

have taken to obtain the same quality with merely ray

tracing all samples. We also argue that this evalua-

tion method would be beneﬁcial in bringing a more

complete understanding of the speed/quality tradeoffs

associated with various parts of a real-time ray trac-

ing framework in general; it is in no way restricted to

reprojection.

We speciﬁcally target the real-time 1 spp case, as

it is the scenario where sample reprojection arguably

provides the most tangible gains. In particular, repro-

jection accelerates the rendering by providing approx-

imate fast results when the balance of speed and qual-

ity is highly important; the quality could be further en-

hanced by various adaptive sparse sampling schemes

(Viitanen et al., 2018). In contrast, when the ray trac-

ing is not done in real time, the gains attained through

reprojection are less important: typically one would

then prefer to ray trace additional high quality sam-

ples at the cost of making an already slow rendering

process slower.

2 SAMPLE REPROJECTION

2.1 Temporal Reprojection

The concept of temporal coherence, that the contents

of successive frames do not usually change signiﬁ-

cantly, can be traced back to at least the early 1970s,

when it was discussed in conjunction with visibility

determination (Sutherland et al., 1974). The follow-

ing decade saw several breakthroughs in the ﬁeld of

ray tracing, with seminal works about recursive ray

tracing (Whitted, 1979), distributed effects such as

motion blur and depth of ﬁeld (Cook et al., 1984), and

Monte Carlo style stochastic ray tracing (path trac-

ing) that computes global illumination through the

rendering equation (Kajiya, 1986). Soon after, an al-

gorithm for using temporal coherence to accelerate

ray tracing for motion picture production was intro-

duced in (Badt, 1988). Speciﬁcally, it gathered object

space information from the previous frame and then

estimated where the objects would be in the current

frame, thus performing forward sample reprojection.

This resulted in having to trace less than 40% of the

pixels in the current frame. The forward reprojection

approach was generalized in (Adelson and Hodges,

1995), where it was reported to yield up to 92% sav-

ings in rendering time.

In (Walter et al., 1999), a render cache was in-

troduced, which enabled interactive ray tracing for

low resolutions (about 8 frames per second for a

320×320 resolution). It builds an acceleration struc-

ture by caching previously rendered samples, storing

their colours and also the 3D data and shading infor-

mation. That allowed for various heuristics to be used

when reprojecting the samples onto the new frame,

such as comparing the depth data and colour contrast

for detecting holes, disocclusions, and other artifacts

(Wald and Slusallek, 2001). While the original render

cache still used forward reprojection, its concept of

storing the earlier data paved way for a backward re-

projection cache (also known as reverse reprojection),

introduced independently in (Nehab et al., 2007) and

(Scherzer et al., 2007).

Backward reprojection works by starting from the

current frame to be rendered instead of an earlier

frame, and for each pixel in the current frame deter-

mining its location in the earlier frame. If the pixel

was visible in the earlier frame and thus was stored in

the cache, it can potentially be reprojected onto the

current frame. Various heuristics can also be used

here in deciding whether to ultimately reproject the

found pixel or not, for instance based on the depth val-

ues or surface normals. While this backward mapping

simpliﬁes the reprojection and mitigates the issue of

GRAPP 2019 - 14th International Conference on Computer Graphics Theory and Applications

368

non-bijectivity, it does bring additional requirements

in terms of storing and handling past data in memory.

For further details and history about temporal co-

herence and reprojection, as well as for reviewing a

multitude of other ways of accelerating ray tracing

to an interactive/real-time level, we refer the reader

to (Wald and Slusallek, 2001) and (Scherzer et al.,

2012).

Nowadays reprojection is used by modern real-

time denoisers for stochastic sampling (Koskela et al.,

2019; Schied et al., 2018; Schied et al., 2017; Mara

et al., 2017), in order to generate a better quality input

before the actual denoising ﬁlter. Moreover, reprojec-

tion is used extensively in rasterized game graphics.

One of the most commonly used reprojection meth-

ods is called Temporal Anti-Aliasing (TAA) (Karis,

2014), which generates an anti-aliased image without

extra spatial samples. Instead, the temporal samples

are reprojected and used for smoothing the edges in

the image. With TAA, the camera is typically sub-

pixel jittered with a Halton sequence for achieving the

same smoothing effect even with a static camera.

2.2 Stereo Reprojection

In stereo reprojection, we reproject samples from one

spatial viewpoint to another at the same time instant.

In the standard stereoscopic case, the eyes can be

thought of as two distinct cameras that are separated

by approximately 6.5 centimeters (the eye separation

of an average human), and we reproject samples from

one camera’s viewpoint to the other.

There are two well-established methods for set-

ting up stereoscopic cameras: a parallel or sensor-

shift camera setup, where the two virtual cameras are

translated only horizontally, and a converged or toe-in

camera setup, which additionally introduces a slight

inward rotation for convergence. Converged camera

setups have been shown to produce visual distortions

such as keystoning (Woods et al., 1993), and thus par-

allel stereoscopic cameras are preferred for viewing

comfort (Allison, 2007).

Stereo reprojection can be thought of as a special

case of temporal reprojection (Adelson and Hodges,

1993). Speciﬁcally, if there is only camera move-

ment and the scene remains otherwise static, there is

no fundamental difference whether the camera move-

ment is interpreted as a change in viewpoint spatially

or temporally.

An early example of stereo reprojection (Ezell

and Hodges, 1990) built on the work of (Badt, 1988)

and combined it with a calculation of stereo dispar-

ity information in order to do the reprojection. With

their method, between 20% and 50% of the pixels

in the target frame needed to be ray traced after re-

projection. A more optimized method (Adelson and

Hodges, 1993) made a simplifying observation that

they could only reproject the x-coordinates of the

samples, based on an assumption that the observer’s

eyes are level (i.e., their head is not tilted). They ob-

tain an estimate of 93% reduction in the amount of

rays that need to be traced for the second eye, albeit

they do not address all problems related to the dispar-

ity between the two views (Ip et al., 1997).

A more general approach that does not assume

horizontally level eyes, introduced in (Ip et al., 1997),

leveraged coherence in the epipolar geometry of a

stereo image pair, subdividing the space with epipolar

planes; their algorithm ran in 30–50% of the time of

their comparison algorithm.

Reprojection based methods can also support ani-

mated rigid objects (Rosado, 2007). If there is a way

to compute the screen space motion vector for an an-

imated object, it can be both forward and backward

reprojected. The motion vectors can be computed for

common rigid body animations such as translation,

rotation and scaling.

With the modern rise in popularity of 3D con-

tent, stereoscopic ray tracing and reprojection algo-

rithms have also evolved to cover more general multi-

view synthesis; see, e.g., (Andersson et al., 2011)

and the references therein. However, as even mono-

scopic real-time ray tracing is only now becoming

tractable, enabling stereoscopic real-time ray tracing

remains a challenge for the near future. The recent

NVIDIA Turing architecture offers hardware acceler-

ation for rendering up to four views in a single render

pass, allowing discrepancy between the eyes also in

the y-coordinate, whereas the acceleration introduced

in their earlier Pascal architecture only supported two

views (implying a narrower ﬁeld of view) and discrep-

ancy only in the x-coordinate, assuming horizontally

level eyes (Bhonde and Shanmugam, 2018). How-

ever, its potential in combination with their ray tracing

hardware is not detailed. Nevertheless, as we high-

light in this paper, sample reprojection provides one

practical way of reducing the computational complex-

ity of stereoscopic real-time ray tracing.

3 QUALITY EVALUATION

As seen in Section 2, the advantage of sample repro-

jection is often expressed in terms of the percentage

of saved rendering time, or especially in ray tracing,

as the percentage of reduction in the amount of traced

rays. While such statistics are useful and descriptive,

they do not convey information about the quality of

Reducing Computational Complexity of Real-Time Stereoscopic Ray Tracing with Spatiotemporal Sample Reprojection

369

the rendered result as such. We feel that the quality

aspect is generally overlooked whenever such ﬁgures

are reported, which can be due to several reasons.

First, when ray tracing was still exclusively a

method for non-real-time rendering, sample reprojec-

tion was applied simply to make the computation time

tolerable in the ﬁrst place, but the long rendering pro-

cess was still continued until the resulting frame was

of high enough quality. Second, when sample repro-

jection is used within the rasterization pipeline, we

do not face a similar issue as in the path tracing ap-

proach, where individual samples are noisy and we

need to accumulate samples in order to decrease the

amount of noise.

However, even in the recent literature concerning

real-time ray tracing, we have not seen a rigorous

evaluation of how much sample reprojection actually

contributes to the quality of the ﬁnal ray traced re-

sult, despite temporal reprojection being a relatively

widely used building block of real-time ray tracing

frameworks. In particular, we think that an intuitive

metric for measuring the quality improvement gained

through reprojection is to estimate what the effective

spp count of the reprojected result is. The effective

spp gives us simultaneously an indication of both the

quality and the reduction in computational complex-

ity.

To outline our approach, we reproject as many

samples onto the target frame as we can, and ray

trace only the missing samples where reprojection

was deemed unsuccessful. The target frame can have

existing data, on top of which we accumulate repro-

jected data and blend them together with a certain ra-

tio (e.g., for stable temporal accumulation, but stereo

accumulation can also be done), or the target frame

can be empty (e.g., reprojecting from one eye to an-

other). Then, through comparisons to a pristine refer-

ence that is ray traced with thousands of samples per

pixel, we can compute the spp of a purely ray traced

image that would effectively yield the same error as

the reprojected image. The error can be evaluated by

common error metrics, such as root mean square er-

ror (RMSE), or the structural similarity index (SSIM)

(Wang et al., 2004), or more sophisticated metrics.

While it can be argued that RMSE and SSIM do

not adequately correspond to the complex subjective

evaluation done in the human visual system, they per-

sist as widely used metrics due to their relative sim-

plicity. Moreover, we think that the choice of the met-

ric is not critical in our case, as we aim to measure the

relative differences between different quality images

instead of concentrating on absolute quantities indi-

cated by the metrics.

4 EXPERIMENTS

We evaluate the effects of spatiotemporal sample re-

projection for seven stereoscopic test scenes, each

having 60 frames with 720p resolution for each eye,

and a moving observer (i.e., moving camera). As a

baseline, we have three diffuse scenes (Sponza, Liv-

ing Room, and Classroom) with static lighting. In or-

der to consider more varied conditions, we also in-

vestigate the Sponza and Living Room scenes with

glossy materials, and with a moving light source. Fig-

ure 2 shows an example 4096 spp reference frame of

each static light scene; the moving light versions of

Sponza and Living Room are done on top the scenes

in Figure 2a and Figure 2b, respectively.

4.1 Implementation

In the stereo reprojection for each individual frame,

we ﬁrst path trace the complete right-eye image with

1 spp (using one primary ray, one secondary ray, and

two shadow rays). At this point, we do not have

any path traced data for the left-eye image. How-

ever, we do assume that we have access to the depth

and shading normal buffers of both eyes via the ren-

derer, so that we can choose which pixels to discard

in the reprojection step in order to avoid ghosting ar-

tifacts. Speciﬁcally, we sample the depths and shad-

ing normals of both current and previous frame, and

also compute the 3D world space positions from these

depths, which can be done since we know the camera

parameters of both frames. Then the differences of

the two world positions and shading normals are com-

pared. Higher differences than scene-speciﬁc limit

values mean that there has been an occlusion and we

need to discard the history data; the current 1 spp path

traced input is then directly used as the output of those

pixels. The scene-speciﬁc limits used in our measure-

ments were each decided based on the scale of the

particular scene.

Then, we want to reproject as much of the right-

eye data as possible into the thus far empty left-eye

image, so we apply backward reprojection for each

pixel in the target left-eye image, hence ﬁlling n%

of the left-eye image with spatially reprojected 1 spp

data. The missing (100 − n)% of the pixels in the

left-eye image, where the reprojected sample was dis-

carded, are ﬁnally path traced with 1 spp. Note that

the difference in reprojecting from right eye to left eye

or vice versa is trivial; our choice of reprojecting from

right eye to left eye is arbitrary. Mixing both repro-

jection directions could also be considered for a more

advanced implementation.

For temporal reprojection, we accumulate data

GRAPP 2019 - 14th International Conference on Computer Graphics Theory and Applications

370

(a) Sponza (b) Living Room (c) Sponza (Glossy)

(d) Living Room (Glossy) (e) Classroom

Figure 2: 4096 spp references of the scenes used in the experiments. Scenes (a) and (b) are also used as a base for Sponza

(Moving Light) and Living Room (Moving Light), respectively.

from earlier frames with a 20% blending ratio, i.e.,

weighing the existing accumulated data with a factor

of 0.8, and combining it with the newest reprojected

frame with a weight factor of 0.2. We found this ratio

to provide a good balance between keeping the frame

sequence temporally stable and incorporating newly

acquired data, while also keeping the implementation

simple. However, a content-aware heuristic for decid-

ing the ratio per scene could also be considered, as

well as one dependent on the camera movement.

We measure the effective spp counts as detailed in

Section 3 in terms of RMSE; for the RMSE value ob-

tained for each frame, we ﬁnd the n and n + 1 spp

datasets, between whose corresponding RMSE val-

ues the obtained RMSE lies, and interpolate the ef-

fective spp based on that. The measurements are done

for stereo reprojection and temporal reprojection sep-

arately, and also with both reprojection methods com-

bined; in the combined case, we ﬁrst apply temporal

reprojection to the right eye, after which the stereo re-

projection is done from right eye to left eye, and the

resulting left-eye quality is evaluated. Note that in this

case we also need to temporally accumulate left-eye

data in order to ﬁll the discarded pixels with accumu-

lated data.

While backward reprojecting data from the right

eye to the left eye, we use bilinear interpolation to

decide how the four closest pixels in the right eye

contribute to the reprojected pixels in the left eye, as

the pixels don’t align perfectly after the reprojection.

We discard invalid samples based on depth and shad-

ing normal values and give weights to the remaining

samples according to their linear distance from the

reprojected left eye pixel’s center. We use the same

sampling scheme for temporal reprojection, where the

data is now backward reprojected from the current

right eye viewpoint to a future right eye viewpoint.

We found bilinear interpolation to give visually and

metrically more pleasing results compared to nearest

neighbour sampling, where only the closest right eye

pixel is sampled. This is due to the fact that bilin-

ear interpolation acts as a simple denoiser against the

stochastic noise introduced by path tracing.

4.2 Results

Table 2 presents the effective spp counts for all

datasets, and for all three reprojection options (stereo,

temporal, and stereo + temporal). The average spp is

taken over all 60 frames, and the framewise minimum

and maximum spp counts are also reported. For stereo

reprojection, we obtain approximately 1.6 spp for all

datasets, with minor variance between frames.

For temporal reprojection, the results are more de-

pendent on the scene contents and the particular cam-

era movements: the average spp counts range from

approximately 7 spp to 12.5 spp, which is a signiﬁcant

improvement in quality even in the worst case. In gen-

eral, we see that the Sponza scenes are more difﬁcult,

which is likely due to them having more complex ge-

ometry in the new data entering the frame as the cam-

era moves. The minimum effective spp is 1, as there

is no previous data to reproject on the ﬁrst frame. It

takes about 5–10 frames for the temporal reprojec-

tion to initially reach a stable spp, as seen also in the

framewise spp graph for Sponza in Figure 3; the con-

vergence speed is dependent on the temporal blend-

ing ratio. The combined stereo+temporal reprojection

Reducing Computational Complexity of Real-Time Stereoscopic Ray Tracing with Spatiotemporal Sample Reprojection

371

0 10 20 30 40 50 60

Frame

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

RMSE

1 spp

2 spp

8 spp

16 spp

Stereo reprojection of 1 spp

Temporal reprojection of 1 spp

Stereo+temporal reprojection of 1 spp

Figure 3: Sponza dataset: Framewise RMSE values of the

reprojected frames, and of comparison data having 1 spp,

2 spp, 8 spp and 16 spp.

expectedly yields the best spp counts for all datasets,

with averages ranging from about 9 spp to 18 spp.

These clearly demonstrate that reprojection is a pow-

erful method despite its simplicity. However, more

research is needed for evaluating the performance in

more dynamic conditions, such as in a virtual reality

environment with the user constantly looking around

in the scene; in our datasets, the camera movement

is either smoothly curved panning (Living Room and

Classroom), or smoothly curved backward movement

(Sponza).

Moreover, Table 1 shows how many percent of the

samples were discarded on average; those samples are

the ones that need to be path traced in the target frame

after the reprojection. Thus, we see that with stereo

reprojection, only 2–4% of the samples have to be

path traced for the left eye on average, while the re-

sulting quality is still 60% higher at 1.6 spp than what

normal 1 spp path tracing would yield. For tempo-

ral reprojection, we observe discard rates of 1.5–4%;

again, we notice that more samples are discarded in

the Sponza sets due to the complex geometry. Fig-

ure 1 visualizes the discarded pixels for an example

frame of Living Room.

Figure 4 shows an example frame comparison of

Classroom with the 1 spp original data, 4096 spp ref-

erence, 16 spp reference, and the reprojected result

with an effective 16.38 spp. We see that the quality

of the reprojection matches the 16 spp reference quite

well also visually, although it exhibits some artifacts

on the rightmost part where new data has just entered

the frame and temporal accumulation has not yet had

enough data to smooth it out.

5 CONCLUSIONS

We explored stereoscopic and temporal sample repro-

jection in the context of real-time ray tracing. We in-

vestigated the quality improvements and the reduction

Table 1: Percentage of discarded pixels after temporal

and stereoscopic reprojection with depth, world position

and shading normal checking. The average, minimum

and maximum for stereo (N=60 frames) and temporal

(N=59 frames) discard percentages are shown.

Stereo

Avg Min Max

Sponza (All scenes) 2.01 1.24 2.96

Living Room (All scenes) 2.50 2.31 2.72

Classroom 4.36 3.58 5.91

Temporal

Avg Min Max

Sponza (All scenes) 3.96 3.57 4.46

Living Room (All scenes) 1.48 0.70 2.27

Classroom 2.19 1.52 2.97

in computational complexity associated with repro-

jection, and proposed to use the effective spp count

as a descriptive metric for them. To substantiate our

standpoint, we provided experimental results quan-

tifying the relative contributions of reprojection in

terms of effective spp. The metric and the concept of

effective spp is not limited to reprojection, but could

also be used to more rigorously assess the relative

contributions of other components in a real-time ray

tracing framework. We think the proposed approach

would be beneﬁcial in evaluating these various com-

ponents and understanding the compromises between

speed and quality associated with them, and thus be-

ing able to make more informed choices when design-

ing and optimizing the frameworks.

In practical real-time applications, reprojection is

typically combined with more sophisticated denoising

ﬁlters for high quality results. The rendering could

be further accelerated with adaptive sparse sampling

schemes. Such topics remain a subject of future in-

vestigation, as well as considering adaptive blending

ratios, especially for fast-paced scenarios like games.

ACKNOWLEDGEMENTS

This work is supported by Business Finland (funding

decision 40142/14, FiDiPro-StreamPro), Academy of

Finland (funding decisions 297548, 310411), EC-

SEL JU project FitOptiVis (project number 783162),

and the Tampere University of Technology Graduate

School.

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GRAPP 2019 - 14th International Conference on Computer Graphics Theory and Applications

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(a) 1 spp (b) 16 spp

Figure 4: Different spp counts (a,b,c) in the Classroom scene compared to the stereoscopically and temporally reprojected

and blended 1 spp (d), whose effective spp is 16.38 spp.

Table 2: Effective spp after three different reprojection schemes, as measured by RMSE. The average spp is taken over all 60

frames, with the respective framewise minimum and maximum spp counts also shown.

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