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Fast Multi-image-based Photon Tracing with Grid-based Gathering

We developed a real-time solution for approximate global

illumination, where the temporal cost in complex scenes is

dramatically reduced. Our approach initially traces photon-rays

with multiple cube-maps, and then gathers the irradiance of

photons using uniform grids filled with low-order spherical

harmonics. Numerous global illumination effects can be rendered

efficiently in our framework.

ABSTRACT

Problem Formation

Improved Multi-image-based Ray-tracing

Limitations for Future Works

References

[1] Yao, C., Wang, B., Chan, B., Yong, J., and Paul, J.-C. Multi-

image based photon tracing for interactive global illumination of

dynamic scenes. Comput. Graph. Forum 29, 4 (2010), 1315—1324.

[2] Szirmay-Kalos, L., Aszodi, B., Lazanyi, I., and Premecz, M.

Approximate ray-tracing on the gpu with distance impostors.

Comput. Graph. Forum 24, 3 (2005), 695—704.

[3] Kajiya, J.T. The rendering equation, In Proceedings of the

SIGGRAPH ‘86, pp. 143—150.

[4] Sloan, P.-P. Stupid spherical harmonics (sh) tricks. In

Lectures of the GDC '08 (2008), pp. 1—41.

[5] Kaplanyan, A., and Dachsbacher, C. Cascaded light

propagation volumes for real-time indirect illumination.

In Proceedings of the I3D '10 (2010), pp. 99—107.

Ray-tracing and light-gathering are the two key steps in two-pass

rendering algorithms, such as photon mapping, etc. Recent method

focusing on multi-image-based photon mapping [1] works well in

simple scenes, but has serious limitations in complex scenes due to

three reasons: a) they intersect a photon-ray iteratively with

distance imposters (cube maps), where, however, the initialization

can be far from accurate, which leads the iterative refinement to

be failed (Figure 1); b) they intersect a photon-ray with all the

distance imposters in the scene, which is costly and unnecessary; c)

the method for radiance estimation called splatting, is not

efficient when there are large amount of photons, since splatting

millions of photons will need the rasterization of billions of pixels.

School of Software, Tsinghua University, P. R. China

Yun Fei and Bin Wang

Introduction

We propose an effective solution focusing on ray-tracing and

intensity-estimating in complex scenes. Our first contribution is a

heuristic ray-tracing scheme that initializes in a more reasonable

way, providing a reliable beginning for the later refinement;

afterwards only one or two cube-maps are used by each photon-ray,

which increases the efficiency of ray-cube-map intersection over

an order of magnitude. Our second contribution is an approximate

grid-based light-gathering technique for all-frequency effects.

Each photon is represented with a spherical harmonics (SH) vector,

which is later stored into two types of uniform grids. One grid

called light-gathering volume, or LGV, is a 3D volume used to

gather smoothed light such as diffuse lighting, and the other one,

called screen-space LGV (SSLGV), is a screen-space grid used to

gather more detailed light such as caustics.

To solve the failure case in the existing algorithm and to improve

the efficiency, we propose a new solution, based on two

observations that: 1) the intersection point is only strongly

related to the ambient objects near to the photon-ray, and 2) the

existing methods failed since their initialization is not reliable.

We detailed our method in two stages:

1) use a cascaded partition scheme to find an intersection close to

be accurate, used as the initialized point (Figure 2). In this step,

the cube-map closest to the photon-ray origin is chosen as the

distance imposter. We then subdivide the 3D plane (the yellow

region) into several intervals. Then we minimize an energy across

these intervals. Then we check whether the energy changing

between the energy in a previous loop to the current one is

sufficiently small. If it is not, we uniformly subdivide the newly

computed 3D fan-shape again (the blue region, for example) and

minimize the energies; otherwise, we exit the loop.

2) From the initialized point we find an exact solution following

the work proposed by Szirmay-Kalos et al.[2], using the cube-map

closest to the initial testing point.

The Energy Function:

To compute the energy function, we firstly fetch two distance

imposters from the cube-map, in the directions of the two

boundaries, denoted as 𝑝𝑖 and 𝑝𝑖+1. Then we individually compute

functions 𝑓 𝑝𝑖 and 𝑓 𝑝𝑖+1 (defined below), and add them up as

the energy function.

𝑓 𝑝 is defined as the difference volume (Figure 3) estimated

between a testing point 𝑝 and the correct intersection. It is

designed based on the two key observations below:

1) the distance from the position of a photon 𝑡 to a point on the

distance impostor 𝑝 should be as close as to the length of its

projection on the ray direction, specifically:

𝑑 𝑝 = 𝑝 − 𝑡 − 𝑝 − 𝑡 , 𝑟 ≈ 0

2) both of the terms, 𝑝 − 𝑡 and 𝑝 − 𝑡 , 𝑟 , should be small.

To fulfill theses two conditions, we compute the volume of a

triangle frame around 𝑝 − 𝑡 and its projection on 𝑟 .

𝑓 𝑥 = 𝑝 − 𝑡 − 𝑝 − 𝑡 , 𝑟 2

𝑝 − 𝑡 + 𝑝 − 𝑡 , 𝑟 , 𝑝 − 𝑡 , 𝑟 > 0

&∞, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Light Gathering Volume

In this section, we introduce our novel strategy for photon

gathering. Our approach can be detailed into three phases: 1)

photon injection, 2) light-gathering, and 3) scene illumination

(Figure 4).

Screen-space Light Gathering Volume

High frequency details such as caustics need higher order of SH-

vectors. When using a lattice filled with SH-approximation in low-

order, the resolution of the grid has to be increased. This

increasing can be unacceptable for high frequency details under

both spatial and temporal considerations. Fortunately, the high-

resolution computation is much less costly to be taken in screen-

space. Therefore, we propose a 2D grid to assist the light-

gathering process (Figure 5).

Injection: Photons are transformed into eye-space and filtered,

according to whether they are caustics photons or not. Then they

are injected into a 2D texture in the manner similar to LGV.

Gathering: For each pixel in the eye-space, the SH-approximation

is extracted from its 4-neighbored pixels and is projected to the

directions to the centroid pixel. The direction is computed using

world space coordinate recorded in the previously rendered

position buffer.

Illumination: After several times of iteration, the SSLGV-texture is

rendered with projection that estimates the intensity along the

surface normal.

Our method shares some artifacts that are pervasive in existing

lattice-based methods, specifically temporal discontinuity and

light bleeding. Besides, the rendering quality of some flattened

“middle”—frequency caustics is still very photon-dependent where

tracing billions of photons is still unavailable in real-time.

Therefore some techniques for importance sampling may be

introduced into our pipeline in the future.

The Light Gathering Volume (LGV) is a 3D texture covering the

entire scene. After ray-traced, photons are injected into the LGV

via two stages: 1) we transform the position that a photon-ray

intersects with objects into the coordinate of texel in the 3D

texture, and 2) we accumulate the SH-approximation of intensity

into the texel. Each texel stores the SH-approximations of the

radiance contributed by injected photons. For each photon 𝑗, the

radiance 𝐿𝑗 is calculated with the following formula (which can be

derived from the Kajiya’s rendering equation [3]):

𝐿𝑗 =𝐴𝐶0

2

4𝑁Φ𝑝 Θ𝑗 , 𝑛

+𝑓𝑟(𝑥)

𝐴: the total area of the scene; 𝑁: the amount of photons cast; 𝐶0:

a variant bandwidth factor [1]; Θ𝑗: the normalized incident

direction of the photon. Φ𝑝: the power of the photon injected;

𝑓𝑟(𝑥): the BRDF around point 𝑥; 𝑛: the normal of surface hit by the

photon.

The radiance 𝐿𝑗 is approximated by spherical harmonics (SH)

vectors [4]. Multiple SH-vectors each of which corresponds to one

photon are accumulated with additive blending. After injection,

the radiance in each texel can represent the local illumination

around the position of the texel (in world space). Then for each

texel, we gather intensity from its six neighborhoods adjacent to it

following Kaplanyan’s light propagation framework [5].

Figure 1: the photon ray 𝑟 is intersected with the

distance imposter. With an

unreliable initialization

point 𝐴 chosen, the wrong

result 𝐵&would be generated

by existing approaches. Even

with two cube maps used

(two blue points), the

correct result is still

unapproachable.

Figure 2: We divide the fan

shape area (yellow)

supported by the center-

photon vector and the ray

direction into several

intervals, and find a

position with the minimum

energy as a “reliable initial

testing point” (point 𝐼 in the

figure), then we refine this

point to the correct result.

Figure 4: The photon injection, light gathering and reprojection,

the figure is adapted from [4].

Figure 3: The difference

volume showed with

trans-lucent blue boxes.

When the 𝑝 − 𝑡 gets

smaller, 𝑓 𝑥 is

determined by

𝑝 − 𝑡 − 𝑝 − 𝑡 , 𝑟 2,

which is the thickness

of the triangle frame.

Figure 5: During the photon

injection, the light contributed

by each photon is accumulated

in the axis perpendicular to the

clipping plane. During gathering,

SH-approximations in the yellow

cells (pixels) are accumulated

into the current grey cell (pixel),

and the one in the red cell

(pixel) is declined for its

distance to the current pixel is

larger than some given radius.

Figure 6: Without pre-computation, our technique renders

dynamic global illumination effects in a complex scene in real-

time on a GTX480).

Figure 7: Comparisons of the results. Our result is comparable to

the referenced results rendered in two hours with V-Ray, as well

as the result rendered in 24 minutes with PBRT.

Contact: E-mail: fyun@acm.org, wangbins@tsinghua.edu.cn

a) 56Hz b) 22Hz

c) 19Hz 38Hz