Efficient Complex Shadows from Environment Maps

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Efficient Complex Shadows from Environment Maps
Maneesh Agrawala Microsoft Research
Aner Ben-Artzi Columbia University
Ravi Ramamoorthi Columbia University
Introduction When adding cast shadows to scenes
illuminated by complex lighting such as high
dynamic-range environment maps, most of the
calculations are spent determining visibility
between the many light-source directions and
every scene point visible to the camera. We
propose a method that selectively samples the
visibility function. By leveraging the coherence
inherent to the visibility of typical scenes, we
predict over 90 of the visibility calculations
by leveraging information from previous
calculations. The difference from the full
calculations is negligible. Visibility coherence
has been used in works such as Guo 1998, Hart
et al. 1999, and Agrawala et al. 2000, but
only for point or area light sources. Those
methods do not scale to environment maps. We
show how to use the complexity of sampled
environment maps to our advantage.
4 ways to reuse blockers discovered in previously
evaluated pixels
Scanline vs. Grid-based pixel order evaluation
Grey pixels have already been evaluated. Blue
pixels are being predicted based on visibility
informatin conatined in the gray pixels indicated
by the arrows. Scanline (left) Traditional
scanline evaluation uses visibility information
from the three pixels above and to the left of
the current pixel. Grid-Based (right) First the
image is fully evaluated at regular intervals.
This produces a coarse grid. Next the center
(shown in blue) of every 4 pixels is evaluated
based on its surrounding 4 neighbors (shown in
grey). All four are equidistant from their
respective finer-grid-level pixel. Again, a
pixel is evaluated at the center of 4 previously
evaluated pixels. At the end of this step, the
image has been regularly sampled at a finer
spacing. This becomes the new coarse level, and
the process repeats. Warping vs. No Warping
When we use the blockers from previously
evaluated pixels, we hav a choice of warping them
to the frame of reference of the current pixel,
or assuming tht the blocker are distant, and
leaving their relative angular direction
unchanged.
Trying All Possibilities We examined all
possible combinations of the components of our
algorithm. We see that scanline produces errors
with uncertainty flooding, whether warping is
used, or not. This is because uncertainty
flooding works best when it assimilates
visibility information from a variety of
viewpoints, not just up and to the left. Even
with boundary flooding, scanline requires
warping. Otherwise, visibility information is
erroneously propagated too far along the scanline
before it is corrected. Grid-based evaluation
actually works better without warping. We
recommend GNU as the best combination.
Fixing Prediction Errors A naïve approach to
predicting the visibility of lights for a
particular pixel is to let the visibility
information form nearby pixels determine the
visibility at the current pixel. Without some
method for marking low-confidence predictions,
and verifying them, the results contain errors as
in the left image.
fix predictions
Performance of Low-Error Combinations After
eliminating SNB, SNU, and SWU based on the images
above, we compared the efficiency or the
remaining algorithms. The entries for the table
indicate the percentage of shadow rays where N?L
gt 0 that were traced by each method. For each
scene an environment map was chosen, and then
sampled as approximately 50, 100, 200, and 400
lights. Notice that the performance of boundary
flooding depends on the number of lights.
3A. Light cells whose neighbors visibility
differs are shadow-traced (blue center).
2A. Lights cells that contain any blocker(s) are
predicted as blocked. Others are predicted as
visible.
Conclusion Visibility coherence can be
efficiently exploited to make accurate
predictions. Such predictions must be tempered
by error-correction techniques. Rather than
using perceptual errors, low-confidence
predictions can be found be leveraging the way in
which they were generated. Specifically, we have
shown that when predictions are based on a group
of predictors, error-correction must be employed
whenever the predictors disagree. This is
manifested in our framework as grid-based
evaluation with uncertainty flooding. For
typical scenes, over 90 of shadow-rays can be
accurately predicted with negligible errors. The
errors that do exist are coherent, leading to
smooth animations in our tests. Our techniques
are technically simple to implement and can be
used directly to render realistic images, or to
speed up the precomputation in PRT
methods. Higher speedups than presented in this
paper may be achieved if some tolerance for
errors exists. We plan to explore a controlled
process for the tradeoff between predictions and
errors in future work. More broadly, we want to
explore coherence for sampling other high
dimensional functions such as the BRDF, and more
generally in global illumination, especially
animations.
0. The visibility for all of the lights has been
determined at 3 pixels (not shown). We will now
use that information to predict the visibility
for lights at new pixel.
Flood and Shadow-trace
predictions
Timings The actual timings for the full
rendering, shown here, are related to, but not
equivalent to the reduction in work as measured
in shadow-rays traced. Each scene was lit by a
200-light sampling, and timed on an Intel Xeon
3.06GHz computer, running Windows XP.
Path A Boundary Flooding Path B Uncertainty
Flooding
Predictions uncertainty tracing
Flood and Shadow-trace
1. For simplicity, we will not consider warping.
Each light in our current pixel (as represented
by its hexagonal cell in the Voronoi diagram),
will receive a blocker (black dots) every time
the corresponding light is blocked in one of the
previously evaluated pixels. If warping were
used, blockers would be warped onto the
appropriate light, instead of always being added
to the same light.
2B. Lights cells that contain the 3 (since we are
using 3 previous pixels) are predicted as
blocked. Those that contain no blockers are
predicted as visible. Light cells containing 1
or 2 blockers are marked as uncertain and
shadow-traced (blue center).
3B. The neighboring light cells of all uncertain
cells are shadow-traced (blue center).
References Agarwal, S., Ramamoorthi, R.,
Belongie, S., and Jensen, H. W.. Structured
Importance Sampling of Environment Maps. In
Proceedings of SIGGRAPH 2003, pages
605612. Agrawala, M., Ramamoorthi, R., Heirich,
A., and Moll, L. Efficient Image-Based Methods
for Rendering Soft Shadows. In Proceedings of
SIGGRAPH 2000, pages 375384. Ben-Artzi, A.,
Ramamoorthi, R., Agrawala, M. Efficient Shadows
from Sampled Environment Maps. Columbia
University Tech Report CUCS-025-04 2004. Guo, B.
Progressive radiance evaluation using directional
coherence maps. In Proceedings of SIGGRAPH 1998,
pages 255-266. Hart, D., Dutre, P., Greenberg,
D. Direct illumination with lazy visibility
evaluation. In Proceedings of SIGGRAPH 1999,
pages 147-154.
Boundary Flooding vs. Uncertainty Flooding
Boundary flooding considers any light on the
boundary between blocked and visible to be a
low-confidence prediction. Uncertainty flooding
considers any light for which there is no
consensus to be a low-confidence prediction. In
both methods, the neighbors of low-confidence
lights are shadow-traced. If the trace reveals
that a prediction is wrong, the shadow-tracing
floods to neighbors of that light until all
shadow-traces return the same visibility as the
prediction. Agrawala et al. 2000 use this for
boundary flooding.
Animations can be found at www.cs.columbia.edu/cg.
More details appear in Ben-Artzi et al. 2004.
Note All shadows have been enhanced to make them
more visible. Actual renderings would contain
softer shadows.