Variance Shadow Maps
William Donnelly
∗
Andrew Lauritzen
†
Computer Graphics Lab, School of Computer Science, University of Waterloo
Figure 1: Comparison of anisotropic filtering vs. no anisotropic filtering. Top: Regular shadow map with bilinear percentage
closer filtering. Bottom: Variance shadow map with mipmapping and 16x anisotropic filtering.
Abstract
Shadow maps are a widely used shadowing technique in real
time graphics. One major drawback of their use is that they
cannot be filtered in the same way as color textures, typi-
cally leading to severe aliasing. This paper introduces vari-
ance shadow maps, a new real time shadowing algorithm.
Instead of storing a single depth value, we s tore the mean
and mean squared of a distribution of depths, from which
we can efficiently compute the variance over any filter re-
gion. Using the variance, we derive an upper bound on the
fraction of a s haded fragment that is occluded. We show
that this bound often provides a go od approximation to the
true occlusion, and can be used as an approximate value for
rendering. Our algorithm is simple to implement on current
graphics processors and solves the problem of shadow map
aliasing with minimal additional storage and computation.
CR Categories: I.3.7 [Computer Graphics]: Three-
Dimensional Graphics and Realism—Color, shading, shad-
owing, and texture
Keywords: real-time rendering, shadow maps, shader pro-
gramming, graphics hardware
∗
e-mail: wdonnelly@math.uwaterloo.ca
†
e-mail: atlaurit@cgl.uwaterloo.ca
1 Introduction
Shadow maps [Williams 1978] and shadow volumes [Crow
1977] are the two most common shadowing algorithms used
in real time applications. Shadow maps have many advan-
tages compared to shadow volumes; for example they are
easy to implement, their cost is less sensitive to geometric
complexity and they can be queried at arbitrary locations.
Unfortunately, like most textures, shadow maps suffer
from aliasing if not filtered properly. Modern graphics hard-
ware provides built-in methods to reduce texture aliasing on
color textures: namely mipmapping and anisotropic filter-
ing. These techniques are inapplicable to standard shadow
maps, since they will simply interpolate the depths of neigh-
boring pixels. Typically real time implementations use
nearest-neighbor sampling of shadow maps, or take several
samples and average the results. This method is expensive,
causes aliasing and does not take full advantage of graphics
hardware’s aforementioned fast, built-in filtering capabili-
ties.
To address the problem of efficiently filtering shadow
maps, we note that each texel of a standard shadow map can
only represent the depth of a single point. Variance shadow
maps improve on this scheme by representing a distribution
of depths at each texel. To approximate such a distribution
using a small amount of data, we store the first and second
moments: the mean depth and mean squared depth. One
major advantage of this representation is that we can ap-
proximate the average of two distributions by averaging the
moments.
When querying the variance shadow map, we use the mo-
ments to compute a bound on the fraction of the distribu-
tion that is more distant than the surface being shaded. We
show that this bound provides a good approximation for the
amount of light reaching any given surface, and therefore
can be used for rendering correctly anti-aliased shadows.
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