- 151 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Convolution Shadow Maps' - mireille

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Convolution Shadow Maps

*MPI Informatik Germany

† Hasselt University

Belgium

‡University College London

UK

Motivation: Screen-space anti-aliasing

Percentage Closer Filtering (NVIDIA)

Convolution Shadow Map (CSM)

Problem statement

Filtering the z values of the Shadow Map

Filtering the CSM data structure

Helix scene

?

?

Benefits of a CSM

- Efficient screen-space anti-aliasing through hardware filtering
- Including mipmapping and anisotropic filtering
- Enables additional convolutions
- Blur filter conceals discretization artifacts
- Improves temporal coherence substantially

Related Work

- Percentage Closer Filtering (PCF) [Reeves et al. 1987]
- average multiple shadow tests
- NVIDIA’s GPU version
- 2x2 pattern
- analogous to bilinear filter
- Trilinear (mipmap) not possible
- Variance Shadow Maps (VSM) [Donnelly et al. 2006]
- Probabilistic approach
- Filtering z and z2
- Estimates upper bound only
- Light leaking artifacts
- Precision problems

Courtesy of Donnelly [Demo]

p

z(p)

c

d(x)

x

Shadow Mapping [Williams 1978]- xR3
- pR2
- x equals p just in different spaces
- Shadow function:s(x):=f(d(x),z(p))
- Binary result:
- 1 if d(x)<=z(p)
- 0 else

p

d(x’)

z(p)

c

x

x’

Shadow test function: s(x)- What kind of function is s(x)?
- Heaviside Step Function: H(t)

Shadow term for x’

p

q

p

z(p)

N

c

d(x)

x

y

y

N

How to filter s(x) ?- Filter s(x) “around” p
- Assume d(y)≈ d(x)
- d(x) representativedistance forN
- Same for PCF
- Then we get:

s(x)≈ ai(d(x)) Bi(z(p))

Non-linearity of the shadow test- =
- Filtering shadow test result != filtering z values
- Our new solution: Transform depth map such that we can write the shadow test as a sum

(1D function)

z(p)

Bi(z(p))

Reconstruction Example

- s(x) ≈ a1(d) +a2(d) +..+ a4(d) +..+ a8(d) +..+a16(d)

= ai(d(x))[w * Bi(z)](p)

Why is this useful?- Fill expansion into convolution formula
- Convolution on s(x) == convolution on Bi(z(p))
- Note: d(x) and z(p) had to be separable!
- Decoupling d(x) and z(p) enables pre-filtering!

sf (x) = [w * f(d(x), z)](p)

a1(d) +..+a4(d)

+…+

a8(d) +..+a16(d)

sf (x) ≈

a1(d) +..+a4(d)

+…+

a8(d) +..+a16(d)

Filtering ExampleOriginal Bi(z)

After filtering Bi(z)

[w * Bi(z)]

+c2

+..+c4

+..+c8

+..+c16

Important properties of a Fourier series- Step function becomes sum of weighted sin()
- Series is separable!
- Constant error due to shift invariance

Issues with a Fourier series

- Ringing suppression
- Reduce higher frequencies
- Steepness of “ramp”
- Offset (transl. invariance!)
- Shift shadow test
- Increases lightness prob.
- Scaling
- Scale shadow test
- Decreases filtering
- See paper for tradeoffs

Limitations and drawbacks

- Influence of reconstruction order M
- Memory consumption increases as M grows
- Performance (filtering) decreases as M grows

M = 1

M = 2

M = 4

M = 8

M = 16

Performance and Memory

- Frame rate for complex scene (see video) ~365k polygons (NVIDIA GeForce 8800-GTX)
- Requires (M/2) 8-bit RGBA textures
- Apply convolution to each texture

256 512 1024 2048

Conclusion

- CSM, a new data structure which enables pre-filtering of shadow maps
- Mipmaps
- High quality screen-space anti-aliasing for shadow rendering
- Improved temporal coherence
- Additional convolution conceals discretization artifacts

Outlook and Extensions

- New separable expansion
- Less memory
- Higher performance
- Better quality at contact points
- Rendering approximate Soft shadows
- Efficient algorithm based on spatial relations

Download Presentation

Connecting to Server..