Direct Volume Rendering Joe Michael Kniss [email protected] cs.utah/~jmk

Direct Volume Rendering

Joe Michael [email protected]

http://www.cs.utah.edu/~jmk

Scientific Computing and Imaging InstituteUniversity of Utah

Outline

1. What is Volume Rendering?

2. Shading models

3. Current hardware methods

4.Visualization 2001 presentation

Volume Rendering

Volume Rendering is a visualization/graphics technique which directly renders data using a reasonable approximation to a physical light transport model.

What?

Overview• Data acquisition

• Reconstruction

• Sample & interpolate

• Transfer function

• Lighting

• Blend/integrate

Volume Rendering

Spiral CT

Filtered back-projection

Tri-linear Interp.

3D T.F.

Light & shadow

Back to Front

OverviewVolume Rendering

Acquisition type Reconstruction

•CT (X-ray)

•MRI

•Simulation

•Inverse Radon

•Inverse Fourier

•None?

Others: PET, SPECT, EEG, MEG, Geological, Atmospheric

InterpolationOverview

Sampled Function

How do we recover a function that is at least C0 continuous??

Real Function

?

Interpolation

• Estimate values between samples

• Reconstruct continuous function

Overview

box

linear

sinc

Catmul-Rom

C0

C0 C1

C00

Interpolation



Overview

box

linear

sinc

Catmul-Rom

Bad

OK Good

Best

Quality

Interpolation



Overview

box

linear

sinc

Catmul-Rom

Easiest

Easy OK

Hard

Use


Sampled Function

Laura Bush


Box

What is the value here?


Box



Box



Box == Nearest Neighbor

Reconstructed function


Linear



Linear



Linear



Linear == Connect the dots



Catmull-Rom == Rolling Hills



Sinc == Roller Coaster


But what about the ringing??



box

linear

sinc

Catmul-Rom

Bad

OK Better

Hmm…

Quality

In reality:

Interpolation

• Bi-linear

• Tri-linear


• Bi-linear = 3 linear interpolations, 2 axes

• Tri-linear = 7 linear interpolations, 3 axes

Interpolation

•1st along x

•2nd along y

•1st along x



Interpolation

•1st along x

•2nd along y

•1st along x

•2nd along y



Interpolation

•1st along x

•2nd along y

•1st along x

•2nd along y

•3rd along z

Transfer Function

• Assign optical properties to data– Color– Opacity

Transfer function

Transfer Function


Transfer function

x

Transfer Function


Transfer function

T(x)

RenderingOverview

Volume DataEye

Image plane

Projection

RenderingOverview

Volume DataEye

Image plane

Ray Casting

But how do we get the final color??

r0r1

RenderingOverview

Solution: Integrate

r0 r11

0

)(r

r

dxxT

r0r1

T(x)

RenderingOverview

Solution: Sum (Riemann)

r0r1

r0 r11

0

)(r

r

dxxT xxTn

i

i 0

)(

RenderingOverview

r0 r1

1

0

)(r

r

dxxT xxTn

i

i 0

)(

Emissive What about occlusion??

n

i

it0

RenderingOverview

r0 r1

Absorption• Use alpha channel for opacity

• Values should approach ZERO

Exponential-1 curve

0

1

)(expr

r

dxxA

RenderingOverview

r0 r1

0

1

)(expr

r

dxxA

n

i

i

n

i

i xxxAxxxA00

)(exp)(exp

n

i

ia0

RenderingOverview

r0 r1

Emission & Absorption

dsdxxAsTr

s

r

r

10

1

)(exp*)(

RenderingOverview


r0 r1

N

i

N

ij

ii at0 1

*

dsdxxAsTr

s

r

r

10

1

)(exp*)(

RenderingOverview


r0 r1

))))((...(( 0011 Batatat nnnn

cout = ci + ai*cin

N

i

N

ij

ii at0 1

* =

RenderingOverview


r0 r1

cout = ci + ai*ci-1

Where did the light come from??

LightingOverview

Eye

Image planer0

r1

Light

LightingOverview

Light

Sample ri

The volume occludes some of the light

N

i

N

ij

i

L

k

ki aat0 1

*

0

*

dsdxxAdttAsTr

s

r

r

l

s

00

1

0

)(exp*)(exp*)(

LightingOverview

Sample ri (s)First scattering/ shadows

l0

LightingOverview

It still doesn’t look like a surface.

Standard shading models need a surface normal

LightingOverview

Solution: use the gradient as the normal

linear

linear derivative

14

10

5

3

LightingOverview

Solution: use the gradient as the normal

linear

linear derivative

14

10

5

3

dx = 3-10 = -7

dy = 5-14 = -9

LightingOverview

Solution: use the gradient as the normal 14

10

5

3

normallight

eyereflection

LightingOverview

Diffuse14

10

5

3

nl

Color = C*(n l)C = object color

LightingOverview

Diffuse + specular14

10

5

3

nl

er

Color = C*(n l) + LC*(r l)P

LC = light color P = specular power

LightingOverview

Diffuse + specular & shadow

Color = [C*(n l) + LC*(r l)P ] * S

S = shadow amount

LightingOverview

Diffuse + specular & shadow + Ambient

Color = [C*(n l) + LC*(r l)P ] * S + C*A

A = Ambient contribution

RenderingOverview

Volume DataEye

Image plane

Ray Casting

r0r1

• Cast a ray through each pixel

•Intersect with volume

•Numerically integrate & return color

RenderingHardware

Volume DataEye

Image plane

Graphics Hardware•Polygons – Proxy geometry

•Textures – Data & interpolation

•Blending operations – Numerical integration

Slices

HardwareSlices

View direction

1 slice

5 slices

20 slices 45 slices 85 slices 170 slices

Hardware

Data texture

Grad texture

Shadow texture

T.F. texture

Shade textureTexture

combiner

Color & opacity

Data texture

Polygon slicing

through texture

HardwareSlicesFrame buffer

Blend each slice with previously rendered

Projection

References

• Nelson Max, Optical Models for Direct Volume Rendering, IEEE Visualization and Computer Graphics (v1 #2 June 1995)

• Mark Levoy, Display of Surfaces from Volume Data, IEEE Computer Graphics and Applications (v8 #3 May 1988)

• Kenneth R. Castleman, Digital Image Processing, Prentice Hall (c1996 ISBN:0-13-211467-4)

Direct Volume Rendering Joe Michael Kniss [email protected] cs.utah/~jmk

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