Volume Rendering - web.cse.ohio-state.eduweb.cse.ohio-state.edu/.../VolumeRendering.pdf · Volume...

Volume Rendering

Lecture 21

AcknowledgementsAcknowledgements

These slides are collected from many sources.A particularly valuable source is the IEEE Visualization conference tutorials.Sources from:Roger Crawfis, Klaus Engel, Markus Hadwiger, Joe Kniss, Aaron Lefohn,

Daniel Weiskopf, Torsten Moeller, Raghu Machiraju, Han-Wei Shen and Ross Whitaker

3/4/2010 R. Crawfis, Ohio State Univ. 2

Visualization of Volumetric DataData


O iOverview

Volume rendering refresherRectilinear scalar fieldsDi t l d i d ti l d lDirect volume rendering and optical modelsVolume rendering integralRay casting and alpha blendingRay casting and alpha blending

Volume resampling on graphics hardware (part 1)Volume resampling on graphics hardware (part 1)Texture-based volume renderingProxy geometry


y g y2D textured slices

Surface GraphicsSurface Graphics

Traditionally graphics objects areTraditionally, graphics objects are modeled with surface primitives (surface graphics)(surface graphics).Continuous in object space


Difficulty with Surface Graphics Difficulty with Surface Graphics

Volumetric object handlinggases, fire, smoke, clouds (amorphous data)sampled data sets (MRI, CT, scientific)

Peeling, cutting, sculptingany operation that exposesany operation that exposes the interior


Volume Graphics Volume Graphics

Typically defines objects on a 3D raster or discreteTypically defines objects on a 3D raster, or discrete grid in object space

Raster grids: structured or unstructuredData sets: sampled, computed, or voxelizedPeeling, cutting … are easy with a volume model


Volume Graphics & Surface GraphicsGraphics


V l G hi CVolume Graphics - Cons

Disadvantages:Large memory and processingLarge memory and processing

powerObject- space aliasingj p gDiscrete transformationsNotion of objects is different


Volume Graphics ProsVolume Graphics - Pros

Advantages:Required for sampled data and

amorphous phenomenaamorphous phenomenaInsensitive to scene complexityInsensitive to surface typeypAllows block operations


Volume Graphics Applications (simulation data set)(simulation data set)

Scientific data set visualization


More Volume Graphics Applications (artistic data set)Applications (artistic data set)

Amorphous entity visualization smoke, steam, fire


Volume Rendering AlgorithmsVolume Rendering Algorithms

Intermediate geometry based (marching cube)Direct volume rendering

Splatting (forward projection)Splatting (forward projection)Ray Casting (backward projection) or resamplingp gCell Projection / scan-conversionImage warping


Image warping

How to visualize?How to visualize?slice

Slicing: display the volume data, mapped to colors, along a slice planealong a slice planeIso-surfacing: generate opaque and semi-opaque

f th fl surfaces on the fly Transparency effects: volume material attenuates volume material attenuates reflected or emitted light

Semi-transparent Iso surface


pmaterial Iso-surface

O iOverview

Volume rendering refresherRectilinear scalar fieldsDi t l d i d ti l d lDirect volume rendering and optical modelsVolume rendering integralRay casting and alpha blendingRay casting and alpha blending

Volume resampling on graphics hardware (part 1)Volume resampling on graphics hardware (part 1)Texture-based volume renderingProxy geometry


y g y2D textured slices

Volume DataVolume Data

Continuous scalar field in 3D

Discrete volume:voxelsSamplingReconstruction


Direct Volume RenderingDirect Volume Rendering

Render volume without extracting any surfacesRender volume without extracting any surfaces(DVR)Map scalar values to optical propertiesMap scalar values to optical properties(color, opacity)Need optical modelNeed optical modelSolve volume renderingintegral for viewing raysg g yinto the volume


Direct Rendering Pipeline IDirect Rendering Pipeline I

Detection of StructuresShadinggReconstruct (interpolate/filter) color/opacitycolor/opacityCompositeFi l I V lid ti ( hFinal Image Validation (change parameters)


Direct Renderin PipelineDirect Rendering Pipeline

ClassifyShade ReconstructShade

Visibilityorder

Compositeorder

Validate


Early Meth dsEarly Methods

Before 1988Before 1988Did not consider transparencydid not consider sophisticated light did not consider sophisticated light transportation theorywere concerned with quick solutionshence more or less applied to binary data


Back T Fr nt Back-To-Front - Frieder et al 1985

A viewing algorithm that traverses and renders A viewing algorithm that traverses and renders the scene objects in order of decreasingdistance from the observer.Maybe derived from a standard -“Painters Algorithm”

1. 2. 3.



2D2DStart traversal at point farthest from the observer,

xA

C D

B

2 ordersEither x or y can be innermost loopIf x is innermost, display order will

C D

p ybe A, C, B, D y Screen

If y is innermost, display order will be C, A, D, BBoth result in the correct image! Both result in the correct image! If voxel (x,y) is (partially) obscured by voxel (x’,y’), then x <= x’ and y <= y’. So project (x,y) before (x’,y’) and the image will be correct


image will be correct


3D3DAxis traversal can still be done arbitrarily, 8 ordersData can be read and rendered as slicesNote: voxel projection is NOT in order of strictly decreasing distance, so this is not the painter’s algorithm.Perspective?

103203

303213

313

003

323223

123023013

113

333333

233133

033

032132

033133

233

030

311

312

313303

302

301

323

331

332

333

321

322

333 132232

332

130230

031131

231331


300 310 320 330

230330

Ray CastingRay Casting

Goal: numerical approximation of the volume rendering integralResample volume at equispaced locations along the rayResample volume at equispaced locations along the rayReconstruct at continuouslocation via tri-linearinterpolationApproximate integral


Ray TracinRay Tracing

“another” typical method from traditional another typical method from traditional graphicsTypically we only deal with primary rays -yp y y p y yhence: ray-castinga natural image-order technique

d f hi h d as opposed to surface graphics - how do we calculate the ray/surface intersection???Since we have no surfaces - we need to carefully Since we have no surfaces we need to carefully step through the volume


Ray CastinRay Casting

Since we have no surfaces we need to carefully Since we have no surfaces - we need to carefully step through the volume: a ray is cast into the volume, sampling the volume at certain intervalsThe sampling intervals are usually equi-distant, but don’t have to be (e.g. importance sampling)At each sampling location a sample is At each sampling location, a sample is interpolated / reconstructed from the grid voxelspopular filters are: nearest neighbor (box), trilinear (tent), Gaussian, cubic splineAl th h t l ki f ?


Along the ray - what are we looking for?

Basic Idea of Ray-casting PipelinePipeline

- Data are defined at the cornersof each cell (voxel)

- The data value inside the voxel is determined using

c1g

interpolation (e.g. tri-linear)

- Composite colors and opacities

c2

3Composite colors and opacitiesalong the ray path

C th t l h ll

c3


- Can use other ray-traversal schemes as well

Evaluati n C mp sitinEvaluation = Compositing

“over” operator Porter & Duff 1984over operator - Porter & Duff 1984

Cin C(0)in

Cout

C, αCi, αi

C(N)out

α⋅+α−⋅= CCC )1( ( ) ( )iCiC 1−=


α+α= CCC inout )1( ( ) ( )outin iCiC 1=

Compositing: Over OperatorCompositing: Over Operatorcf = (0,1,0)af = 0 4af = 0.4

c = af*cf + (1 - af)*ab*cb

c = (1 0 0)

( )a = af + (1 - af)*ab

cb = (1,0,0)ab = 0.9 c = (0.54,0.4,0)

a = 0.94


Volumetric Ray Integration Volumetric Ray Integration

color

opacity

1.0


object (color, opacity)

Interp lati nInterpolation

hbinary smooth

Closest value Weighted average


Tri Linear Interp lati nTri-Linear Interpolationeye

image pixel

viewing rayv ew g ay

trilinear

voxel

interpolation

sample point


Interpolation KernelsInterpolation Kernels

volumetric compositing

color


opacity

1.0




interpolation kernel volumetric compositing

color

interpolation kernel volumetric compositing

opacity

1.0

color c = c s αs(1 - α) + c

opacity α= α s (1 - α) + α




volumetric compositinginterpolation kernel

color

volumetric compositinginterpolation kernel

opacity

1.0





color


opacity

1.0





color


opacity

1.0





color


opacity

1.0





color


opacity

1.0





color


opacity



Lev y Pi liLevoy - Pipeline

Acquired values

Data preparation

P d lPrepared values

classificationshading

V l l V l itiVoxel colors

Ray-tracing / resampling Ray-tracing / resampling

Voxel opacities

Sample colorscompositing

Sample opacities

3/4/2010 R. Crawfis, Ohio State Univ. 41Image Pixels

Ray Marching Ray Marching

Use a 3D DDA algorithm to step through regular or rectilinear grids.


Adaptive Ray Samplingp y p g[Hanrahan et al 92]

Sampling rate is adjusted to the significance of the traversed data


ClassificationClassification

How do we obtain the emission andHow do we obtain the emission and absorption values?

l l scalar value s

T(s)

emission RGB


absorption A

Ray Traversal SchemesRay Traversal SchemesIntensityy

Max

AAverage

AccumulateFirstFirst

3/4/2010 R. Crawfis, Ohio State Univ. 45Depth

Ray Traversal Fi tRay Traversal - First

IntensityIntensity

First

Depth

First

DepthFirst: extracts iso-surfaces (again!)done by Tuy&Tuy ’84


on y uy& uy 8

Ray Traversal ARay Traversal - Average

IntensityIntensity

Average

DepthDepth

Average: produces basically an X-ray picture


Ray Traversal MIPRay Traversal - MIP

IntensityIntensityMax

DepthDepth

Max: Maximum Intensity Projectionused for Magnetic Resonance Angiogram


used for Magnetic Resonance Angiogram

Maximum Intensity Projection (1)Maximum Intensity Projection (1)

No emission or absorptionPixel value is maximum scalar value along the viewing rayy

Scalar value SMaximum Smax

Advantage: no transfer function required

rays0 s

Advantage: no transfer function requiredDrawback: misleading depth information


Works well for MRI data (esp. angiography)

Maximum Intensity Projection (2)Maximum Intensity Projection (2)

/ b


Emission/Absorption MIP

Ray Traversal A l tRay Traversal - Accumulate

IntensityIntensity

Accumulate

DepthDepth

Accumulate: make transparent layers visible!Levoy ‘88


Levoy 88

T f f tiTransfer functionv = f (x)

“ here’svthe edge ”

v0

x

α


vv0

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