volume visualization 2 - university of manchester

Volume Visualization (2)

Louise M. LeverW T Hewitt

November 2006MSC ACS CS605Manchester

2vol viz/03Supercomputing, Visualization & e-Science 52

Surface Extraction MethodsDividing Cubes[7]

Observation: the size of many polygons produced by Marching Cubes are often smaller than pixel size

Basic idea1. Classify each voxel as inside, outside or on the surface2. Subdivide surface voxels to image resolution3. Output points with normals


Surface Extraction MethodsDividing Cubes

1. Classify each voxel in a volumeVoxel is interior if all data values are above surface valueVoxel is exterior if all data values are below surface valueOtherwise surface intersects the voxel



2. Subdivide Surface voxels to image resolutionIn x, y, and z create small voxels that correspond to the final image resolution. If original data is 256x256x256 and final image is 512x512, subdivide twice in x, y and z

Resample the intensities for the new voxels using tri-linear interpolation

For each new voxel, test if surface voxel as in step 1



3. Calculate NormalsFor each surface voxel interpolate gradient vectors for surface intersections using central differencesCalculated surface normal at each surface pointOutput points with normal, points are pixel sized.


Surface Extraction MethodsMarching Cubes vs. Dividing Cubes

Both extract surface models from volume dataMarching Cubes

Creates trianglesModels rendered using conventional graphics techniquesEfficient for small volumes

Dividing CubesCreates points with normalsEfficient for larger volumes


Surface Extraction MethodsSummary

AdvantagesRendering methods are known: shadows, depth cueing etc.Changing views/lights requires only re-rendering of geometric primitivesCan be done in hardware

DisadvantagesCan introduce artifacts and ambiguitiesThrows away data between surfacesNot capable of imaging volume interiorsNot capable of imaging continuum


Direct Rendering MethodsIntroduction

To render the volume directly without recourse to intermediate geometryTo allow the display of weak and fuzzy surfacesCan relax the condition that a surface is either present or notTwo methods will be covered

Ray Casting [1]Splatting [10]


Direct Rendering MethodsRay Casting

Basic idea1. Shade the acquired data to obtain a volume of colour values2. Classify the data to obtain a volume of opacity values3. Cast a ray through both volumes and takes samples along the ray4. At each sample point calculate the colour and opacity using tri-linear

interpolation5. Composite the colour and opacity samples along the ray to produce a

total colour for the ray.



1. Shade the acquired data to obtain a volume of colour valuesCalculate normals for each voxel using central differencesusing Phong or some other shading method, calculate a colour for each voxel, creating a volume of colours

2. Classify the data to obtain a volume of opacity valuesUse one of the classification techniques shown earlier (binary, region boundary surfaces etc.) to assign an opacity for each sample locationIsovalue contour surfaces — Good for display of multiple concentric surfacesRegion boundary surfaces — Good for data with lots of fuzzy surfaces



Opacity Classification — Isovalue Contour SurfacesEnsures that data values near to fv are mapped to similar opacities Tails off in inverse proportion to gradient magnitude i.e surface strength

αv

α(xi) gradientmagnitude | ∇ f(xi)|

fv acquiredvalue f(xi)

a(xi) = αv

1

1 - 1 |fv - f(xi)|

|∇f(xi)|r

0{ if f(xi) = fv

if within range

otherwise

opacity



Opacity Classification - Region Boundary SurfacesAssigns opacities to a number of fixed sample values Interpolates between them so that every voxel has an opacity

αva

α(xi)gradientmagnitude | ∇ f(xi)|

fvaacquiredvalue f(xi)

opacity

αvb

αvc

fvb fvc



3. Cast a ray through the volume of opacities and colours and take samples along the ray

4.

At each sample point, calculate the colour and opacity using trilinearinterpolation of the voxel vertex values

pixel p(i,j)

image plane

viewpoint

data volume

sample points

entry point

exit point

ray




5. Composite the colour and opacity along each rayComposite along each ray to give a total colour for the ray and hence the originating pixelUses the Porter and Duff “Over” operator[27]

C(0)inC(N)out C(i), α(i))

Cout Cin 1 α i( )–( ) C i( )α i( )+=



Direct Rendering MethodsRay Casting — Serial optimizations

Early Ray Termination [19]Stop tracing when total opacity = 1, since no point tracing any further

Hierarchical Spatial Enumeration [18]Pyramids, Octrees,Avoids tracing through parts of the volume that don’t contain any relevant data



Adaptive Screen Sampling[18]

Calculate a subset of the pixels Interpolate intermediate values Replace interpolated values in areas of high gradient

Calculated from ray

interpolated pixels



Adaptive Ray Sampling [20]

Sampling rate is adjusted according to the significance of the traversed data

Sampling rate <-> gradient magnitudeSampling rate <-> material opacity

5

6 5

5

5

55

6

6

6

6

3 233

2

2

3

3

3

3

3

3

3



Templates [21]rays in parallel viewing perform the same set of steps which is saved as a template

Space leaping [22]techniques to construct a bounding object around the interesting part of the volume, so that empty space can be quickly traversed

template


Direct Rendering MethodsSplatting [8][9][10]

Can be likened to throwing a snowball onto a glass plateBasic Idea

Determine in what order to traverse the volumeClassify and shade the voxels in each sliceProject or splat each slice onto the image planeDetermine the extent of the splat’s contribution and attenuate according to some filterMerge the attenuated splats to calculate the pixel contributions


Direct Rendering MethodsSplatting

1. Determine in what order to traverse the volumeVoxels are projected in order of their distance from the image plane aslice at a timeTherefore need to calculate which slice is nearest the image planeThis ensures that close voxels obscure distant voxels

2. Classify and Shade the voxels in each sliceClassify the voxels according to some opacity transfer function or look up tableCalculate the gradient using central differences and use this information in the shading formula



3. Project each voxel in a slice onto the image planeA reconstruction filter, usually a Gaussian is used to determine the extent of the splat (its footprint) on the image plane

Voxel(r,g,b,α)

Projection

planeon image



4. Attenuate according to the filterThe classified, shaded voxels (r,g,b,a tuples) are then attenuated according to where they fall within the footprintVoxels projected into the middle of the footprint will have the highest contribution

5. Merge the attenuated splatsComposite the attenuated r,g,b,a tuples that fall within footprint to give a pixel value for the image buffer


Direct Rendering MethodsSummary

AdvantagesNon-binary classificationShows structure between surfacesDisplays small and poorly defined featuresReadily parallelisable

DisadvantagesExpensive - cost is proportional to volume size (n3)Combining volume and geometry data is difficultCan’t take advantage of computer graphics hardware


Mixing Volume and Geometry DataSurface Based Intermixing [24]

Convert volume data to geometric data using surface reconstruction algorithms Mix with the required geometry and renderAdvantages

Can use graphics hardware and normal computer graphics techniquesLow memory and storage needs

DisadvantagesCan’t see internal dataSensitive to object complexity


Mixing Volume & Geometry DataVolume Based Intermixing [23]

Voxelise the geometry dataMix with the sampled volume & render using direct methodsAdvantages

Access to entire volume not just surfacesInsensitive to object complexity

DisadvantagesLarge amount of memory and storageLong processing timeClassification is difficult


Volume and Geometry DataPoint Based Intermixing [25]

Adds a “point” to the set of geometric primitives where a point is a 3D location and normal

Normals are calculated for each voxel using central differencesThresholding can be used to cut down the number of points

AdvantagesInteractiveCan take advantage of computer graphics hardware

DisadvantagesRepeated normal estimation for every changeHoles may appear


Volume and Geometry DataZ-merging [23]

Render volume using surface reconstruction or direct methodsRender geometry separatelyMerge using some depth storing technique

AdvantagesCan use either direct or indirect methodsCan be implemented in hardwareInteraction

DisadvantagesRe-renders all the data if the model is changed


Volume and Geometry DataRay Merging [28]

Trace rays through volume and geometry datasets producing two vectors of valuesCombine the two vectors to produce pixel valuesAdvantages

Handles transparencyUses complete volumeHandles small features and complex objects

Disadvantages Not interactiveLots of memory required


APIs for Volume Visualization

OpenGL Volumizer (www.sgi.com/software/volumizer)Developed by SGILibrary of C++ classesAimed at O2, Octane and Onyx2I.e., needs 2D and/or 3D texture hardware

Adds volumetric primitive


Volumizer Supports

Mixing primitivesVolume deformationCo-resident volumesTime-varying volumesArbitrary regions of interest


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