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Data Visualization

Data Visualization. Lecture 8 3D Scalar Visualization Volume Rendering : Further Ray Casting plus Other Approaches. Cast rays through image plane into volume, and measure light received Kajiya and von Hertzen (1984) Max (1995). Classical Approach - Volume Rendering Integral. C(s)=light

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Data Visualization

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  1. Data Visualization Lecture 8 3D Scalar Visualization Volume Rendering : Further Ray Casting plus Other Approaches

  2. Cast rays through image plane into volume, and measure light received Kajiya and von Hertzen (1984) Max (1995) Classical Approach - Volume Rendering Integral C(s)=light reflected at point s volume m(s) = density at point s image plane s L I = L0C(s)m(s) exp[ -s0m(t)dt ] ds light density attenuation

  3. Approximate using Riemann sums (n = number of steps) Approximate exponential by Taylor series and introduce opacity, a, and unit spacing Calculate recursively front-to-back as... Simplifying the Integral I = L0C(s)m(s) exp[ -s0m(t)dt ] ds I = Sni=0 C(iDs)m(iDs)Ds Pi-1j=0 exp [-m (jDs)Ds] I = Sni=0 C(i)a(i) Pi-1j=0 (1 - a(j)) Cout = Cin + (1-ain)aiCi aout = ain + ai(1 - ain) {stop when a = 1} Compositing associative but not commutative ie can group but cannot re-order

  4. Sample points occur within cells, not at grid points, so we need to interpolate Do we: classify at grid points, then interpolate colour / opacity interpolate data values, then classify ? Classify - interpolate classification done as pre-processing smoothing effect can obscure detail Interpolate - classify classification now within the inner loop of the ray cast (sample points are view dependent) in return, fine detail can be picked out Interpolation

  5. There is a danger in interpolation after classification Naïve colour interpolation would assign 3 parts yellow, 1 part blue to centre point… a=1 a=1 a=1 a=0 Classify - Interpolate … but if opacity of bottom left is zero? Correct approach is to weight according to opacity, so colour at centre is yellow!

  6. A Note on Shading • The appearance of volume rendered images depends critically on the reflectance calculation used to shade the samples...

  7. A Note on Shading • Recall from isosurface rendering - that surface normal is equal to the gradient vector of f At (xi,yj,zk), df/dx = 0.5*(f i+1,j,k - f i-1,j,k) df/dy = 0.5*(f i,j+1,k - f i,j-1,k) df/dz = 0.5*(f i,j,k+1 - f i,j,k-1) This gives us normals at all grid points

  8. A Note on Shading • If the classification is done at the vertices, there is a choice: • Gouraud-type: shade vertices and then interpolate to get reflected colour at sample point • Phong-type: interpolate normals at vertices to get sample normal and then calculate shading • Phong-type gives better quality - at the cost of more computational effort

  9. Ray Casting • Advantages • Non binary classification • Shows structure between surfaces • Readily parallelisable • Disadvantages • Computationally expensive - cost proportional to number of voxels (compositing is expensive) • Does not take advantage of triangle rendering hardware

  10. Ray Casting Examples • The following sequence of slides were produced using the ray casting technique available in the vtk software • The slides show for the bonsai tree data set how different aspects can be highlighted by control of the opacity transfer • The slides also show, by animation, a comparison of different approaches to interpolation and shading • Thanks to Chris Goodyer for creating the images

  11. Legend • NN = classify vertex, shade, nearest neighbour interpolate • Trilin Vertex = classify vertex, trilinear interpolate, shade • Trilin Sample = trilinear interpolate, classify, shade

  12. Bonsai TreeNN – TrilinVertex – TrilinSample NN TrilinVertex TrilinSample

  13. Bonsai Tree BranchesNN – TrilinVertex - TrilinSample

  14. Bonsai Tree LeavesNN – TrilinVertex - TrilinSample

  15. SkullNN – TrilinVertex - TrilinSample

  16. Texture-based Volume Rendering • Volume rendering by ray casting is time-consuming • one ray per pixel • each ray involves tracking through volume calculating samples, and then compositing • different for each viewpoint • Alternative approach - using texture maps - can exploit graphics hardware

  17. Modern graphics hardware includes facility to draw a textured polygon The texture is an image with red, green, blue and alpha components… … this is used in computer graphics to avoid constructing complex geometric models Texture Mapping … and we can exploit this in volume rendering

  18. Texture-based Volume Rendering • Draw from back-to-front a set of rectangles • first rectangle drawn as an area of coloured pixels, with associated opacity, as determined by transfer function and interpolation - and merged with background in a compositing operation (supported by hardware) • successive rectangles drawn on top

  19. For a given viewing direction, we would need to select slices perpendicular to this direction This requires interpolation to get the values on the slices Until recently this has only been possible with expensive graphics boards 3D Texture-based Volume Rendering volume image plane 3D texture mapping

  20. 2D Texture-based Volume Rendering • Simpler solution - 2D texture mapping: • view volume as set of slices parallel to co-ordinate planes -Precompute the textured planes for each of the 3 directions -Choose the orientation best suited to viewing direction

  21. Texture-based Volume Rendering

  22. Comparison of Ray Casting and Texture Approaches Ray casting Texture-based Texture-based Ray casting http://www.cora.nwra.com/Ogle/ http://vg.swan.ac.uk/vlib http://www.amiravis.com

  23. Close Up Ogle: texture-based Vlib: ray casting

  24. To get fast traversal, shear volume by translating each slice… then can resample as shown Project front-to-back to get intermediate image Then warp image Shear Warp Rendering

  25. Example of Shear Warp Rendering

  26. New Hardware Advances • Holy grail: real-time volume rendering • Main searcher has been Kaufman through Cube architectures • VolumePro System first commercially available from Mitsubishi’s RealTime Visualization, now from TeraRecon • Uses shear-warp rendering http://www.rtviz.com/home.html

  27. Another commonly used method is splatting Fuzzy balls around each voxel projected on to image plane Composited in the image plane VolumeToGeom in IRIS Explorer Splatting

  28. Summary of Volume Rendering Techniques • Ray casting • Splatting • Both high quality, computationally expensive • Texture-based • Shear-warp • Both lower quality, but faster

  29. Reading • Overviews of Volume Visualization • Todd Elvins, `A Survey of Algorithms for Volume Visualization’, Computer Graphics, 1992 • Ken Brodlie and Jason Wood, Computer Graphics Forum, 2001 • Michael Meissner et al, ‘A Practical Evaluation of Popular Volume Rendering Algorithms’, http://www.gris.uni-tuebingen.de/~bartz/Publications/paper/volvis2000.pdf • Ray Casting - Classic Paper • Marc Levoy, `Display of Surfaces from Volume Data’, IEEE CG&A, 1988 • Book • Introduction to Volume Rendering, Lichtenbelt, Crane, Naqvi, Hewlett-Packard Professional Books

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