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1 Volume Graphics - Pros Volume Graphics - Cons Advantages: - PDF document

Feb 22, 2024 •543 likes •670 views

Overview Volume Rendering Surface graphics is not enough for ... Introduction to volume graphics Volume rendering techniques Lecture 21 Contour surfaces Ray Casting Cell Projection Slides gathered from Roger Crawfis ,

  1. Overview Volume Rendering � Surface graphics is not enough for ... � Introduction to volume graphics � Volume rendering techniques Lecture 21 � Contour surfaces � Ray Casting � Cell Projection Slides gathered from Roger Crawfis , Torsten Moeller, Raghu Machiraju, � Splatting Han-Wei Shen and Ross Whitaker 5/12/2003 R. Crawfis, Ohio State Univ. 2 Surface Graphics Difficulty with Surface Graphics � Traditionally, graphics objects are � Volumetric object handling modeled with surface primitives � gases, fire, smoke, clouds (amorphous data) ( surface graphics ). � sampled data sets (MRI, CT, scientific) � Continuous in object space � Peeling, cutting, sculpting � any operation that exposes the interior 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 3 4 Volume Graphics & Surface Volume Graphics Graphics � Defines objects on a 3D raster, or discrete � grid in object space � Raster grids: structured or unstructured � Data sets: sampled, computed, or voxelized � Peeling,cutting … are easy with a volume model 5/12/2003 R. Crawfis, Ohio State Univ. 5 5/12/2003 R. Crawfis, Ohio State Univ. 6 1

  2. Volume Graphics - Pros Volume Graphics - Cons � Advantages: � Disadvantages: � Required for sampled data and � Large memory and processing amorphous phenomena power � Insensitive to scene complexity � Object- space aliasing � Insensitive to surface type � Discrete transformations � Allows block operations � Notion of objects is different 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 7 8 Volume Graphics Applications More Volume Graphics (simulation data set) Applications (artistic data set) � Scientific data set visualization � Amorphous entity visualization � smoke, steam, fire 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 9 10 Volume Rendering Algorithms How to visualize? slice � Slicing: display the volume � Intermediate geometry based data, mapped to colors, (marching cube) along a slice plane � Direct volume rendering � Iso-surfacing: generate opaque and semi-opaque � Splatting (forward projection) surfaces on the fly � Ray Casting (backward projection) or � Transparency effects: resampling volume material attenuates reflected or emitted light � Cell Projection / scan-conversion Semi-transparent � Image warping Iso-surface material 5/12/2003 R. Crawfis, Ohio State Univ. 11 5/12/2003 R. Crawfis, Ohio State Univ. 12 2

  3. Semi -Transparent - How? Semi -Transparent - How? � Radiative transport � Rendering Integral theory (Sabella, Max, …) Transport of Light � model the interaction of t light with the material ( ) s ds ( ) ∫ = − α I ( t ) c s e observer t 0 t t 1 t Emission(+) 0 s Scattering(+) ( ) C(t): shade ∫ ρ α = ( s ) k u du α (t): opacity Absorption(-) ρ (t): “density” t 0 � Discretize Integral!! light 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 13 14 Solution of Integral Evaluation = Compositing � Numerically! � “over” operator - Porter & Duff 1984 � I.e. discretize rendering integral C(0) in C in � replace integral with a Riemann sum C, α � Iterative integral evaluation - “over” operator C i , α i � difference: Front-To-Back and Back-To-Front C out C(N) out ( ) ( ) out = ⋅ − α + ⋅ α = − C C ( 1 ) C C i C i 1 out in in 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 15 16 Compositing: Over Operator Direct Rendering Pipeline I c f = (0,1,0) a f = 0.4 � Detection of Structures � Shading � Reconstruct (interpolate/filter) c = a f * c f + (1 - a f )* a b * c b color/opacity a = a f + (1 - a f )* a b � Composite c b = (1,0,0) � Final Image Validation (change c = (0.54,0.4,0) a b = 0.9 parameters) a = 0.94 5/12/2003 R. Crawfis, Ohio State Univ. 17 5/12/2003 R. Crawfis, Ohio State Univ. 18 3

  4. Direct Rendering Pipeline II Direct Rendering Pipeline III � Better yet, reconstruct the function and � For continuous media or functions without delay the classification until after the interfaces, such as temperature: resampling: � Reconstruct (interpolate/filter) color/opacity � Reconstruct (interpolate/filter) function � Composite values. � Final Image Validation (change parameters) � Apply the transfer function or color table to each sample � Composite � Final Image Validation (change parameters) 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 19 20 Direct Rendering Pipeline Vs. Surface Graphics � Transformation - similar, however some optimizations possible (shearing) Classify Reconstruct � Classification - similar for scalar data, new Shade concepts needed for vector/multi-modal data Visibility Composite � Interpolation - similar, plus accuracy issues of order discretization of the rendering integral � Shading - similar concepts for surface effects (diffuse, specular) � Compositing - novel for transparencies based on rendering integral Validate 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 21 22 Early Methods Back-To-Front - Frieder et al 1985 � Before 1988 � A viewing algorithm that traverses and renders the scene objects in order of decreasing � Did not consider transparency distance from the observer. � did not consider sophisticated light � Maybe derived from a standard - transportation theory “Painters Algorithm” � were concerned with quick solutions � hence more or less applied to binary data 1. 2. 3. 5/12/2003 R. Crawfis, Ohio State Univ. 23 5/12/2003 R. Crawfis, Ohio State Univ. 24 4

  5. Back-To-Front - Frieder et al 1985 Back-To-Front - Frieder et al 1985 � 2D � 3D x A � Start traversal at point farthest � Axis traversal can still be done arbitrarily, 8 orders B from the observer, � Data can be read and rendered as slices � 2 orders C D � Note: voxel projection is NOT in order of strictly � Either x or y can be innermost loop decreasing distance, so this is not the painter’s algorithm. � If x is innermost, display order will be A, C, B, D � Persepctive? y Screen 003 013 023 033 103 113 123 133 033 � If y is innermost, display order will be C, A, D, B 203 213 223 233 133 303 313 323 333 233 032 � Both result in the correct image! 333 132 303 313 323 333 232 031 � If voxel (x,y) is (partially) obscured by voxel (x’,y’), then 332 131 302 312 322 332 x <= x’ and y <= y’. So project (x,y) before (x’,y’) and the 231 030 331 130 image will be correct 301 311 321 331 230 330 300 310 320 330 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 25 26 Ray Tracing Ray Casting � “another” typical method from traditional � Since we have no surfaces - we need to carefully graphics step through the volume: a ray is cast into the volume, sampling the volume at certain intervals � Typically we only deal with primary rays - hence: ray-casting � The sampling intervals are usually equi-distant, but don’t have to be (e.g. importance sampling) � a natural image-order technique � At each sampling location, a sample is � as opposed to surface graphics - how do we interpolated / reconstructed from the grid calculate the ray/surface intersection??? voxels � Since we have no surfaces - we need to carefully � popular filters are: nearest neighbor (box), step through the volume trilinear (tent), Gaussian, cubic spline � Along the ray - what are we looking for? 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 27 28 Basic Idea of Ray-casting Pipeline Ray Traversal Schemes Intensity Max - Data are defined at the corners of each cell (voxel) Average - The data value inside the c1 voxel is determined using interpolation (e.g. tri-linear) c2 Accumulate - Composite colors and opacities First c3 along the ray path - Can use other ray-traversal schemes as well Depth 5/12/2003 R. Crawfis, Ohio State Univ. 29 5/12/2003 R. Crawfis, Ohio State Univ. 30 5

  6. Ray Traversal - First Ray Traversal - Average Intensity Intensity Average First Depth Depth � First : extracts iso-surfaces (again!) � Average : produces basically an X-ray picture done by Tuy&Tuy ’84 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 31 32 Ray Traversal - MIP Ray Traversal - Accumulate Intensity Intensity Max Accumulate Depth Depth � Max : Maximum Intensity Projection � Accumulate : make transparent layers visible! used for Magnetic Resonance Angiogram Levoy ‘88 5/12/2003 R. Crawfis, Ohio State Univ. 5/12/2003 R. Crawfis, Ohio State Univ. 33 34 Levoy - Pipeline Volumetric Ray Integration Acquired values Data preparation color Prepared values opacity shading classification Voxel colors Voxel opacities Ray-tracing / resampling Ray-tracing / resampling 1.0 Sample colors Sample opacities compositing object (color, opacity) Image Pixels 5/12/2003 R. Crawfis, Ohio State Univ. 35 5/12/2003 R. Crawfis, Ohio State Univ. 36 6

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