Visualization – Definition visualization: to form a mental vision, image, or picture of (something not visible or present to the sight, or of an abstraction) ; to make visible to Introduction to the mind or imagination Scientific Visualization [Oxford Engl. Dict., 1989] Stefan Bruckner tool to enable a user insight into data Simon Fraser University / “The purpose of computing is Vienna University of Technology insight, not numbers.” [R. Hamming, 1962] Stefan Bruckner 1 Visualization – Goals Visualization – Areas Visualization, … Three major areas … to explore inherent spatial Volume reference Nothing is known, Visualization Scientific Vis used for data exploration Visualization Flow … to analyze y ?! Visualization 2D/3D There are hypotheses, Vis used for verification or falsification nD Information … to present Visualization ?! usually no spatial “everything” known about the data, Vis used for communication of results reference Stefan Bruckner 2 Stefan Bruckner 3 InfoVis vs. SciVis SciVis – Examples (1) N-dimensional vs. 2/3-dimensional Volume data SciVis can be N-dimensional too (time series, simulation data, …) Abstract data vs. spatial data InfoVis data may also have spatial attributes InfoVis data may also have spatial attributes (country, state, …) Discrete data vs. continuous data InfoVis data may be sampled from a continuous domain Stefan Bruckner 4 Stefan Bruckner 5 1
SciVis – Examples (2) Medicine Flow data sketch from Leonardo Da medical illustrations by Vinci‘s anatomical notebooks Clarice Ashworth Francone Stefan Bruckner 6 Stefan Bruckner 7 Cartography Meteorology map with iso-pressure lines weather fronts isolines to visualize wind flow map for pilots compass deviations visualization Stefan Bruckner 8 Stefan Bruckner 9 Experimental Flow Investigation Visualization Scenarios Fixation of tufts, ribbons on ... aircraft in wind tunnels complexity, ship hull in fluid tanks tech. demands interactive steering Introduction of smoke interactive particles (in wind tunnel) visualization Introduction of dye (in passive fluids) benefits, visualization possibilities Stefan Bruckner 10 Stefan Bruckner 11 2
Visualization Pipeline Data Focus of visualization, Acquisition everything is centered around the data Data are given Driving factor (besides user) in choice and attribution of the visualization technique Enhancement Data are processed Data are processed Important questions Important questions In what domain are the data given? Mapping Data are mapped to, ( data space ) e.g., geometry What is the type of data? Rendering ( data characteristics ) Images generated Which representation makes sense? Stefan Bruckner 12 Stefan Bruckner 13 Data Space vs. Data Characteristics Grids – General Information data characteristics Important questions 1D 2D 3D Which data organization is optimal? Where do the data come from? 1D y=f(x) spatial curve x (t) Is there a neighborhood relationship? ace How is the neighborhood information stored? How is the neighborhood information stored? data spa 2D flow v ( x ) 2D How is navigation within the data possible? Calculations with the data possible ? Are the data structured? 3D scalar field d( x ) 3D flow v ( x ) Stefan Bruckner 14 Stefan Bruckner 15 Grid - Types Grids - Survey Cartesian grid block-structu } dy struc- ortho- equi- cartesian tured gonal dist. grids (dx=dy) x [x max ,0] } grids dx grids Curvilinear grid grids x [0,y max ] regular x [0,0] [ , ] grids (dx dy) id (d d ) rde grids Unstructured grid x [0] rectilinear grids c [0] e [0] Scattered data curvi-linear grids x [1] unstructured grids hybrid grids miscell. Stefan Bruckner 16 Stefan Bruckner 17 3
Volume Visualization Volume Data VolVis = visualization of volume data Medicine Mapping 3D 2D CT, MRI, PET, Ultrasound Volume data 3D 1D data Biology Confocal microscopy, Confocal microscopy Scalar data, 3D data space, space filling Scalar data 3D data space space filling histological cuts User goals Geology Gain insight in 3D data Seismic surveys Structures of special interest + context Material testing Industrial CT Stefan Bruckner 18 Stefan Bruckner 19 3D Data Space Concepts and Terms sampled data analytical data (measurement) (modelling) Cartesian/regular grid Most common, e.g., CT/MRI scans iso-surfacing voxel space voxel space geometric surfaces geometric surfaces (discrete) (analytic) Curvilinear/unstructured grid voxelization Less frequently, e.g., (direct) volume surface simulation data rendering rendering pixel space (discrete) Stefan Bruckner 20 Stefan Bruckner 21 Volume Rendering (1) Volume Rendering (2) Deals with the visual Initially volumes were visualized using two- representation of 3D dimensional cuts functions Extraction of surface geometry for isosurfaces Frequently, but not in the volume (e.g. Marching Cubes [Lorensen exclusively, functions are y, and Cline 1987]) ]) scalar-valued Volume rendering introduced almost Often aquired using simultaneously by [Levoy 1988] and [Drebin et sampling (e.g., medical al. 1988] domain) Stefan Bruckner 22 Stefan Bruckner 23 4
Surface vs. Volume Rendering Volume Ray Casting Surface rendering Volume: 1D value defined in 3D Indirect volume visualization f( x ) R 1 , x R 3 Intermediate representation: iso-surface Ray: Half-line Pros: Less memory, fast rendering r (t) R 3 , t R 1 >0 ( ) , Volume rendering Volume rendering Intensity profile: values Direct volume visualization along a ray Usage of transfer functions f( r (t)) R 1 , t R 1 >0 Pros: illustrate the interior, semi-transparency Image plane: starting points of rays Stefan Bruckner 24 Stefan Bruckner 25 Pipeline – Overview Pipeline – Reconstruction volume rendering pipeline volume rendering pipeline reconstruction reconstruction reconstruction reconstruction classification classification c ass c ass cat o cat o classification classification c ass c ass cat o cat o shading shading shading shading compositing compositing compositing compositing data set final image data set final image Reconstruction (1) Reconstruction (2) Usually volume data sets are given as a grid of discrete samples image plane For rendering purposes, we want to treat them as continuous three-dimensional functions We need to choose an appropriate We need to choose an appropriate eye reconstruction filter data set Requirements: high-quality reconstruction, but small performance overhead Stefan Bruckner 28 5
Reconstruction (3) Trilinear Interpolation Simple extension of linear interpolation to three dimensions Advantage: current GPUs automatically do sample point sample point trilinear interpolation of 3D textures cell cell cell cell voxel voxel Stefan Bruckner 30 Stefan Bruckner 31 Other Reconstruction Filters Comparison of Reconstruction Filters (1) If very high quality is required, more complex Marschner-Lobb test signal (analytically reconstruction filters may be required evaluated) Marschner-Lobb function is a common test signal to evaluate the quality of reconstruction filters [Marschner and Lobb 1994] [ ] The signal has a high amount of its energy near its Nyquist frequency Makes it a very demanding test for accurate reconstruction Stefan Bruckner 32 Stefan Bruckner 33 Comparison of Reconstruction Filters (2) Comparison of Reconstruction Filters (3) Trilinear reconstruction of Marschner-Lobb Cubic reconstruction of Marschner-Lobb test test signal signal Stefan Bruckner 34 Stefan Bruckner 35 6
Comparison of Reconstruction Filters (4) Comparison of Reconstruction Filters (5) B-Spline reconstruction of Marschner-Lobb Windowed sinc reconstruction of Marschner- test signal Lobb test signal Stefan Bruckner 36 Stefan Bruckner 37 Comparison of Reconstruction Filters (6) Pipeline – Classification Marschner-Lobb test signal (analytically volume rendering pipeline evaluated) reconstruction reconstruction c ass classification classification c ass cat o cat o shading shading compositing compositing data set final image Stefan Bruckner 38 Classification (1) Classification (2) Projecting a 3D data set onto a 2D image is During Classification the user defines the problematic appearence of the data Not all information contained in the volume is Which parts are transparent? relevant to the user Which parts have which color? Classification allows the user to extract the Classification allows the user to extract the important parts of the data Stefan Bruckner 40 7
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