Scientific Data Visualization Foundation

Transcription

1 Scientific Data Visualization Foundation Data Sources Scientific Visualization Pipelines Data Acquisition Methods GeoVisualization 1 Scientific Data Sources Common data sources: Scanning devices Computation (mathematical) processes Measuring Application tools usually coupled with Haptic feedback devices Stereo output (glasses) Interactivity ---- demanding of the rendering algorithm 2 1

2 Scanning - Domains Biomedical scanners: MRI, CT, SPECT, PET, Ultrasound, confocal microscopes. Surface scanner (range data, surface details) Geospatial sensor 3 Surface Scanner Laser Scanner Structured Light Scanner 4 2

3 Scanning - Applications Medical education, illustration and training Biomedical research 5 6 3

4 Scanning Applications (2) Surgical simulation for treatment planning Medical diagnosis and Tele-medicine Inter-operative visualization in brain surgery, biopsies, etc. (computer-aided surgery) Industrial purposes (quality control, security) Games with realistic 3D effects? 7 Scanning Applications (3) Range data: Digital library, Virtual museum, etc. Geographical Information Systems 8 4

5 Scientific Computation Data sources (domain): Mathematical analysis, ODE/PDE, Finite element analysis (FE), Supercomputer simulations, etc Applications: Scientific simulation, Computational fluid dynamics (CFD), etc. 9 Measuring - Domains Data sources (domain): Orbiting satellites, Spacecraft, Seismic devices, Statistical Data. Applications: for military intelligence, weather and atmospheric studies, planetary and interplanetary exploration, oil exploitation, earth quake studies, Statistical Analysis - Info Vis (Financial Data ) 10 5

6 11 Visualization Functional Model Shows data flow, transformation, and functional dependencies between processes Data flow diagram (DFD) Data source: creates data Data sink: consumes data Filter: data transformation Data store: data storage Data synchronization 12 6

7 DFD example 3D medical imaging system: CT/MRI scanning Raw data Data reconstruction slices Surface extraction write triangles pixels Data file rendering images

8 DFD example (2) Visualizing function: F( x, y, z) R Sampling F(x,y,z) Point array Cutting plane Iso-Surface extraction Meshed samples Line contouring polygons display lines display display

9 Visualization pipeline Data objects: data and methods to create, access & delete data Process objects: processes to transform data Source object (or read object): creates data. Filter object: transform data Mapper object (or write object): consume (display, output) data. Pipeline connections require type and multiplicity consistency 17 Pipeline example Sampling F(x,y,z) Iso-surface extraction Cutting planes Contouring Display Display Display 18 9

10 Looping Pipeline Example: velocity field Sampling points Probe data with points for velocity V i Compute motion P P V t i1 i i Display points Input field data 19 Executing Pipeline Pipeline is executed only when there is a change to input data or process parameter Demand-driven approach: when output is requested (VTK style) Event-driven approach: every change leads to pipeline re-execution 20 10

11 Data Characteristics Visualization data is discrete Digital technology Analytic property unknown sampling necessary Interpolation necessary Regularity Regular (structured) data Irregular (unstructured) data Dimensionality 1D (curve, line), 2D (surface), 3D (volume) Multiple use of lower dimensional techniques for higher dimensional problems. 21 Dataset model Dataset = structure + attributes Structure: spatial info and relationships Topology: cells Geometry: points Attributes: properties temperature, velocity, etc Associated with the structure Example: height field (2D or 3D cells) structure dataset attributes topology geometry Scalar,vector Tensor, cells points 22 11

12 Cells and Points Cells type connectivity list Ci = {P1, P2, Pn} Primary cells: smallest unit in topology Composite cells: groups of primary cells Points Pointers to point storage Use set: U(Pi) = {Ci: Pi in Ci} 23 Cell types vertex line poly-line triangle polygon triangle-strip quadrilateral pixel voxel tetrahedron pyramid hexahedron 24 12

13 Attributes Information associated with structure (usually with points) Common attribute types Scalar: temperature, density, pressure, etc Vector: velocity, trajectory, gradient, etc. Normals: direction only Tensors: k-dimensional array (e.g. stress & strain) User-defined data Texture coordinates 25 Type of datasets Structured points Regular, rectangular lattice of points Cells: pixels or voxels 2D (image, pixmap, bitmap), 3D (volume) Simple data structures 26 13

14 Type of datasets (2) Rectilinear grid Regular lattice Non-uniform spacing Structured grid Regular topology Irregular geometry 27 Type of datasets (3) Unstructured grid Irregular topology Irregular geometry Finite element grid tetrahedral grid, etc. Unstructured points No topology Unstructured geometry Particle systems Smoothed Particle Hydrodynamics 28 14

15 Data Acquisition Methods X-Rays Computed Tomography (CT or CAT) MRI (or NMR) PET / SPECT Ultrasound Microscopy Computational Geospatial (remote sensing, satellite imaging) synthetic methods 29 X-Rays photons produced by an electron beam 30 15

16 X-Rays (2) Cheap and relatively easy to use commonly used to image gross bone structure and lungs excellent for detecting foreign metal objects Potentially damaging to biological tissue main disadvantage -> lack of anatomical structure all other tissue has very similar absorption coefficient for x- rays 31 CT or CAT - Principles Computerized Tomography: 3D extension of X-rays based on the principle that a three-dimensional object can be reconstructed from its two dimensional projections measures the attenuation of X- rays from many different angles a computer reconstructs the organ under study in a series of cross sections or planes combine X-ray pictures from various angles to reconstruct 3D structures 32 16

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18 CT Reconstruction: Filtered Back Projection (FBP) Radon transform: the projection data Fourier Slice Theorem: the 1D Fourier transform of the projection data at a given angle is the same as the radial data passing through the origin at the same angle in the 2D Fourier transform domain data. y f(x,y) x s g (s) 35 Fourier Slice Theorem g ( s) f ( x, y)exp( i( x cos( ) y sin( )) dxdy F(, ) G ( ) F( g f ( s cos( ) t sin( ), s sin( ) t cos( )) dt ( s)) g ( s)exp( is) ds f ( s cos( ) t sin( ), s sin( ) t cos( ))exp( is) dsdt f ( x, y)exp( 2i( xu yv)) dxdy F( u, v) where 2u cos( ), 2v sin( ) 36 18

19 CT Reconstruction: FBP (2) Inverse radon transform can be achieved by filtering the projection images with a ramp filter in frequency space, and then back-projecting the filtered projections onto a reconstruction grid. ˆ 1 f ( x, y) β { R[ f ( x, y)]} R f ( x, y) { R[ f ( x, y)]} F( u, v)exp[2i( ux yv)] dxdy F(, )exp[2i( x cos y sin )] dd F(, k )exp[2i( x cosk y sin k )] dd 37 CT Reconstruction: Algebraic reconstruction technique (ART) Initial Guess v 3 v 2 v 1 p i p i+1 p i-1 Back- Projection Reconstructed model Actual Data Slices Projection w v w v w 11 1 v w v 2 2 w w 1N 2N v v N N p p 1 2 w j = w v w M 1 1 v M 2 2 w MN v N p M 38 19

20 CT Reconstruction: ART (2) Object reconstructed on a discrete grid by a sequence of alternating grid projections and correction back-projections. Projection: measures how close the current state of the reconstructed object matches one of the scanner projections Back-projection: corrective factor is distributed back onto the grid many projection/back-projection steps needed for a certain tolerance margin 39 CT - FBP vs. ART FBP ART Computationally cheap Clinically usually 500 projections per slice problematic for noisy projections Still slow better quality for fewer projections better quality for non-uniform project. guided reconstruct. (initial guess!) 40 20

21 MRI Nuclear Magnetic Resonance (NMR) (or Magnetic Resonance Imaging - MRI) most detailed anatomical information high-energy radiation is not used. Reconstruction process similar to CT, but in frequency domain. 41 MRI - Signal to Noise Ratio proton density pictures - measures H MRI is good for tissues, but not for bone signal recorded in Frequency domain!! Noise - the more protons per volume unit, the more accurate the measurements - better SNR through decreased resolution 42 21

22 PET Functional imaging modality (not structural): blood flows, Glucose metabolism, etc. Injecting radiotracer, which decays by Positron Emission Gamma photons can be emitted and detected. Follow the movements of the injected compound and its metabolism Reconstruction techniques similar to CT 43 PET Images 44 22

23 Comparison CT and MRI show that you have a brain; PET show that you use it! 45 Ultrasound Use high-frequency sound (ultrasonic) waves to produce images of structures in human body Above the range of sound audible to humans (typically above 1MHz) Aimed at a specific area of the body Change in tissue density reflects waves, and echoes are then recorded Delay of reflected signal and amplitude determines the position of the tissue Can be used for both still images and moving objects 46 23

24 Ultrasound (2) Very safe commonly used to examine fetuses in utero, also for heart, liver, kidneys, eye, gallbladder, breast, and major blood vessels least expensive but noisy irregular sampling - reconstruction problems 47 3D Microscopy Laser confocal microscope laser lens Confocal pinholes Dichroic mirror Detector object 48 24

25 3D Microscopy (2) Structures of microscopic scale (cells, tissues/muscles, blood vessel) Structures often unknown Slices collected as focal planes Low contrast, low intensity gradients, bad signal to noise ratio. Photo-bleaching : iso-surface extraction is difficult. 49 Computational Problems in Science and Engineering Input: physical domain, load, boundary conditions Mathematical models: PDE, ODE, etc Output: function and variable values over a continuous physical domain. Means: Domain discretization, approximation and interpolation (Newton, Finite difference, FEM) Data: discrete values and solutions Visualization: input, process, results 50 25

26 CM - Approach Continuous solution doesn t exist (for most part) Numerical Approximation/Solution 1. Discretize solution space - Grid generation explicit 2. Replace continuous operators with discrete ones 3. Solve for physical quantities 51 CM -Grid Types Structured Grids: regular uniform Unstructured Grids: rectilinear curvilinear regular irregular hybrid curved 52 26

27 CM - Grid Examples 53 Synthetic Methods 3D Discretization Techniques :Voxelization Scan Conversion of Geometric Objects Planes / Triangles Cylinders Sphere Cone NURBS, Bezier patches 54 27

28 Synthetic Methods Solid Texture, Hyper Texture - 3D Textures Fur Marble Hair Turbulent flow 3D Regular grid has texture values 55 28