CSE 788 Mathema-cal and Algorithmic Founda-ons for Data Visualiza-on. Winter 2011 Han- Wei Shen

Transcription

1 CSE 788 Mathema-cal and Algorithmic Founda-ons for Data Visualiza-on Winter 2011 Han- Wei Shen

2 Class Objec-ves Give you an overview of data visualiza-on research Focus more on scien-fic data Overview the basic mathema-cs and algorithms Introduce you the state- of- the- art research in visualiza-on Provide you possible future research direc-ons

3 Reference Books There is no required textbook Reference books: The visualiza-on handbook by Charles D. Hansen and Christopher R. Johnson (Elsevier) Mathema-cal methods in the physical sciences by Mary L. Boas (Wiley) Research papers published in various top visualiza-on conferences and journals (IEEE Vis, IEEE Transac-ons on Visualiza-on and Computer Graphics, EuroVis, Pacific Vis, etc)

4 Reference Books Principles of mathema-cal analysis, by Walter Rudin Free PDF: Introduc-on to real analysis by William Trench Elementary differen-al geometry by Bare] O neill

5 Grading Homeworks and paper summaries: 25% Presenta-on: 15 % Labs: 20% Final project: 40% All done individually

6 Another Class CSE 888, Wednesday 11:30 am. to 12:30 pm. Extension of this class We will read addi-onal papers related to the topics discussed in this class Student presenta-ons

7 What is Visualiza-on? A branch of computer graphics research A process of conver-ng numerical data into visual images Focused more on data analysis than pre]y pictures

8 Visual Analysis Pipeline Data acquisi-on/genera-on Data prepara-on Feature extrac-on and visual mapping Rendering Analysis Images and Anima-ons

9 Data Acquisi-on and Genera-on Spa-al Data Medical imaging: CT, MRI, DT imagery Numerical simula-ons: PDEs Other devices: Radar, LiDAR, etc

10 Examples of PDEs PDE: Par-al Differen-al Equa-ons General forms: solve the func-on in the form of: F (x 1,...x n,u, u(x 1,x 2,...,x n ) u,... u, x 1 x n 2 x 1 x 2 u,...) =0 Result: Mul-variate scalar and vector func-ons

11 Examples of PDEs Heat equa-on: U t = U α 2 x 2 Wave equa-on: 2 U t 2 = c2 2 U x 2 Laplace equa-on: 2 φ x φ y 2 =0 Scien-fic Compu-ng and Numerical Methods

12 Data Acquisi-on and Genera-on Non- spa-al Data Network Data (Graphs and trees) Text Data (documents) Matrix data (spread sheets)

13 Visual Analysis Pipeline Data acquisi-on/genera-on Data prepara-on Feature extrac-on and visual mapping Rendering Analysis Images and Anima-ons

14 Data Prepara-on Reconstruc-on Smoothing/De- noising Re- sampling Transforma-on (cosine, wavelet, Fourier transform) Projec-on to lower dimensions Compression/down- sampling Par--oning/Bricking/Distribu-on Mul-- resolu-on hierarchy Data layout and stripping Histogram/entropy calcula-on... and more

15 Visual Analysis Pipeline Data acquisi-on/genera-on Data prepara-on Feature extrac-on and visual mapping Rendering Analysis Images and Anima-ons

16 Feature Extrac-on Generic features: isosurfaces, streamlines, pathlines, cri-cal points (local extreme points) Specific features: vortex cores, material boundary, flow separa-on lines

17 Visual Analysis Pipeline Data acquisi-on/genera-on Data prepara-on Feature extrac-on and visual mapping Rendering Analysis Images and Anima-ons

18 Visual Mapping and Rendering The process of conver-ng data to visual forms Volume rendering Op-cal models Transfer func-ons f(s, s) =(r, g, b, α) Polygon rendering (e.g. for isosurfaces) Ray tracing Raster graphics using GPUs Advanced illumina-on and stylized rendering

19 Illumina-on and NPR

20 Visual Analysis Pipeline Data acquisi-on/genera-on Data prepara-on Feature extrac-on and visual mapping Rendering Analysis Images and Anima-ons

21 Analysis The recent focus in visualiza-on research The purpose of visualiza0on is insight, not pre5y pictures (paraphrased from Richard Hamming s the purpose of compu0ng is insight, not numbers

22 Analysis Topological Surface topology: Reeb graph, contour trees Vector field topology: loca-ons and types of cri-cal points (sink, source, saddles) Geometrical Space curves: curvature, torsion Surface: first and second fundamental forms, various types of curvatures Sta-s-cal Histogram, various types of distribu-on models Informa-on theory: entropy measures

23 Visual Analysis Pipeline Data acquisi-on/genera-on Data prepara-on Feature extrac-on and visual mapping Rendering Analysis Images and Anima-ons

24 Images and Anima-ons The output of the visual data analysis pipeline Analysis of image and anima-on output can be used to adjust the visualiza-on parameters Many metrics available to evaluate the quality of visualiza-on Visual computa-on can be accelerated by considering the final image proper-es (visibility, projec-on, etc) image space method

25 Image Based Visualiza-on Algorithm Example: image based streamline seeding

26 Topics this quarter Scalar data visualiza-on and analysis Differen-al calculus basics (par-al differen-al) Real func-on of one or mul-ple variables Level sets (isosurfaces) of scalar func-ons Topological analysis of level sets Differen-al geometry basics Curves and surfaces Direct volume rendering Op-cal model, basic ray tracing algorithms, transfer func-ons Quick overview of level set and PDEs

27 Topics this quarter (cont d) Vector data visualiza-on and analysis Vector calculus basics Par-cle tracing and numerical ODE (ordinary differen-al equa-on) Vector field topology: cri-cal point classifica-on Flow visualiza-on techniques Quick overview of tensor data visualiza-on

28 Topics this quarter (cont d) Sta-s-cs based data visualiza-on and analysis Random variables and distribu-ons Mul-variate distribu-ons Es-ma-on Informa-on theory and entropy measures Applica-ons in visualiza-on