Dense Flow Visualization Lecture 10 February 27, 2020 General - PowerPoint PPT Presentation

CS53000 - Spring 2020 Introduction to Scientific Visualization Dense Flow Visualization Lecture 10 February 27, 2020

General Overview Dense methods in 2D Dense methods in 3D Dense methods on curved surfaces CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 2

Dense Vector Field Representations in 2D CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 3

Digression Noise in signal processing: signal produced by a stochastic (random) process Noise “color” describes its power distribution: how the signal’s energy is distributed across the frequency range Notion of noise extends to images (2D stochastic signals) CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 4

Visible Color Spectrum NB: wavelength = 1/frequency CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 5

�������������������������������������������� White Noise CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 6

����������������������������������� Blue Noise CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 7

������������������������������������������� Pink Noise CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 8

White Noise Noise image (2D signal) CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 9

Blue Noise Noise image (2D signal) CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 10

Pink Noise Noise image (2D signal) CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 11

Line Integral Convolution 1D smoothing of white noise image along flow direction (streamline) CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 12

LIC: Basic Idea Value of each pixel in output image computed as convolution of value of neighboring pixels along the flow � ∞ f ( τ ) g ( t − τ ) d τ f ∗ g ≡ −∞ Integration of streamlet from each pixel Assuming pixel-wise constant vector (Euler) In both directions Length (pixel-wise) controlled by kernel size CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 13

����������������� LIC: Basic Idea Value of each pixel in output image computed as convolution of value of neighboring pixels along the flow � ∞ f ( τ ) g ( t − τ ) d τ f ∗ g ≡ −∞ Integration of streamlet from each pixel Assuming pixel-wise constant vector (Euler) In both directions Length (pixel-wise) controlled by kernel size CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 13

������������������ ����������������� LIC: Basic Idea Value of each pixel in output image computed as convolution of value of neighboring pixels along the flow � ∞ f ( τ ) g ( t − τ ) d τ f ∗ g ≡ −∞ Integration of streamlet from each pixel Assuming pixel-wise constant vector (Euler) In both directions Length (pixel-wise) controlled by kernel size CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 13

������������������ ����������������� ���������������������������� LIC: Basic Idea Value of each pixel in output image computed as convolution of value of neighboring pixels along the flow � ∞ f ( τ ) g ( t − τ ) d τ f ∗ g ≡ −∞ Integration of streamlet from each pixel Assuming pixel-wise constant vector (Euler) In both directions Length (pixel-wise) controlled by kernel size CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 13

LIC: Fine tuning Aliasing problems induced by white noise input texture can be solved by applying low pass filter (blurring) in pre-processing Simple convolution kernel: box Special convolution kernels can be used to show flow direction (periodic motion) Normalization applied after convolution to preserve brightness and contrast CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 14

LIC: How does it work? Correlation of pixels along the flow No correlation orthogonal to the flow Resulting pictures are similar to visualizations achieved with oil film applied onto surface of embedded body in wind tunnel experiments B. Cabral, C. Leedom, Imaging Vector Fields Using Line Integral Convolution, ACM SIGGRAPH ‘93 CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 15

LIC: How does it work? Correlation of pixels along the flow No correlation orthogonal to the flow Resulting pictures are similar to visualizations achieved with oil film applied onto surface of embedded body in wind tunnel experiments B. Cabral, C. Leedom, Imaging Vector Fields Using Line Integral Convolution, ACM SIGGRAPH ‘93 CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 15

LIC: Results Basic LIC http://www.erc.msstate.edu/~zhanping/Research/FlowVis/LIC/LIC.htm CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 16

CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 17

LIC: Results + Color coded vector field magnitude http://www.erc.msstate.edu/~zhanping/Research/FlowVis/LIC/LIC.htm CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 18

CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 19

LIC: Results + Histogram equalization http://www.erc.msstate.edu/~zhanping/Research/FlowVis/LIC/LIC.htm CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 20

CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 21

LIC: Results + High-pass filtering http://www.erc.msstate.edu/~zhanping/Research/FlowVis/LIC/LIC.htm CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 22

CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 23

FastLIC: Speeding things up Exploit redundancy of streamlines covering many pixels Number of streamlines needed to cover entire image is only 2% of number of pixels! Use correlation between convolution coefficients Integrate flow using RK 45 + cubic interpolation Algorithm is 10x faster than standard LIC D. Stalling, H.-C. Hege, Fast and Resolution Independent Line Integral Convolution, ACM SIGGRAPH ‘95 CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 24

Enhanced LIC Recycle texture: Improve contrast by iteratively taking last computed LIC texture as input for next iteration Combined with final high-pass filtering A. Okada, D. L. Kao, Enhanced Line Integral Convolution and Feature Detection, IS & T / SPIE Electronics Imaging ‘97 CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 25

Enhanced LIC Results http://www.erc.msstate.edu/~zhanping/Research/FlowVis/LIC/LIC.htm Standard LIC Enhanced LIC CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 26

Enhanced LIC Results http://www.erc.msstate.edu/~zhanping/Research/FlowVis/LIC/LIC.htm Standard LIC Enhanced LIC CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 26

Multifrequency LIC Kiu & Banks, Vis96 Change frequency of noise texture image based on flow properties (e.g speed) CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 27

Dense Vector field Representations in 3D CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 28

����������������������� Dense Vector field Representations in 3D CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 28

Volumetric LIC Cabral & Leedam Interrante CS530 / Spring 2020 : Introduction to Scientific Visualization. Feb 27, 2020 10. Dense Flow Visualization 29