Lecture 7: Image Sources, Convolution, Scene Graphs COMPSCI/MATH - - PowerPoint PPT Presentation

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Lecture 7: Image Sources, Convolution, Scene Graphs COMPSCI/MATH - - PowerPoint PPT Presentation

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Lecture 7: Image Sources, Convolution, Scene Graphs COMPSCI/MATH 290-04 Chris Tralie, Duke University 2/4/2016 COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs Announcements Mini Assignment 2 Due Next Monday 11:55

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Lecture 7: Image Sources, Convolution, Scene Graphs

COMPSCI/MATH 290-04

Chris Tralie, Duke University

2/4/2016

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Announcements

◮ Mini Assignment 2 Due Next Monday 11:55 PM ◮ Group Assignment 1 will be released before Monday ◮ Find partners!

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Table of Contents

◮ 3D Rotations Continued ⊲ Image Sources ⊲ Convolution ⊲ Scene Graphs

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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3D Rotations: Coordinate Frame Interpretation

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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3D Rotations: Euler Angles Visualization

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Table of Contents

⊲ 3D Rotations Continued ◮ Image Sources ⊲ Convolution ⊲ Scene Graphs

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Ray Casting for Specular Reflections

⊲ Project onto normal, flip normal component, preserve parallel component

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Ray Casting for Specular Reflections

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Ray Casting for Specular Reflections

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Ray Casting for Specular Reflections

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Ray Casting for Specular Reflections

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Ray Casting for Specular Reflections

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Ray Casting for Specular Reflections

⊲ Dilution of precision ⊲ Need fine angle resolution to capture!

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources: Proof

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources: More Examples

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources: Second Order

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources: Second Order

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources: Second Order

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources: Second Order

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Image Sources: Third Order (!)

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Image Sources: Third Order

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Image Sources: Third Order

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Image Sources: Third Order

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Image Sources: Third Order

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Image Sources: Third Order

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Image Sources: Occlusions

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Image Sources: Occlusions

Ray needs to hit target before anything else

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Image Sources: Point Containment

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Image Sources: Point Containment

Intersection with line (plane in 3D) must be in interior of polygon

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Table of Contents

⊲ 3D Rotations Continued ⊲ Image Sources ◮ Convolution ⊲ Scene Graphs

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Impulse Response

⊲ Convert lengths of all paths into times, amplitude records decay

Direct Path

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Impulse Response

⊲ Convert lengths of all paths into times, amplitude records decay

Direct Path

⊲ What causes decay?

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution

⊲ Convolution: What do sounds sound like in this environment?

Direct Path

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution

⊲ Add overlapping signals, delayed and decayed

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution

⊲ Add overlapping signals, delayed and decayed

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution

⊲ Add overlapping signals, delayed and decayed

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution

⊲ Add overlapping signals, delayed and decayed

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution

⊲ Add overlapping signals, delayed and decayed

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution

⊲ Add overlapping signals, delayed and decayed

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution: Result

⊲ Add overlapping signals, delayed and decayed

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Convolution: Notation / Equation

x[n]: Discretely sampled signal describing the sound h[n]: Discretely sampled signal describing impulse

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution: Notation / Equation (RAFFLE POINT)

x[n]: Discretely sampled signal describing the sound h[n]: Discretely sampled signal describing impulse

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution: Notation/Equation

x[n]: Discretely sampled signal describing the sound h[n]: Discretely sampled signal describing impulse (x ∗ h)[n] =

N

  • k=0

h[k]x[n − k]

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Convolution: Notation/Equation

x[n]: Discretely sampled signal describing the sound h[n]: Discretely sampled signal describing impulse (x ∗ h)[n] =

N

  • k=0

h[k]x[n − k] Roles can switch!

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Gaussian Interpolation

Given non-integer bin index n0 with amplitude a h[n] = ae−(n−n0)2/2σ2/  

k=2σ

  • k=−2σ

e−(n−n0)2/2σ2  

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Convolution Examples

Interactive demo

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Table of Contents

⊲ 3D Rotations Continued ⊲ Image Sources ⊲ Convolution ◮ Scene Graphs

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Scene Graph: Human body

Figure courtesy of http://www.euclideanspace.com/physics/kinematics/joints/ COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Scene Graph: Human body

MOCAP interactive example

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Scene Graph: Bedroom

Liu, Tianqiang, et al. ”Creating consistent scene graphs using a probabilistic grammar.” ACM Transactions on Graphics (TOG) 33.6 (2014): 211. COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Scene Graph: Library

Liu, Tianqiang, et al. ”Creating consistent scene graphs using a probabilistic grammar.” ACM Transactions on Graphics (TOG) 33.6 (2014): 211. COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs

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Scene Graph: Euler Angles Visualization

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Designing Scene Graphs

Interactive Example

COMPSCI/MATH 290-04 Lecture 7: Image Sources, Convolution, Scene Graphs