Lecture 14: Shape Google: Rigid Shape Statistics COMPSCI/MATH - - PowerPoint PPT Presentation

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Lecture 14: Shape Google: Rigid Shape Statistics COMPSCI/MATH - - PowerPoint PPT Presentation

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Lecture 14: Shape Google: Rigid Shape Statistics COMPSCI/MATH 290-04 Chris Tralie, Duke University 3/1/2016 COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics Announcements Group Assignment 1 Full Submission Due Tomorrow

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Lecture 14: Shape Google: Rigid Shape Statistics

COMPSCI/MATH 290-04

Chris Tralie, Duke University

3/1/2016

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Announcements

⊲ Group Assignment 1 Full Submission Due Tomorrow (Wednesday) 11:55 PM ⊲ Rank Top 3 Final Project Choices By Friday 3/5 (Groups of 3-4) ⊲ Attendance Policy Clarification ⊲ Midterm Next Thursday 3/10

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Table of Contents

◮ Shape Statistics / Algorithms ⊲ Comparing Shape Statistics ⊲ Classification / Performance Evaluation

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Random Sampling By Area

Goal: Given a shape, return similar shapes in a database

Tralie 2010 ⊲ Focus on point clouds ⊲ Focus on shapes similar under rigid motion

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Random Sampling By Area

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Centroid Centering / RMS Scaling

For a point cloud { xi}N

i=1

⊲ Subtract off centroid ⊲ Root mean square scale. Want

  • 1

N

N

  • i=1

|| xi||2 = 1

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Matching Criteria

⊲ Concise To Store ⊲ Quick to compute ⊲ Efficient to match ⊲ Discerning ⊲ Noise tolerant ⊲ Rotation Invariant

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

⊲ Quick To Compute

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

⊲ Quick To Compute

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

⊲ Quick To Compute ⊲ Concise To Store

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

⊲ Quick To Compute ⊲ Concise To Store

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant ⊲ Discerning

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

⊲ Quick To Compute ⊲ Concise To Store ⊲ Rotation Invariant ⊲ Discerning

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells

What can’t it tell apart? SHOW VIDEO

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells And Sectors

SHOW VIDEO

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells And Sectors

Still Rotation Invariant?

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Shape Histogram: Shells And Sectors

⊲ Sort sectors within each shell ⊲ Record PCA eigenvalues within each shell

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images

Johnson/Herbert 1999, Figure Huang 2010

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images: Rubber Duck

Johnson/Herbert 1999

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images

⊲ Quick To Compute

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images

⊲ Quick To Compute

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images

⊲ Quick To Compute ⊲ Concise To Store

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images

⊲ Quick To Compute ⊲ Concise To Store (Can compress images)

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images

⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images

⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant (Careful with principal axis stability)

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images

⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant (Careful with principal axis stability) ⊲ Discerning

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Spin Images

⊲ Quick To Compute ⊲ Concise To Store (Can compress images) ⊲ Rotation Invariant (Careful with principal axis stability) ⊲ Discerning

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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D2: Distance Histograms

Osada 2003, Figure from Huang 2010

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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D2: Primitive Examples

Osada 2003

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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D2: Real Examples

Osada 2003

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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D1: Randomly Sample Points

Osada 2003

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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D3: Randomly Sample Areas

Osada 2003

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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D4: Randomly Sample Volumes

Osada 2003

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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A3: Randomly Sample Angles

Osada 2003

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

⊲ Efficient To Compute / Concise To Store

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

⊲ Efficient To Compute / Concise To Store

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

⊲ Discerning

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

⊲ Discerning (Only fully describes convex objects)

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

⊲ Rotation Invariant

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

⊲ Rotation Invariant (Rotate To Align With PCA Axes)

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

⊲ Robust To Noise?

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Extended Gaussian Image

⊲ Not Robust To Noise!

Funkhouser 2004

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Table of Contents

⊲ Shape Statistics / Algorithms ◮ Comparing Shape Statistics ⊲ Classification / Performance Evaluation

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Normalize Histograms By Mass

h′[i] = h[i] N

k=1 h[k]

In other words, all bins should sum to 1

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Histogram Euclidean Distance

For histograms h1 and h2 dE(h1, h2) =

  • N
  • i=1

(h1[i] − h2[i])2 Just thinking of h1 and h2 as high dimensional Euclidean vectors! Each histogram bin is a dimension

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Histogram Cosine Distance

dC(h1, h2) = cos−1

  • h1 ·

h2 || h1|||| h2||

  • COMPSCI/MATH 290-04

Lecture 14: Shape Google: Rigid Shape Statistics

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Euclidean Distance Shortcomings

5 10 15 20 25 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Euclidean Distance Fail

Histogram 1 Histogram 2 Histogram 3

They all have the same distance!

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Euclidean Distance Shortcomings

5 10 15 20 25 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Earth Mover's Distance Illustration

Histogram 1 Histogram 2

Move earth from blue to red

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Earth Mover’s Distance

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Chi Squared Distance

dχ(h1, h2) = 1 2

N

  • i=1

(h1[i] − h2[i])2 h1[i] + h2[i] Exclude values for which h1[i] = h2[i] = 0

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Table of Contents

⊲ Shape Statistics / Algorithms ⊲ Comparing Shape Statistics ◮ Classification / Performance Evaluation

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Evaluation Strategy

Do leave one out technique Use each item as test item in turn, compare to database ◮ Summarize evaluation statistics over entire database by averaging them

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Precision / Recall

Rusinkiewiz/Funkhouser 2009

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics

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Other Evaluation Metrics

⊲ Average Precision (Area Under Precision/Recall Curve) ⊲ Mean Reciprocal Rank (1/rank of first correct item) ⊲ Median Reciprocal Rank 1 is perfect score

COMPSCI/MATH 290-04 Lecture 14: Shape Google: Rigid Shape Statistics