shape analysis and retrieval 600 658 l.
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Shape Analysis and Retrieval (600.658). (Michael) Misha Kazhdan. Short Bio. Undergraduate degree in mathematics Started Ph.D. in mathematics Switched to computer graphics. Research . Research Focus Methods for automatically analyzing 3D models Methods for visualization Past research

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short bio
Short Bio
  • Undergraduate degree in mathematics
  • Started Ph.D. in mathematics
  • Switched to computer graphics
research
Research

Research Focus

  • Methods for automatically analyzing 3D models
  • Methods for visualization

Past research

  • Shape representations
  • Shape alignment
  • Shape matching
  • Symmetry detection
seminar
Seminar

Shape matching:Given a database of 3D models and a query shape, determine which database models are most similar to the query.

applications
Applications
  • Entertainment
  • Medicine
  • Chemistry/Biology
  • Archaeology
  • Etc.
applications6
Applications
  • Entertainment
    • Model generation
  • Medicine
  • Chemistry/Biology
  • Archaeology
  • Etc.

Movie Courtesy of Summoner

applications7
Applications
  • Entertainment
  • Medicine
    • Automated diagnosis
  • Chemistry/Biology
  • Archaeology
  • Etc.

Images courtesy of NLM

applications8
Applications
  • Entertainment
  • Medicine
  • Chemistry/Biology
    • Docking and binding
  • Archaeology
  • Etc.

Image Courtesy of PDB

applications9
Applications
  • Entertainment
  • Medicine
  • Chemistry/Biology
  • Archaeology
    • Reconstruction
  • Etc.

Image Courtesy of Stanford

seminar10
Seminar
  • Whole shape matching
    • How do you test if two models are similar?
  • Alignment
  • Partial shape matching
seminar11
Seminar
  • Whole shape matching
  • Alignment
    • How do you match across transformations that do not change the shape of a model?
  • Partial shape matching

=

seminar12
Seminar
  • Whole shape matching
  • Alignment
    • How do you match across transformations that do not change the shape of a model?
  • Partial shape matching
seminar13
Seminar
  • Whole shape matching
  • Alignment
  • Partial shape matching
    • How do you test if one model is a subset of another model?
course structure
Course Structure

Paper presentation:

  • Two papers a week
  • Everybody reads
  • Students present

Final project:

  • New method / implementation of existing ones
  • Proposals due October 19th
  • Presented December 6th, 7th (last week of classes)
about you
About you

Background:

  • Graphics?
  • Mathematics?
  • Coding?

Specific interests?

Undergrad/Masters/Ph. D.?

Year?

shape matching
Shape Matching

General approach:Define a function that takes in two models and returns a measure of their proximity.

D

,

D

,

M1

M2

M1

M3

M1 is closer to M2 than it is to M3

database retrieval
Database Retrieval
  • Compute the distance from the query to each database model

M1

M2

D(Q,Mi)

Q

3D Query

Mn

Database Models

database retrieval18
Database Retrieval
  • Sort the database models by proximity

~

M1

M1

~

M2

M2

D(Q,Mi)

Q

3D Query

~

Mn

Mn

Database Models

Sorted Models

database retrieval19
Database Retrieval
  • Return the closest matches

~

M1

M1

~

~

M2

M2

M1

D(Q,Mi)

Q

3D Query

~

M2

~

Mn

Mn

Best Match(es)

Database Models

Sorted Models

evaluation
Evaluation

Classify models:

  • Retrieval is good if the closest matches in the database are in the same class as the query

1

2

3

4

5

6

7

8

9

Query

Ranked Matches

similarity matrix
Similarity Matrix

Given a database of models {M1,…,Mn}:Generate the nxn matrix whose (i,j)th entry is equal to D(Mi,Mj).

  • Darkness representssimilarity
  • If models are sortedby class, good resultsgive dark diagonalblocks
precision vs recall
Precision vs. Recall

A graph giving the accuracy of the retrieval.

Answers the question:How easy is it to get back n% of the models in the query’s class?

1

2

3

4

5

6

Query

7

8

9

Ranked Matches

precision vs recall23

1

0.8

0.6

Precision

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

Recall

Precision vs. Recall
  • Precision-recall curves
    • Recall = retrieved_in_class / total_in_class
    • Precision = retrieved_in_class / total_retrieved

1

2

3

4

5

6

7

8

9

Query

Ranked Matches

precision vs recall24

1

0.8

0.6

Precision

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

Recall

Precision vs. Recall
  • Precision-recall curves
    • Recall = 0 / 5
    • Precision = 0 / 0

1

2

3

4

5

6

7

8

9

Query

Ranked Matches

precision vs recall25

1

0.8

0.6

Precision

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

Recall

Precision vs. Recall
  • Precision-recall curves
    • Recall = 1 / 5
    • Precision = 1 / 1

1

2

3

4

5

6

7

8

9

Query

Ranked Matches

precision vs recall26

1

0.8

0.6

Precision

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

Recall

Precision vs. Recall
  • Precision-recall curves
    • Recall = 2 / 5
    • Precision = 2 / 3

1

2

3

4

5

6

7

8

9

Query

Ranked Matches

precision vs recall27

1

0.8

0.6

Precision

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

Recall

Precision vs. Recall
  • Precision-recall curves
    • Recall = 3 / 5
    • Precision = 3 / 5

1

2

3

4

5

6

7

8

9

Query

Ranked Matches

precision vs recall28

1

0.8

0.6

Precision

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

Recall

Precision vs. Recall
  • Precision-recall curves
    • Recall = 4 / 5
    • Precision = 4 / 7

1

2

3

4

5

6

7

8

9

Query

Ranked Matches

precision vs recall29

1

0.8

0.6

Precision

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1

Recall

Precision vs. Recall
  • Precision-recall curves
    • Recall = 5 / 5
    • Precision = 5 / 9

1

2

3

4

5

6

7

8

9

Query

Ranked Matches

precision vs recall30
Precision vs. Recall

Average the p/r plots over all the queries

  • Recall normalizes for class size
  • Graphs that are shifted up correspond to better retrieval