Shape Analysis and Retrieval (600.658)

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Shape Analysis and Retrieval(600.658)

• (Michael) Misha Kazhdan

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Short Bio

• Undergraduate degree in mathematics
• Started Ph.D. in mathematics
• Switched to computer graphics

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Research

• Research Focus
• Methods for automatically analyzing 3D models
• Methods for visualization
• Past research
• Shape representations
• Shape alignment
• Shape matching
• Symmetry detection

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Seminar

• Shape matchingGiven a database of 3D models and
  a query shape, determine which database models
  are most similar to the query.

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Applications

• Entertainment
• Medicine
• Chemistry/Biology
• Archaeology
• Etc.

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Applications

• Entertainment
• Model generation
• Medicine
• Chemistry/Biology
• Archaeology
• Etc.

Movie Courtesy of Summoner
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Applications

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

Images courtesy of NLM
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Applications

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

Image Courtesy of PDB
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Applications

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

Image Courtesy of Stanford
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Seminar

• Whole shape matching
• How do you test if two models are similar?
• Alignment
• Partial shape matching

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Seminar

• Whole shape matching
• Alignment
• How do you match across transformations that do
  not change the shape of a model?
• Partial shape matching

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Seminar

• Whole shape matching
• Alignment
• How do you match across transformations that do
  not change the shape of a model?
• Partial shape matching

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Seminar

• Whole shape matching
• Alignment
• Partial shape matching
• How do you test if one model is a subset of
  another model?

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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)

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About you

• Background
• Graphics?
• Mathematics?
• Coding?
• Specific interests?
• Undergrad/Masters/Ph. D.?
• Year?

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Shape Matching

• General approachDefine a function that takes in
  two models and returns a measure of their
  proximity.

D
,
D
,
M1
M1
M3
M2
M1 is closer to M2 than it is to M3
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Database Retrieval

• Compute the distance from the query to each
  database model

M1
M2
D(Q,Mi)
Q
3D Query
Mn
Database Models
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Database Retrieval

• Sort the database models by proximity

M1
M1

M2
M2
D(Q,Mi)
Q
3D Query

Mn
Mn
Database Models
Sorted Models
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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
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Evaluation

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

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Query
Ranked Matches
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Similarity Matrix

• Given a database of models M1,,MnGenerate
  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

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Precision vs. Recall

• A graph giving the accuracy of the retrieval.
• Answers the questionHow easy is it to get back
  n of the models in the querys class?

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Query
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Ranked Matches
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Precision vs. Recall

• Precision-recall curves
• Recall retrieved_in_class / total_in_class
• Precision retrieved_in_class / total_retrieved

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Query
Ranked Matches
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Precision vs. Recall

• Precision-recall curves
• Recall 0 / 5
• Precision 0 / 0

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Query
Ranked Matches
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Precision vs. Recall

• Precision-recall curves
• Recall 1 / 5
• Precision 1 / 1

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Query
Ranked Matches
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Precision vs. Recall

• Precision-recall curves
• Recall 2 / 5
• Precision 2 / 3

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Query
Ranked Matches
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Precision vs. Recall

• Precision-recall curves
• Recall 3 / 5
• Precision 3 / 5

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Query
Ranked Matches
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Precision vs. Recall

• Precision-recall curves
• Recall 4 / 5
• Precision 4 / 7

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Query
Ranked Matches
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Precision vs. Recall

• Precision-recall curves
• Recall 5 / 5
• Precision 5 / 9

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Query
Ranked Matches
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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