shape analysis and retrieval (600.658) (michael) misha kazhdan
TRANSCRIPT
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Shape Analysis and Retrieval(600.658)
(Michael) Misha Kazhdan
![Page 2: Shape Analysis and Retrieval (600.658) (Michael) Misha Kazhdan](https://reader034.vdocuments.site/reader034/viewer/2022052509/56649d205503460f949f4779/html5/thumbnails/2.jpg)
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 matching:Given 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 approach:Define a function that takes in two models and returns a measure of their proximity.
D , D ,M1 M1 M3M2
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
3D Query
Database Models
Q
M1
M2
Mn
D(Q,Mi
)
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Database Retrieval
• Sort the database models by proximity
3D Query
Database Models Sorted Models
D(Q,Mi
)Q
M1
M2
Mn
M1
M2
Mn
~
~
~
ji
MQDMQD ji
)~
,()~
,(
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~
Database Retrieval
• Return the closest matches
Best Match(es)
3D Query
Database Models Sorted Models
D(Q,Mi
)Q
M1
M2
Mn
M1
M2
Mn
~
~
~
ji
MQDMQD ji
)~
,()~
,(
M1~
M2
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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
Ranked Matches
Query
44
77
11
55
22
88
66
33
99
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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
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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?
Ranked Matches
Query
44
77
11
55
22
88
66
33
99
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Precision vs. Recall
• Precision-recall curves– Recall = retrieved_in_class / total_in_class– Precision = retrieved_in_class / total_retrieved
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
1
Recall
Precision
1
Ranked Matches
Query
44
77
11
55
22
88
66
33
99
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Precision vs. Recall
• Precision-recall curves– Recall = 0 / 5– Precision = 0 / 0
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
1
Recall
Precision
1
Ranked Matches
Query
44
77
11
55
22
88
66
33
99
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Precision vs. Recall
• Precision-recall curves– Recall = 1 / 5– Precision = 1 / 1
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
1
Recall
Precision
1
Ranked Matches
Query
44
77
11
55
22
88
66
33
99
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Precision vs. Recall
• Precision-recall curves– Recall = 2 / 5– Precision = 2 / 3
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
1
Recall
Precision
1
Ranked Matches
Query
44
77
11
55
22
88
66
33
99
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Precision vs. Recall
• Precision-recall curves– Recall = 3 / 5– Precision = 3 / 5
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
1
Recall
Precision
1
Ranked Matches
Query
44
77
11
55
22
88
66
33
99
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Precision vs. Recall
• Precision-recall curves– Recall = 4 / 5– Precision = 4 / 7
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
1
Recall
Precision
1
Ranked Matches
Query
44
77
11
55
22
88
66
33
99
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Precision vs. Recall
• Precision-recall curves– Recall = 5 / 5– Precision = 5 / 9
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
1
Recall
Precision
1
Ranked Matches
Query
44
77
11
55
22
88
66
33
99
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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