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Shape Analysis and Retrieval (600.658)

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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Shape Analysis and Retrieval (600.658)

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  1. Shape Analysis and Retrieval(600.658) (Michael) Misha Kazhdan

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

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

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

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

  6. Applications • Entertainment • Model generation • Medicine • Chemistry/Biology • Archaeology • Etc. Movie Courtesy of Summoner

  7. Applications • Entertainment • Medicine • Automated diagnosis • Chemistry/Biology • Archaeology • Etc. Images courtesy of NLM

  8. Applications • Entertainment • Medicine • Chemistry/Biology • Docking and binding • Archaeology • Etc. Image Courtesy of PDB

  9. Applications • Entertainment • Medicine • Chemistry/Biology • Archaeology • Reconstruction • Etc. Image Courtesy of Stanford

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

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

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

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

  14. 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)

  15. About you Background: • Graphics? • Mathematics? • Coding? Specific interests? Undergrad/Masters/Ph. D.? Year?

  16. 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

  17. Database Retrieval • Compute the distance from the query to each database model M1 M2 D(Q,Mi) Q 3D Query Mn Database Models

  18. Database Retrieval • Sort the database models by proximity ~ M1 M1 ~ M2 M2 D(Q,Mi) Q 3D Query ~ Mn Mn Database Models Sorted Models

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

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