Shape Analysis and Retrieval ( ) (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 Shape representations Shape alignment Shape matching Symmetry detection

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

Applications Entertainment Medicine Chemistry/Biology Archaeology Etc.

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

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

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

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

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

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

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

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

Course Structure Paper presentation: Two papers a week Everybody reads Students present Final project: New method / implementation of existing ones Proposals due October 19 th Presented December 6 th, 7 th (last week of classes)

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

Shape Matching General approach: Define a function that takes in two models and returns a measure of their proximity. D,D, M1M1 M1M1 M3M3 M2M2 M 1 is closer to M 2 than it is to M 3

Database Retrieval Compute the distance from the query to each database model 3D Query Database Models Q M1M1 M2M2 MnMn D(Q,M i )

Database Retrieval Sort the database models by proximity 3D Query Database ModelsSorted Models D(Q,M i ) Q M1M1 M2M2 MnMn M1M1 M2M2 MnMn ~ ~ ~

~ Database Retrieval Return the closest matches Best Match(es) 3D Query Database ModelsSorted Models D(Q,M i ) Q M1M1 M2M2 MnMn M1M1 M2M2 MnMn ~ ~ ~ M1M1 ~ M2M2

Evaluation Classify models: –Retrieval is good if the closest matches in the database are in the same class as the query Ranked Matches Query

Similarity Matrix Given a database of models { M 1,…, M n }: Generate the n x n matrix whose ( i,j ) th entry is equal to D ( M i, M j ). –Darkness represents similarity –If models are sorted by class, good results give dark diagonal blocks

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

Precision vs. Recall Precision-recall curves –Recall = retrieved_in_class / total_in_class –Precision = retrieved_in_class / total_retrieved Recall Precision 1 Ranked Matches Query

Precision vs. Recall Precision-recall curves –Recall = 0 / 5 –Precision = 0 / Recall Precision 1 Ranked Matches Query

Precision vs. Recall Precision-recall curves –Recall = 1 / 5 –Precision = 1 / Recall Precision 1 Ranked Matches Query

Precision vs. Recall Precision-recall curves –Recall = 2 / 5 –Precision = 2 / Recall Precision 1 Ranked Matches Query

Precision vs. Recall Precision-recall curves –Recall = 3 / 5 –Precision = 3 / Recall Precision 1 Ranked Matches Query

Precision vs. Recall Precision-recall curves –Recall = 4 / 5 –Precision = 4 / Recall Precision 1 Ranked Matches Query

Precision vs. Recall Precision-recall curves –Recall = 5 / 5 –Precision = 5 / Recall Precision 1 Ranked Matches Query

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