Shape Analysis. Introduction. Introduction. Motivation. Introduction. Introduction. Thomas Funkhouser Princeton University CS526, Fall 2006

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1 Introduction Cyberware, ATI, & 3Dcafe Analysis Thomas Funkhouser Princeton University CS526, Fall 2006 Cyberware Cheap Scanners ATI Fast Graphics Cards 3D Cafe World Wide Web Someday 3D models will be as common as images are today Motivation Stanford & Utah Introduction De Espona & Utah Previous research has asked: How do we acquire 3D data? Utah VW Bug Utah Teapot Stanford Bunny Future research will ask: How do we find 3D data? Utah VW Bug Analysis algorithms also are needed to create useful 3D models from raw 3D data Introduction Introduction Georgia Tech and Geometric Query Analysis Descriptor Object Recognition Matching Object Database of 3D Models Analysis Index Construction Index Object Retrieval Similar Objects Clustering & Learning Class Specification Object Classification Matching Class Object Synthesis Novel Objects 3D Model 2D Image 1

2 Lecture Outline ) * ) * ) * Ayellet Tal, Technion & Princeton University How can we find significant geometric features robustly? How can we decompose a 3D model into its parts? Ayellet Tal, Technion & Princeton University Emil Praun ) * Cup Handle ) * How can we decompose a 3D model into its parts? How can we align features of 3D models? 2

3 Image courtesy of Ilya Vakser, GRAMM ) * ) * Query 1) 2) 3) 4) Ranked Matches How can we compute a measure of geometric similarity? How can we find 3D models best matching a query? Florida State Univ. Darpa E3D Project ) * ) * Query Classes How can we find a given 3D model in a large database? How can we determine the class of a 3D model? ) * Viewpoint Lecture Outline How can we learn classes of 3D models automatically? 3

4 , ), ) vp41620.wrl, ) Image courtesy of Ayellet Tal, Technion & Princeton University, ) Bill Regli, Drexel University Darpa E3D Project, ) Morphine, ) 4

5 %& ', ), ) ', ), ) %& Hippocampus-amygdala study in schizophrenia Stanford University Boeing ' %& Image courtesy of Polina Golland, MIT Image courtesy of Ilya Vakser, GRAMM ' %& %& Delson & Freiss, ) Lecture Outline ' 5

6 -.' / / Matching 0123' ' 0-' ' ' ' % % 3D Query Descriptor Best Matches 3D Query Descriptor Best Matches 3D Database 3D Database % % 3D Query Descriptor Best Matches 3D Query Descriptor Best Matches 3D Database 3D Database 6

7 % 3D Query Descriptor 3D Database Best Matches % Different Transformations translation, scale, rotation, mirror) Image courtesy of Ramamoorthi et al. % Different Articulated Poses % Scanned Surface Viewpoint & Stanford Utah & De Espona % Different Genus Different Tessellations % No Bottom &*Q?@A% 7

8 Taxonomy of 3D Matching Methods Amenta & Osada Image courtesy of Taxonomy of 3D Matching Methods Mao Chen / - )-, -,- / - )-, -,- Feature 1 Tables Desks Feature 2 File cabinets Example Distributions ' ' %' ' We are starting with discussion of a simple method to introduce the basic ideas Audio 3D Surface 2D Contour 3D Volume Distributions 9' Which Function? ' θ θ A3 angle) D1 distance) D2 distance) D3 area) D4 volume) 3D Models D2 Distributions [Ankerst 99] 8

9 D2 Distribution D2 Distribution % % / 512 bytes 64 values) 0.5 seconds 10 6 samples) D2 Distribution D2 Distribution % Translation Rotation {Mirror Scale w/ normalization) / Normalized Means % / D2 Distribution D2 Distribution % 1% Noise % Ellipsoids with Different Eccentricities 9

10 D2 Distribution 8 % Line Segment Cylinder Sphere Circle Cube Two Spheres : ; 6 < ;= >? 2 ; Line Segment Circle Cylinder 10

11 k e b a e e e n g e p n w r r t p t l l al bl btbp bt cr cr cw hr hn lp lg me mg ok pn pe pe re sd sa sp sb te tk al bl btbp bt cr cr cw hr hn lp lg me mg ok pn pe pe re sd sa sp sb te tk Sphere Two Spheres 2A ; D2 distributions for 5 tanks gray) and 6 cars black) & / 2/ <B<><?< 2/ 6/ : : 51 potted plants 33 faces 15 desk chairs 22 dining chairs 100 humans 28 biplanes 14 flying birds 11 ships 11

12 Precision 100% 50% 0% D2 Random 0% 50% 100% Recall Storage Compute Compare Nearest Norm Descriptor bytes) Time s) Time us) Neighbor DCGain DCGain LFD ,700 1,300 66% 64% 21% REXT , % 60% 13% SHD , % 58% 10% GEDT , % 58% 10% EXT % 56% 6% SECSHEL , % 55% 3% VOXEL , % 54% 2% SECTORS % 53% 0% CEGI , % 48% -10% EGI , % 47% -11% D % 43% -18% SHELLS % 39% -27% RANDOM % 26% -54% Next Times 2 12