**Tutorial: Breakthroughs in 3-D Reconstruction and Motion** Analysis Jana Kosecka (CS, GMU) Yi Ma (ECE, UIUC) Shankar Sastry (EECS, Berkeley) Stefano Soatto (CS, UCLA) Rene Vidal (Berkeley, John Hopkins) Omid Shakernia (EECS, Berkeley) ICRA2003, Taipei

**PRIMARY REFERENCE** ICRA2003, Taipei

**Breakthroughs in 3D Reconstruction and Motion Analysis** Lecture A: Overview and Introduction Yi Ma Perception & Decision Laboratory Decision & Control Group, CSL Image Formation & Processing Group, Beckman Electrical & Computer Engineering Dept., UIUC http://decision.csl.uiuc.edu/~yima ICRA2003, Taipei

**TUTORIAL LECTURES** • A. Overview and introduction (Ma) • B. Preliminaries: geometry & image formation (Ma) • C. Image primitives & correspondence (Kosecka) • D. Two-view geometry (Kosecka) • E. Uncalibrated geometry and stratification (Ma) • F. Multiview recon. from points and lines (Kosecka) • G. Reconstruction from scene knowledge (Ma) • H. Step-by-step building of 3-D model (Kosecka) • I. Landing of unmanned aerial vehicles (Kosecka) • J. Multiple motion estimation (Ma) ICRA2003, Taipei

**TUTORIAL LOGICAL FLOW ** IMAGING and VISION:From 3D to 2D and then back again GEOMETRY FOR TWO VIEWS GEOMETRY FOR MULTIPLE VIEWS MULTIVIEW GEOMETRY WITH SYMMETRY APPLICATIONS: Image based modeling, vision based control ICRA2003, Taipei

**Reconstruction from images – The Fundamental Problem ** Input: Corresponding “features” in multiple perspective images. Output: Camera pose, calibration, scene structure representation. ICRA2003, Taipei

**surface** curve line point practice projective algorithm affine theory Euclidean 2 views algebra 3 views geometry 4 views optimization m views Fundamental Problem: An Anatomy of Cases ICRA2003, Taipei

**VISION AND GEOMETRY – An uncanny deja vu? ** “The rise of projective geometry made such an overwhelming impression on the geometers of the first half of the nineteenth century that they tried to fit all geometric considerations into the projective scheme. ... The dictatorial regime of the projective idea in geometry was first successfully broken by the German astronomer and geometer Mobius, but the classical document of the democratic platform in geometry establishing the group of transformations as the ruling principle in any kind of geometry and yielding equal rights to independent consideration to each and any such group, is F. Klein's Erlangen program.” -- Herman Weyl, Classic Groups, 1952 Synonyms: Group = Symmetry ICRA2003, Taipei

**APPLICATIONS – Autonomous Highway Vehicles ** ICRA2003, Taipei Image courtesy of California PATH

**Rate: 10Hz; Accuracy: 5cm, 4o ** APPLICATIONS – Unmanned Aerial Vehicles (UAVs) ICRA2003, Taipei Courtesy of Berkeley Robotics Lab

**APPLICATIONS – Real-Time Virtual Object Insertion** ICRA2003, Taipei UCLA Vision Lab

**APPLICATIONS – Real-Time Sports Coverage ** First-down line and virtual advertising ICRA2003, Taipei Courtesy of Princeton Video Image, Inc.

**APPLICATIONS – Image Based Modeling and Rendering ** ICRA2003, Taipei Image courtesy of Paul Debevec

**APPLICATIONS – Image Alignment, Mosaicing, and Morphing ** ICRA2003, Taipei

**GENERAL STEPS – Feature Selection and Correspondence ** • Small baselines versus large baselines • Point features versus line features ICRA2003, Taipei

**GENERAL STEPS – Structure and Motion Recovery ** • Two views versus multiple views • Discrete versus continuous motion • General versus planar scene • Calibrated versus uncalibrated camera • One motion versus multiple motions ICRA2003, Taipei

**GENERAL STEPS – Image Stratification and Dense Matching ** Left Right ICRA2003, Taipei

**GENERAL STEPS – 3-D Surface Model and Rendering** • Point clouds versus surfaces (level sets) • Random shapes versus regular structures ICRA2003, Taipei

**Breakthroughs in 3D Reconstruction and Motion Analysis** Lecture B: Rigid-Body Motion and Imaging Geometry Yi Ma Perception & Decision Laboratory Decision & Control Group, CSL Image Formation & Processing Group, Beckman Electrical & Computer Engineering Dept., UIUC http://decision.csl.uiuc.edu/~yima ICRA2003, Taipei

**OUTLINE ** • 3-D EUCLIDEAN SPACE & RIGID-BODY MOTION • Coordinates and coordinate frames • Rigid-body motion and homogeneous • coordinates • GEOMETRIC MODELS OF IMAGE FORMATION • Pinhole camera model • CAMERA INTRINSIC PARAMETERS • From metric to pixel coordinates SUMMARY OF NOTATION ICRA2003, Taipei

**Coordinates of a point in space:** Standard base vectors: 3-D EUCLIDEAN SPACE - Cartesian Coordinate Frame ICRA2003, Taipei

**Coordinates of the vector :** 3-D EUCLIDEAN SPACE - Vectors A “free” vector is defined by a pair of points : ICRA2003, Taipei

**Cross product between two vectors:** 3-D EUCLIDEAN SPACE – Inner Product and Cross Product Inner product between two vectors: ICRA2003, Taipei

**Coordinates are related by:** RIGID-BODY MOTION – Rotation Rotation matrix: ICRA2003, Taipei

**Coordinates are related by:** Velocities are related by: RIGID-BODY MOTION – Rotation and Translation ICRA2003, Taipei

**Homogeneous coordinates:** Homogeneous coordinates/velocities are related by: RIGID-BODY MOTION – Homogeneous Coordinates 3-D coordinates are related by: ICRA2003, Taipei

**IMAGE FORMATION – Perspective Imaging** “The Scholar of Athens,” Raphael, 1518 ICRA2003, Taipei Image courtesy of C. Taylor

**Frontal** pinhole IMAGE FORMATION – Pinhole Camera Model Pinhole ICRA2003, Taipei

**Homogeneous coordinates** IMAGE FORMATION – Pinhole Camera Model 2-D coordinates ICRA2003, Taipei

**metric** coordinates Linear transformation pixel coordinates CAMERA PARAMETERS – Pixel Coordinates ICRA2003, Taipei

**Calibration matrix** (intrinsic parameters) Projection matrix Camera model CAMERA PARAMETERS – Calibration Matrix and Camera Model Pinhole camera Pixel coordinates ICRA2003, Taipei

**Projection of a 3-D point to an image plane** IMAGE FORMATION – Image of a Point Homogeneous coordinates of a 3-D point Homogeneous coordinates of its 2-D image ICRA2003, Taipei

**Homogeneous representation of its 2-D image** Projection of a 3-D line to an image plane IMAGE FORMATION – Image of a Line Homogeneous representation of a 3-D line ICRA2003, Taipei

**SUMMARY OF NOTATION – Multiple Images ** . . . • Images are all “incident” at the corresponding features in space; • Features in space have many types of incidence relationships; • Features in space have many types of metric relationships. ICRA2003, Taipei