1. MASKS © 2004 Invitation to 3D vision Uncalibrated Camera Chapter 6 Reconstruction from Two Uncalibrated Views Modified by L A Rønningen Oct 2008

2. MASKS © 2004 Invitation to 3D vision Uncalibrated Camera pixel coordinates calibrated coordinates Linear transformation

3. MASKS © 2004 Invitation to 3D vision Uncalibrated Camera Pixel coordinates Projection matrix Uncalibrated camera Image plane coordinates Camera extrinsic parameters Perspective projection Calibrated camera X0X0 X0X0 X0X0 X0X0 X0X0 X0X0 X0X0 X0X0 X0X0

4. MASKS © 2004 Invitation to 3D vision Taxonomy on Uncalibrated Reconstruction is known, back to calibrated case is unknown Calibration with complete scene knowledge (a rig) – estimate Uncalibrated reconstruction despite the lack of knowledge of Autocalibration (recover from uncalibrated images) Use partial knowledge Parallel lines, vanishing points, planar motion, constant intrinsic Ambiguities, stratification (multiple views)

5. MASKS © 2004 Invitation to 3D vision Motion in the distorted space Uncalibrated coordinates are related by Conjugate of the Euclidean group Calibrated spaceUncalibrated space

6. MASKS © 2004 Invitation to 3D vision Calibrated vs. Uncalibrated Space Distances and angles are modified by S

7. MASKS © 2004 Invitation to 3D vision Uncalibrated Epipolar Geometry Epipolar constraint Fundamental matrix Equivalent forms of

8. MASKS © 2004 Invitation to 3D vision Properties of the Fundamental Matrix Image correspondences Epipolar lines Epipoles

9. MASKS © 2004 Invitation to 3D vision Properties of the Fundamental Matrix A nonzero matrix is a fundamental matrix if has a singular value decomposition (SVD) with for some. There is little structure in the matrix except that

10. MASKS © 2004 Invitation to 3D vision Decomposing the Fundamental Matrix Decomposition of is not unique Unknown parameters - ambiguity Corresponding projection matrix Decomposition of the fundamental matrix into a skew symmetric matrix and a nonsingular matrix