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Multi-View Geometry

Multi-View Geometry. Review: Pinhole Camera. Review: Perspective Projection. Review: Perspective Projection. Points go to Points Lines go to Lines Planes go to whole image or Half-planes Polygons go to Polygons. Perspective cues. Perspective cues. Perspective cues.

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Multi-View Geometry

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  1. Multi-View Geometry

  2. Review: Pinhole Camera

  3. Review: Perspective Projection

  4. Review: Perspective Projection • Points go to Points • Lines go to Lines • Planes go to whole image or Half-planes • Polygons go to Polygons

  5. Perspective cues

  6. Perspective cues

  7. Perspective cues

  8. Review: Intrinsic Camera Parameters Y M Image plane C Z v X Focal plane m u

  9. Review: Extrinsic Parameters Y M Image plane Y C Z v X X Z Focal plane m u By Rigid Body Transformation:

  10. Recovering 3D from images • What cues in the image provide 3D information?

  11. Visual cues • Shading Merle Norman Cosmetics, Los Angeles

  12. Visual cues • Shading • Texture The Visual Cliff, by William Vandivert, 1960

  13. Visual cues • Shading • Texture • Focus From The Art of Photography, Canon

  14. Visual cues • Shading • Texture • Focus • Motion

  15. Visual cues • Shading • Texture • Focus • Motion • Shape From X • X = shading, texture, focus, motion, ...

  16. 3D World Points • Camera Centers • Camera Orientations Multi-View Geometry Relates

  17. 3D World Points • Camera Centers • Camera Intrinsic Parameters • Image Points Multi-View Geometry Relates • Camera Orientations

  18. Stereo scene point image plane optical center

  19. Stereo • Basic Principle: Triangulation • Gives reconstruction as intersection of two rays • Requires • calibration • point correspondence

  20. Stereo Constraints p’ ? p Given p in left image, where can the corresponding point p’in right image be?

  21. Epipolar Line p’ Y2 X2 Z2 O2 Epipole Stereo Constraints M Image plane Y1 p O1 Z1 X1 Focal plane

  22. Epipolar Constraint

  23. P p p’ O’ O From Geometry to Algebra

  24. P p p’ O’ O From Geometry to Algebra

  25. Linear Constraint:Should be able to express as matrix multiplication.

  26. Review: Matrix Form of Cross Product

  27. Review: Matrix Form of Cross Product

  28. Matrix Form

  29. The Essential Matrix

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