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Omnidirectional Vision

Omnidirectional Vision. CSC 59866CD Fall 2004. Lecture 6 Omnidirectional Cameras. Zhigang Zhu, NAC 8/203A http://www-cs.engr.ccny.cuny.edu/~zhu/ Capstone2004/Capstone_Sequence2004.html. Lecture Outline. Applications Robot navigation, Surveillance, Smart rooms

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Omnidirectional Vision

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  1. Omnidirectional Vision CSC 59866CD Fall 2004 Lecture 6 Omnidirectional Cameras Zhigang Zhu, NAC 8/203A http://www-cs.engr.ccny.cuny.edu/~zhu/ Capstone2004/Capstone_Sequence2004.html

  2. Lecture Outline • Applications • Robot navigation, Surveillance, Smart rooms • Video-conferencing/ Tele-presence • Multimedia/Visualization • Page of Omnidirectional Vision(Many universities and companies….) • http://www.cis.upenn.edu/~kostas/omni.html • Design Requirements • 360 degree FOV, or semi-sphere or full sphere in one snapshot • Single effective viewpoint • Image Resolutions – one or more cameras? • Image Sharpness – optics as well as geometry • Several Important Designs • Catadioptric imaging : mirror (reflection) + lens ( refraction) • Mirrors: Planar, Conic, Spherical, Hyperboloidal, Ellipsoidal, Paraboloidal • Systematic design ( S. Nayar’s group) • Calibrations • Harder or simpler?

  3. Sensor Design • Catadioptric imaging : • mirror (reflection) + lens ( refraction) • Theory of Catadioptric Image Formation ( S. Nayar’s group) • "A Theory of Single-Viewpoint Catadioptric Image Formation" , Simon Baker and Shree K. Nayar ,International Journal of Computer Vision, 1999. • Mirrors • Planar • Conic, Spherical • Hyperboloidal, Ellipsoidal • Paraboloidal • Cameras (Lens) • Perspective (pinhole) or orthogonal (tele-centric lens) projection • One or more? • Implementations • Compactness - size, support, and installation • Optics – Image sharpness, reflection, etc.

  4. Planar Mirror • Panoramic camera system using a pyramid with four (or more) planar mirrors and four (or more) cameras (Nalwa96) has a single effective viewpoint Mirror pyramid 6 cameras 4 camera design and 6 camera prototype: FullView - Lucent Technology http://www.fullview.com/

  5. Planar Mirror • Panoramic camera system using a pyramid with four (or more) planar mirrors and four (or more) cameras (Nalwa96) has a single effective viewpoint Geometry of 4 camera approach: four separate cameras in 4 viewpoints can generate images with a single effective viewpoint

  6. Planar Mirror Approach • A single effective viewpoint • More than one cameras • High image resolution

  7. Planar Mirror Approach • A single effective viewpoint • More than one cameras • High image resolution

  8. viewpoint pinhole Conic Mirror • Viewpoints on a circle • semispherical view except occlusion • Perspective projection in each direction • Robot Navigation (Yagi90, Zhu96/98)

  9. Intersection of incoming rays are along this line Locus of viewpoints Spherical Mirror • Viewpoints on a spherical-like surface • Easy to construct (Hong91 -UMass )

  10. viewpoint Rotation of the hyperbolic curve generates a hyperboloid P1 P2 pinhole Hyperboloidal Mirror • Single Viewpoint • if the pinhole of the real camera and the virtual viewpoint are located at the two loci of the hyperboloid • Semi-spherical view except the self occlusion

  11. Hyperboloidal Mirror • ACCOWLE Co., LTD, A Spin-off at Kyoto University • http://www.pluto.dti.ne.jp/~accowle1/ • Spherical Mirror • Hyperbolic Mirror Image: High res. in the top

  12. pinhole P2 P1 viewpoint Ellipsoidal Mirror • Single Viewpoint • if the pinhole of the real camera and the virtual viewpoint are located at the two loci of the ellipsoid • Semi-spherical view except the self occlusion

  13. B P1 Hyperboloidal mirror O P Ellipsoidal mirror pinhole C pp1 Panoramic Annular Lens - geometric mathematical model for image transform & calibration panoramic annular lens (PAL) - invented by P. Greguss * 40 mm in diameter, C-mount * view: H: 360, V: -15 ~ +20 * single view point (O)

  14. Panoramic Annular Lens • panoramic annular lens (PAL) • - invented by P. Greguss • * 40 mm in diameter, C-mount • * view: H: 360, V: -15 ~ +20 • single view point (O) • C-Mount to CCD Cameras Image: High res. In the bottom

  15. Cylindrical panoramic un-warping Two Steps: (1). Center determination (2) Distortion rectification 2-order polynomial approximation

  16. viewpoint P1 P2 tele-lens Paraboloidal Mirror • Semi-spherical view except the self occlusion • Single Viewpoint at the locus of the paraboloid, if • Tele-lens - orthographic projection is used • Mapping between image, mirror and the world invariant to translation of the mirror. This greatly simplifies calibration and the computation of perspective images from paraboloidal images

  17. Paraboloidal Mirror • Remote Reality – A Spin-off at Columbia University • http://www.remotereality.com/ Camcorder Web Camera Back to Back : Full Spherical View

  18. Paraboloidal Mirror • Remote Reality – A Spin-off at Columbia University • http://www.remotereality.com/

  19. Catadioptric Camera Calibration • Omnidirectional Camera Calibration – Harder or Easier? • In general, the reflection by the 2nd order surface makes the calibration procedure harder • However, 360 view may be helpful • Paraboloidal mirror + orthogonal projection • Mapping between image, mirror and the world invariant to translation of the mirror. • Projections of two sets of parallel lines suffice for intrinsic calibration from one view • C. Geyer and K. Daniilidis, "Catadioptric Camera calibration", In Proc. Int. Conf. on Computer Vision, Kerkyra, Greece, Sep. 22-25, pp. 398-404, 1999.

  20. Image Properties of Paraboloid System (Assuming aspect ratio = 1) • The Image of a Line • is a circular arc if the line is not parallel to the optical axis • Is projected on a (radial) line otherwise • Dual Vanishing Points • There are two VPs for each set of parallel lines, which are the intersections of the corresponding circles • Collinear Centers • The center of the circles for a set of parallel lines are collinear • Vanishing Circle • The vanishing points of lines with coplanar directions* lie on a circle ( all the lines parallel to a common plane)

  21. Image Properties of Paraboloid System (with aspect ratio) • The Image Center • Is on the (“vanishing”) line connecting the dual vanishing points of each set of parallel lines • Can be determined by two sets of parallel lines • Projection of a Line with unknown aspect ratio • Is an elliptical arc in the general case • The Aspect Ratio • Is determined by the ratio of the lone-short axes of the ellipse corresponding to a line • Intrinsic Calibration • Estimate aspect ratio by the ratio of ellipse • Estimate the image center by the intersection of vanishing lines of two sets of parallel lines in 3-D space

  22. Calibration of Paraboloid System • The Image Center • Is on the (“vanishing”) line connecting the dual vanishing points of each set of parallel lines • Can be determined by two sets of parallel lines

  23. Calibration of Paraboloid System • The Image Center • Yellow “vanishing” line of horizontal set of parallel lines • Pink “vanishing” line of vertical set of parallel lines • The Vanishing Circle (Red dotted) • The vanishing points of lines with coplanar directions ( on a plane in this example) Projected to the plane of the calibration pattern

  24. Next • Next: Features END

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