Transcript Introduction - Computer Science

3D Computer Vision
and Video Computing
Omnidirectional Vision
CSc I6716
Fall 2005
Topic 2 of Part II
Omnidirectional Cameras
Zhigang Zhu, City College of New York [email protected]
3D Computer Vision
and Video Computing
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Lecture Outline
Applications
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Robot navigation, Surveillance, Smart rooms
Video-conferencing/ Tele-presence
Multimedia/Visualization
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Page of Omnidirectional Vision (Many universities and companies….)
 http://www.cis.upenn.edu/~kostas/omni.html
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Design Requirements
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Several Important Designs
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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
Catadioptric imaging : mirror (reflection) + lens ( refraction)
Mirrors: Planar, Conic, Spherical, Hyperboloidal, Ellipsoidal, Paraboloidal
Systematic design ( S. Nayar’s group)
Calibrations
 Harder or simpler?
3D Computer Vision
and Video Computing
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Catadioptric imaging :
 mirror (reflection) + lens ( refraction)
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Theory of Catadioptric Image Formation ( S. Nayar’s group)
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"A Theory of Single-Viewpoint Catadioptric Image Formation" , Simon Baker
and Shree K. Nayar ,International Journal of Computer Vision, 1999.
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Mirrors
 Planar
 Conic, Spherical
 Hyperboloidal, Ellipsoidal
 Paraboloidal
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Cameras (Lens)
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Sensor Design
Perspective (pinhole) or orthogonal (tele-centric lens) projection
One or more?
Implementations
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Compactness - size, support, and installation
Optics – Image sharpness, reflection, etc.
3D Computer Vision
and Video Computing
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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/
3D Computer Vision
Planar Mirror
and Video Computing
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Panoramic camera system using a pyramid with four (or
more) planar mirrors and four (or more) cameras
(Nalwa96) has a single effective viewpoint
Viewpoint of the
Virtual camera
P1
P2
Geometry of 4 camera approach: four separate cameras in 4
viewpoints can generate images with a single effective viewpoint
3D Computer Vision
and Video Computing
Planar Mirror Approach
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A single effective viewpoint
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More than one cameras
High image resolution
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3D Computer Vision
and Video Computing
Planar Mirror Approach
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A single effective viewpoint
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More than one cameras
High image resolution
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3D Computer Vision
and Video Computing
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Conic Mirror
Viewpoints on a circle
semispherical view except occlusion
Perspective projection in each direction
Robot Navigation (Yagi90, Zhu96/98)
viewpoint
pinhole
3D Computer Vision
and Video Computing
Spherical Mirror
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Viewpoints on a spherical-like surface
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Easy to construct (Hong91 -UMass )
Locus of
viewpoints
Intersection of incoming rays
are along this line
3D Computer Vision
and Video Computing
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Single Viewpoint
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Hyperboloidal Mirror
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
viewpoint
Rotation of the
hyperbolic curve
generates a
hyperboloid
P1
P2
pinhole
3D Computer Vision
and Video Computing
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ACCOWLE Co., LTD, A Spin-off at Kyoto University
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Hyperboloidal Mirror
http://www.accowle.com/english/
Spherical Mirror
Hyperbolic Mirror
Image: High res. in the top
3D Computer Vision
and Video Computing
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Single Viewpoint
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Ellipsoidal Mirror
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
pinhole
P2
P1
viewpoint
3D Computer Vision
and Video Computing
Panoramic Annular Lens
- geometric mathematical model
for image transform & calibration
P1
panoramic annular lens (PAL)
- invented by Pal Greguss
* 40 mm in diameter, C-mount
P
B
Hyperboloidal mirror
O
pinhole C
* view: H: 360, V: -15 ~ +20
* single view point (O)
p p1
Ellipsoidal mirror
3D Computer Vision
and Video Computing
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
Panoramic Annular Lens
Image: High res. In the bottom
3D Computer Vision
and Video ComputingCylindrical
panoramic un-warping
Two Steps:
(1). Center determination
(2) Distortion rectification
2-order polynomial approximation
Circular to cylindrical transformation
after eliminating radial distortion
3D Computer Vision
and Video Computing
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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
viewpoint
P1
P2
tele-lens
3D Computer Vision
and Video Computing
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Paraboloidal Mirror
Remote Reality – A Spin-off at Columbia University
http://www.remotereality.com/
Camcorder
Web Camera
Back to Back : Full
Spherical View
3D Computer Vision
and Video Computing
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Paraboloidal Mirror
Remote Reality – A Spin-off at Columbia University
http://www.remotereality.com/
3D Computer Vision
and Video ComputingCatadioptric
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Omnidirectional Camera Calibration – Harder or Easier?
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Camera Calibration
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.
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Projections of two sets of parallel lines suffice for intrinsic
calibration from one view
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C. Geyer and K. Daniilidis, "Catadioptric Camera calibration",
In Proc. Int. Conf. on Computer Vision, Kerkyra, Greece, Sep.
22-25, pp. 398-404, 1999.
3D Computer Vision
and Video Computing
Image
Properties of Paraboloid System
(Assuming aspect ratio = 1)
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The Image of a Line
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Dual Vanishing Points
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There are two VPs for each set of parallel lines, which are
the intersections of the corresponding circles
Collinear Centers
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is a circular arc if the line is not parallel to the optical axis
Is projected on a (radial) line otherwise
The center of the circles for a set of parallel lines are
collinear
Vanishing Circle
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The vanishing points of lines with coplanar directions* lie
on a circle ( all the lines parallel to a common plane)
3D Computer Vision
and Video Computing
Image
Properties of Paraboloid System
(with aspect ratio)
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The Image Center
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Projection of a Line with unknown aspect ratio
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Is an elliptical arc in the general case
The Aspect Ratio
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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
Is determined by the ratio of the lone-short axes of the
ellipse corresponding to a line
Intrinsic Calibration
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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
3D Computer Vision
and Video Computing
Calibration
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of Paraboloid System
The Image Center
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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
3D Computer Vision
and Video Computing
Calibration
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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
3D Computer Vision
Next
and Video Computing
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Turn in your projects and schedule meetings with me
END