3D Computer Vision

and Video Computing Omnidirectional VisionOmnidirectional Vision

Topic 11 of Part 3Omnidirectional Cameras

CSC I6716Spring 2003

Zhigang Zhu, NAC 8/203Ahttp://www-cs.engr.ccny.cuny.edu/~zhu/VisionCourse-I6716.html

3D Computer Vision

and Video Computing Lecture OutlineLecture 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?

3D Computer Vision

and Video Computing Sensor DesignSensor 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.

3D Computer Vision

and Video Computing Planar MirrorPlanar Mirror

Panoramic camera system using a pyramid with four (or more) planar mirrors and four (or more) cameras (Nalwa96) has a single effective viewpoint

4 camera design and 6 camera prototype:

FullView - Lucent Technology http://www.fullview.com/

6 cameras

Mirror pyramid

3D Computer Vision

and Video Computing Planar MirrorPlanar Mirror

Panoramic camera system using a pyramid with four (or more) planar mirrors and four (or more) cameras (Nalwa96) has a single effective viewpoint

P1

P2

Viewpoint of the Virtual camera

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 ApproachPlanar Mirror Approach

A single effective viewpoint More than one cameras High image resolution

3D Computer Vision

and Video Computing Planar Mirror ApproachPlanar Mirror Approach

A single effective viewpoint More than one cameras High image resolution

3D Computer Vision

and Video Computing Conic MirrorConic 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 MirrorSpherical Mirror

Viewpoints on a spherical-like surface Easy to construct (Hong91 -UMass )

Intersection of incoming rays are along this lineLocus of

viewpoints

3D Computer Vision

and Video Computing Hyperboloidal MirrorHyperboloidal 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

pinhole

P1

viewpoint

P2

Rotation of the hyperbolic curve generates a hyperboloid

3D Computer Vision

and Video Computing Hyperboloidal MirrorHyperboloidal 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

3D Computer Vision

and Video Computing Ellipsoidal MirrorEllipsoidal 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

pinhole

viewpoint

P1

P2

3D Computer Vision

and Video Computing 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)

- geometric mathematical model for image transform & calibration

p p1

pinhole

P1

P

B

O

C

Ellipsoidal mirror

Hyperboloidal mirror

3D Computer Vision

and Video Computing 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

3D Computer Vision

and Video ComputingCylindrical panoramic un-warping

Circular to cylindrical transformationafter eliminating radial distortion

Two Steps:

(1). Center determination

(2) Distortion rectification

2-order polynomial approximation

3D Computer Vision

and Video Computing Paraboloidal MirrorParaboloidal 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

P1

viewpoint

tele-lens

P2

3D Computer Vision

and Video Computing Paraboloidal MirrorParaboloidal 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 Paraboloidal MirrorParaboloidal Mirror

Remote Reality – A Spin-off at Columbia University

http://www.remotereality.com/

3D Computer Vision

and Video ComputingCatadioptric Camera CalibrationCatadioptric 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.

3D Computer Vision

and Video ComputingImage Properties of Paraboloid System Image Properties of Paraboloid System

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)

(Assuming aspect ratio = 1)

3D Computer Vision

and Video ComputingImage Properties of Paraboloid System Image Properties 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

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

(with aspect ratio)

3D Computer Vision

and Video ComputingCalibration of Paraboloid System 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

3D Computer Vision

and Video ComputingCalibration of Paraboloid System 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

3D Computer Vision

and Video Computing NextNext

Turn in your projects and schedule meetings with me

END