Fixed-Center Pan-Tilt Projector and Its Calibration Methods
Ikuhisa Mitsugami Norimichi Ukita Masatsugu KidodeGraduate School of Information ScienceNara Institute of Science and Technology
Objectives: Drawing graphics on the planar surfaces in the environment by projectors.
Precisely at where we would like it be.Without any distortions.Enable to move it freely on the planes.Even when it moves across a boundary of two planes, it should lie in the similar way to a paper poster folded along the planes.
How to accomplish it?Steerable (enable to pan and tilt) mechanism. “Fixed-center pan-tilt (FC-PT) projector.”Multiple FC-PT projectors can be used for larger space.
wall Rrelation
image plane P1
projector
board
lightprojector
board
light
pan
tilt
projector
screen 2
projected point
screen 13D translation
plane R
initial orientation
tangent plane Q
(X, Y)another orientation
initial center direction
center direction at the orientation
(u, v)
u v
)tan,(tan tp ),( tp
),( tp
1
tilt axis
pan axis
Introduction
Normal (fixed) projector
Normal pan-tilt projector
FC-PT projector.
Implementation of FC-PT Projector
Projection to One Plane
Projection to Multiple Planes
Experimental Results
Rough estimation of projection center
Precise fixing Future Works
Advantages of FC-PT Projector
Automatic set-up of FC-PT projectors.Cooperation with cameras.
Cooperation of multiple FC-PT projectors.For display of larger graphics than the capacity of one projector.Correction of misalignment among the graphics of the projectors.
SpecificationProjector: PLUS VISION V3-131
Projection System: DLPResolution: 1024*767 (XGA)Brightness: 1000 lmContrast Ratio: 2000:1
Steerable stageOrientation accuracy: 0.002 degRotating speed: 10 deg/s
(X, Y)(x, y)
image plane P1
wall Rrelation
),( tp
image plane P2
image plane P1
wall Rprojector relation
(X, Y)(x, y)
wall Rprojector
),( tp
image plane P2
image plane P1
relation
corresponding area of P1
wall Rtangent plane QFC-PT projector
corresponding area of P2 rela
tion Hwall R
tangent plane QFC-PT projector
XY
Introduction of “tangent plane” Q.Image planes of all orientations can be projected on Q.As Q does not move, the relation between Q and R is fixed.Their relation H can be determined by 4 pairs of coordinates on Q and R.
(horizontal view) (vertical view)
tangent plane Q plane R0
image plane
inversely distorted graphic
graphic to draw'QPH
)','( tp ),( )()( gra
kgrak vu
),( )()( proj
proj vu
'P),( )()( gra
kgrak YX
FC-PT projector
Rc
Rm
graphic Gm
corresponding area of Rm
Tm: intersection of Gm and Rm
centerdirection
tangent plane QSm: projection o
f Tm
R’c
By connectivities of multiple planes in the environment and 2D coordinate of every plane,
transformations parameters between 2D coordinates of every 2 planes are calculated.
To display graphics on planes, all we have to do are: locate the FC-PT projector anywhere we like,measure the 2D metric size of the plane, anddirect the projector to 4 corners of the plane and record them.
FC-PT projector can provide: 1) Easy set-up, 2) Precise display, 3) Real-time process.
Gc is calculated from Gm by the transformation between Rm and Rc
Rc
Rm
Sm
graphic Gc
FC-PT projector
R’m
Tc: intersection of Gc and Rc
tangent plane Q
corresponding area of Rc
Sc: projection of Tc
centerdirection
Input imageto projector
Projection resulton the walls
