1. Fixed-Center Pan-Tilt Projector and Its Calibration Methods Ikuhisa Mitsugami Norimichi Ukita Masatsugu Kidode Graduate School of Information Science Nara 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 R relation image plane P 1 projector board light projector board light pan tilt projector screen 2 projected point screen 1 3D translation plane R initial orientation tangent plane Q (X, Y) another orientation initial center direction center direction at the orientation (u, v) u v 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. Specification Projector: PLUS VISION V3-131 Projection System: DLP Resolution: 1024*767 (XGA) Brightness: 1000 lm Contrast Ratio: 2000:1 Steerable stage Orientation accuracy: 0.002 deg Rotating speed: 10 deg/s (X, Y) (x, y) image plane P 1 wall R relation image plane P 2 image plane P 1 wall R projector relation (X, Y) (x, y) wall R projector image plane P 2 image plane P 1 relation corresponding area of P 1 wall R tangent plane Q FC-PT projector corresponding area of P 2 relation H wall R tangent plane Q FC-PT projector X Y 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 R 0 image plane inversely distorted graphic graphic to draw FC-PT projector RcRc RmRm graphic G m corresponding area of R m T m : intersection of G m and R m center direction tangent plane Q S m : projection of T m 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, and direct 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. G c is calculated from G m by the transformation between R m and R c RcRc RmRm SmSm graphic G c FC-PT projector R’ m T c : intersection of G c and R c tangent plane Q corresponding area of R c S c : projection of T c center direction Input image to projector Projection result on the walls