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Auto-Calibration of Multi-Projector Display Walls

Auto-Calibration of Multi-Projector Display Walls. Marc Pollefeys ( marc@cs.unc.edu ) UNC-Chapel Hill. Andrew Raij ( raij@cise.ufl.edu ) UNC-Chapel Hill University of Florida. Multi-Projector Display. Projector misalignment The tedious solution -- align by hand

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Auto-Calibration of Multi-Projector Display Walls

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  1. Auto-Calibration of Multi-Projector Display Walls Marc Pollefeys (marc@cs.unc.edu) UNC-Chapel Hill Andrew Raij (raij@cise.ufl.edu) UNC-Chapel Hill University of Florida ICPR 2004

  2. Multi-Projector Display • Projector misalignment • The tedious solution -- align by hand • Many automatic camera-based methods [Raskar Viz1999, Chen Vis2000, Yang Viz2001, Raij Procams2003, …] ICPR 2004

  3. Multi-Projector Display cont’d • Undefined display area ICPR 2004

  4. Related Work – Display Area • Rectangle on Screen • Require manual placement and / or interaction to achieve desired display area properties • Yang Vis2001, Rehg CARV2002, Raij Procams2003, Ashdown CVPR2004 • Raskar CVPR2001, Raskar SIGGRAPH2003 – Requires tilt sensors and rigidly attached projector-camera pairs • Okatani ICCV2003 – Requires calibrated projectors ICPR 2004

  5. Main Contribution • We propose a fully automatic method for defining the display area of a planar multi-projector display • Single camera • No fiducials, interaction or additional sensors • Uncalibrated projectors • Note planar screen makes auto-calibration harder ICPR 2004

  6. Our Testbed: PixelFlex2 • Planar, casually-aligned, multi-projector display system developed at UNC-Chapel Hill • 8 projectors in 4x2 configuration, roughly 12' x 6' image • Calibration camera sees all projectors • Original system uses 4 fiducials to define display area Note: without photometric correction ICPR 2004

  7. Outline of our Approach • Find camera-projector homographies • Projector calibration with planar auto-calibration (TriggsECCV98) • Reconstruct calibration camera, projectors and display plane. • Define world-aligned frame in plane and choose display area. ICPR 2004

  8. Step 1: Camera-Projector Homographies Projector 1 2 4 5 6 7 8 3 Features Hcp Camera ICPR 2004

  9. Step 2: Projector Auto-Calibration xc • Projector ≡ Camera • The image of the circular points must lie on the image of the absolute conic (IAC) in all views Ω∞ X π∞ πd ωc ωp Hcpxc Hcp C P ICPR 2004

  10. Projector Auto-Calibration cont’d (0, yp) • n projectors (n ≥ 3) • 2n+2 constraints • n+5 unknowns • Camera is calibrated - ωc is known • Camera image of circ. points xc unknown • Projector - fpi, yp unknown • pixels are square • principal point same in all projectors, offset vertically • Note: Separate offset yields 2n+4 unknowns > 2n+2 • Levenberg-Marquardt least squares minimization of n ||xcTωcxc ||2 + ∑||(Hcpxc)Tωp(Hcpxc)||2 p=1 ICPR 2004

  11. Initialization to Minimization C • For each hypothesis on Kp and for each projector π1 π2 SVD-based Pose Estimation for Planar Scenes (TriggsECCV98) Projector Kp-1HcpKc Camera xc1 xc2 ||xcTωcxc ||2 + ∑||(Hcpxc)Tωp(Hcpxc)||2 n p=1 ICPR 2004

  12. Initialization (cont’d) • Clear minima produced by initialization algorithm ICPR 2004

  13. Intrinsics are consistent for different geometric configurations Estimated Projector Intrinsics ICPR 2004

  14. Step 3: Reconstruction π1 π2 • Camera-projector baseline is normalized to 1 so n reconstructions are in different frames, up to scale • Merge by normalizing by distance from camera to plane K1-1Hc1Kc P1 C SVD π1 π2 Kn-1HcnKc Pn C ICPR 2004

  15. Step 4: Display Area Selection • Display area is a world-aligned rectangle in the plane of desired aspect ratio • Vertical = Horizontal V Plane Normal • Assume camera x-axis is horizontal (i.e. allows tilting) and perform orthogonal projection on plane • Can choose rectangle of desired aspect ratio since reconstruction up to scale ICPR 2004

  16. Results Camera, projector array, and plane reconstruction. 16:9 max inscribed area viewport shown in yellow. Camera image with dotted lines extending towards vanishing points. Vanishing points found by projection of world direction basis into camera. ICPR 2004

  17. Conclusions • Contributions • Automatic estimation of intrinsics of array of projectors projecting on a plane • Automatic estimation of projector extrinsics and display plane • Automatic selection of world-aligned viewport of proper aspect ratio • In sum, fully automatic calibration of a planar multi-projector /camera system without physical calibration objects and/or interaction. ICPR 2004

  18. Conclusions cont’d • Discussion • Possible even though only scene observed by the camera and projectors is a plane! • “Metric" calibration is not highly accurate (intrinsics, etc.), but this is ok for the application. Perceptually, display area will appear to be a properly-aligned rectangle. • Future Work • Precise evaluation of calibration accuracy • Improve calibration with max likelihood estimation based on bundle-adjustment. • Calibrate for camera intrinsics, radial distortion in both camera and projectors. ICPR 2004

  19. Acknowledgements • This work was partially supported by: • NSF Career award IIS 0237533 • Department of Energy ASC VIEWS Program B519834 • DARPA DARWARS program ONR N00014-03-1-0589. • The UNC PixelFlex Display Research Team Henry Fuchs Herman Towles Chris Ashworth Sundeep Tirumalareddy ICPR 2004

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