Image Mosaicing from Uncalibrated Views of a Surface of Revolution

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Image Mosaicing from Uncalibrated Viewsof a
Surface of Revolution

• Carlo Colombo, Alberto Del Bimbo, Federico
  Pernici
• Dipartimento di Sistemi e Informatica Università
  di Firenze
• Via Santa Marta 3, I-50139 Firenze, Italy
• colombo,delbimbo,pernici_at_dsi.unifi.it

Pernici BMVC2004
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The Problem

• Problems
• Find the transformation relating each image
  coordinate system
• Varying SOR structure / camera parameters
  (internal,external).

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Past and Related Approaches

• Can et. al. PAMI2002 12-DOF transformation.
  The retina is modeled as a rigid quadratic
  surface. Uncalibrated weak perspective camera.
• Puech et al. PR2001 Works on Right circular
  cylinder. Needs precalibrated cameras.
• Colombo,Delbimbo,Pernici. PAMI2004(to appear)
  Single view 3D metric reconstruction from a
  single uncalibrated view of a SOR.
• Wong et.al PAMI2003 Multiview camera
  calibration from SOR (only apparent contour
  used).
• Jiang et.al. PAMI2003 Turntable sequences.
  Rotating points are fitted to conics.

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Our Approach

• The mosaic consist in two steps
• Warping
• Alignment and compositing

• The Warping step removes the image formation
  process and allows the imaged SOR regions to be
  mapped on a common reference plane.

• In the Alignment and compositing step, an unknown
  translation is computed to register the images in
  the reference plane.

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Imaged SOR parameterization.

• The problem can be solved by estimating the
  imaged surface parameterization in all views.

• The estimated parameterization is then projected
  onto a coaxial cylindrical surface and unrolled
  onto the plane .

• SOR parameterization

Scaling function
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SOR Single view geometry

• can be inferred from and from at least
  two visible cross section.
• Two cross section are also sufficient for camera
  calibration.

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SOR Single view geometry

• Imaged cross sections are related through Planar
  Homology

• Apparent contour is symmetric under the
  Armonic Homology

• Apparent contour is tangent to a cross
  section ( ) at the contact point.

contact point
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Calibration from two imaged cross section.

• All the entities for the imaged geometry of the
  SOR together with internal camera parameters can
  be algebraically computed from two imaged cross
  section

• Four solutions two complex conjugate pair forms
  a complete quadrangle

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Calibration from two imaged cross section.

• Pinhole camera with 3 DOF (principal point,
  focal length).

• The Image of the Absolute Conic.

• Four constraints. Three independent.

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Imaged Sor Parametrization metric z

• The imaged meridian can be rectified to metric
  by an homography parameterized by the internal
  camera parameters.

contact point
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Imaged Sor Parametrization metric z

• Rectifying homography can be computed by
  intersecting the vanishing line with

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Imaged Sor Parametrization euclidean

• Laguerre formulas gives the angular parameter.

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Image warping.

• Imaged Sor meridians and parallels are mapped
  onto mutually orthogonal straight line.

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Example

• the estimated imaged meridians at degree.

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Image Alignment.

• The alignment is vey similar to that used for
  cylindrical panoramas
• The scaling factor for all the images is
  specified by the two cross section in the views
  (metric z is known up to a scaling factor).
• Direct registration is employed to recover the
  translation . In order to cope for small
  jitter along z also a vertical translation is
  estimted
• The intensity error is minimized between two
  images

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Example

• Four uncalibrated views of a vase with
  overlapping pictorial content.

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Example

• Four uncalibrated views of a vase with
  overlapping pictorial content.

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Manual initial guess

• The leftmost image was used twice in order to
  close the visual loop

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Alignment and compositing
Vase Panorama
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Conclusion

• Projective properties of SOR and relationship
  with camera geometry (uncalibrated setting).
• Camera calibration from two coaxial parallel 3D
  circle.
• Application flattened mosaic can be regarded as
  a virtual paint . Character recognition.
• With a pre-calibrated camera a single ellipse is
  sufficient.
• Limitations ellipse fitting affects calibration
  results.
• Future research multiview calibration,
  detection and removal of surface specular
  highlights.

Thank you
Pernici BMVC2004