Image Mosaicing from Uncalibrated Views of 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}@dsi.unifi.it Pernici BMVC2004

The Problem Problems: Find the transformation relating each image coordinate system Varying SOR structure / camera parameters (internal,external). Pernici BMVC2004

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. Pernici BMVC2004

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. Pernici BMVC2004

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 Pernici BMVC2004

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. Colombo,Delbimbo,Pernici PAMI2005 January [ ] Pernici BMVC2004

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 Pernici BMVC2004

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 Pernici BMVC2004

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. Pernici BMVC2004

Imaged Sor Parametrization: metric z The imaged meridian can be rectified to metric by an homography parameterized by the internal camera parameters. contact point Pernici BMVC2004

Imaged Sor Parametrization: metric z Rectifying homography can be computed by intersecting the vanishing line with Pernici BMVC2004

Imaged Sor Parametrization: euclidean Laguerre formulas gives the angular parameter. Pernici BMVC2004

Image warping. Imaged Sor meridians and parallels are mapped onto mutually orthogonal straight line. Pernici BMVC2004

Example the estimated imaged meridians at degree. Pernici BMVC2004

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 Pernici BMVC2004

Example Four uncalibrated views of a vase with overlapping pictorial content. Pernici BMVC2004

Example Four uncalibrated views of a vase with overlapping pictorial content. Pernici BMVC2004

Manual initial guess The leftmost image was used twice in order to close the visual loop Pernici BMVC2004

Alignment and compositing “Vase Panorama” Pernici BMVC2004

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