Image Mosaicing from Uncalibrated Views of a Surface
§ 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 BMVC 2004
The Problems: • Find the transformation relating each image coordinate system • Varying SOR structure / camera parameters (internal, external). Pernici BMVC 2004
Past and Related Approaches • [Can et. al. PAMI 2002] 12 -DOF transformation. The retina is modeled as a rigid quadratic surface. Uncalibrated weak perspective camera. • [Puech et al. PR 2001] Works on Right circular cylinder. Needs precalibrated cameras. • [Colombo, Delbimbo, Pernici. PAMI 2004(to appear)] Single view 3 D metric reconstruction from a single uncalibrated view of a SOR. • [Wong et. al PAMI 2003] Multiview camera calibration from SOR (only apparent contour used). • [Jiang et. al. PAMI 2003] Turntable sequences. Rotating points are fitted to conics. Pernici BMVC 2004
Our Approach • The mosaic consist in two steps: 1. Warping 2. 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 BMVC 2004
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 BMVC 2004
SOR Single view geometry • can be inferred from and from at least two visible cross section. [ Colombo, Delbimbo, Pernici PAMI 2005 January ] • Two cross section are also sufficient for camera calibration. Pernici BMVC 2004
SOR Single view geometry • Imaged cross sections are related through Planar Homology • Apparent contour is symmetric under the Armonic Homology contact point • Apparent contour is tangent to a cross section ( ) at the contact point. Pernici BMVC 2004
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 BMVC 2004
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 BMVC 2004
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 BMVC 2004
Imaged Sor Parametrization: metric z • Rectifying homography can be computed by intersecting the vanishing line with Pernici BMVC 2004
Imaged Sor Parametrization: euclidean • Laguerre formulas gives the angular parameter. Pernici BMVC 2004
Image warping. • Imaged Sor meridians and parallels are mapped onto mutually orthogonal straight line. Pernici BMVC 2004
Example • the estimated imaged meridians at degree. Pernici BMVC 2004
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 BMVC 2004
Example • Four uncalibrated views of a vase with overlapping pictorial content. Pernici BMVC 2004
Example • Four uncalibrated views of a vase with overlapping pictorial content. Pernici BMVC 2004
Manual initial guess • The leftmost image was used twice in order to close the visual loop Pernici BMVC 2004
Alignment and compositing “Vase Panorama” Pernici BMVC 2004
Conclusion • Projective properties of SOR and relationship with camera geometry (uncalibrated setting). • Camera calibration from two coaxial parallel 3 D 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 BMVC 2004
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