Axial-Cones: Modeling Spherical Catadioptric Cameras for Wide-Angle Light Field Rendering

Yuichi Taguchi 1    Amit Agrawal 1    Ashok Veeraraghavan 1    Srikumar Ramalingam 1    Ramesh Raskar 2
1 Mitsubishi Electric Research Labs (MERL)      2 MIT Media Lab
SIGGRAPH Asia 2010
Photo of Spherical Mirror Array   Photo of Refractive Sphere Array
Photo of Spherical Mirror Array   Photo of Refractive Sphere Array
Axial-Cone Modeling for Spherical Mirrors   Axial-Cone Modeling for Refractive Spheres
Axial-Cone Modeling for Efficient Light Field Rendering
150° x 150° FOV Mercator Projection   90° x 90° FOV Perspective Projection
Output Wide-Angle Refocusing Results and Depth Maps


Catadioptric imaging systems are commonly used for wide-angle imaging, but lead to multi-perspective images which do not allow algorithms designed for perspective cameras to be used. Efficient use of such systems requires accurate geometric ray modeling as well as fast algorithms. We present accurate geometric modeling of the multi-perspective photo captured with a spherical catadioptric imaging system using axial-cone cameras: multiple perspective cameras lying on an axis each with a different viewpoint and a different cone of rays. This modeling avoids geometric approximations and allows several algorithms developed for perspective cameras to be applied to multi-perspective catadioptric cameras.

We demonstrate axial-cone modeling in the context of rendering wide-angle light fields, captured using a spherical mirror array. We present several applications such as spherical distortion correction, digital refocusing for artistic depth of field effects in wide-angle scenes, and wide-angle dense depth estimation. Our GPU implementation using axial-cone modeling achieves up to three orders of magnitude speed up over ray tracing for these applications.


High-res QuickTime mov (83 MB)


  author =	{Yuichi Taguchi and Amit Agrawal and Ashok Veeraraghavan and Srikumar Ramalingam and Ramesh Raskar},
  title =	{Axial-Cones: Modeling Spherical Catadioptric Cameras for Wide-Angle Light Field Rendering},
  journal =	{ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia 2010)},
  volume =	{29},
  number =	{6},
  month =	{Dec},
  year =	{2010},
  pages =	{172:1--172:8}

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Axial Light Field for Curved Mirrors: Reflect Your Perspective, Widen Your View
Yuichi Taguchi, Amit Agrawal, Srikumar Ramalingam, and Ashok Veeraraghavan
CVPR 2010 (Oral presentation)
[ PDF (6.0 MB) ] [ Supplementary Material ] [ Talk Slides (22 MB) ] [ Talk Video @ ]

Opposite configuration of axial-cone modeling. In this paper, we use multiple real images captured on the axis of a rotationally symmetric mirror to generate a single virtual perspective image. A cone of rays in each real image is mapped to a unique cone of rays in the virtual image.
Analytical Forward Projection for Axial Non-Central Dioptric and Catadioptric Cameras
Amit Agrawal, Yuichi Taguchi, and Srikumar Ramalingam
ECCV 2010 (Oral presentation)
[ PDF (4.5 MB) ]

Axial-cone modeling enables efficient back projection (mapping from an image pixel to a 3D ray) for axially-symmetric catadioptric cameras. How can we perform efficient forward projection (mapping from a 3D point to an image pixel)? This paper describes an analytical solution.

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