Radial Imaging Systems

A picture taken by a conventional camera captures the scene from the camera's single viewpoint. In many applications in computer vision and computer graphics, it is desirable to capture the scene from a large number of viewpoints. In this project, we explore a class of imaging systems, called radial imaging systems, that capture a scene from a large number of viewpoints within a single image using a camera and a curved mirror. Specifically, we examine the class of radial imaging systems that consist of a conventional camera looking through a hollow cone mirrored on the inside. The field of view of the camera gets folded inwards and the scene is imaged from circular loci of virtual viewpoints, in addition to the viewpoint of the camera. We have analyzed the field of view and resolution characteristics as well as the structure of the viewpoint locus for this class of imaging systems. We have built radial imaging systems that can, from a single image, recover the frontal 3D structure of an object, generate the complete texture map of a convex object, and estimate the parameters of an analytic BRDF for an isotropic material. In addition, one of our systems can recover the complete geometry of a convex object by capturing only two images.

Publications

"Multiview Radial Catadioptric Imaging for Scene Capture,"
S. Kuthirummal and S. K. Nayar,
ACM Trans. on Graphics (also Proc. of ACM SIGGRAPH),
Jul, 2006.
[PDF] [bib] [©]

Images

  Reconstructing 3D Textures:

This radial imaging system includes a cylindrical mirror and can be used to recover the geometry of a 3D texture. In a single image, the system captures the scene from a circular loci of viewpoints in addition to the real viewpoint of the camera.

     
  Captured Images of 3D Textures:

Images of 3D textures -- the bark of a tree and a slice of bread -- captured by the radial imaging system shown above. Points on the 3D texture are imaged at least twice. In a radial imaging system, the epipolar lines are radial and hence scan-line matching ambiguities do not arise as in the case of conventional rectified stereo systems. Thus, the geometry of the object is more robustly recovered.

     
  Reconstructed 3D Textures:

Views of the geometry of 3D Textures recovered from the captured images shown above.

     
  Sampling and Estimating BRDFs:

This radial imaging system includes a cylindrical mirror and can be used to sample the BRDF of an isotropic material by taking only one image. The sample is placed at a specific distance along the optical axis of the system. Multiple internal reflections within the cylindrical mirror cause the sample to be observed by four circular loci of virtual viewpoints, in addition to the real viewpoint of the camera.

     
  Captured Images of Paint Samples:

Images of small circular disks painted with metallic and red satin paints, captured by the system shown above. One can see that via reflections the samples are imaged along four circles, implying that the samples are imaged by four circular loci of viewpoints. The measurements for these viewing directions and a single lighting direction are used to fit an analytic isotropic BRDF model to the samples.

     
  Rendering with the Estimated BRDFs:

The Buddha model rendered with the analytic BRDF model parameters for metallic and red satin paints estimated from the captured images shown above.

     
  Reconstructing Faces:

This radial imaging system includes a conical mirror and can be used to recover the geometry of a face by capturing just a single image. The system captures the scene from a circular loci of viewpoints in addition to the camera's real viewpoint.

     
  Captured Images of Faces:

Images of faces captured by the above radial imaging system. Since points on a face are imaged at least twice, along a radial line, we can apply stereo to recover face geometry.

     
  Reconstructed Face Models:

Views of the face models reconstructed from the captured images shown above.

Interactive Flash Demonstration

     
  Capturing Complete Texture Maps of Convex Objects:

This radial imaging system includes a conical mirror and can be used to capture the complete texture map of a convex object in a single image. (Sometimes the bottom surface might not be imaged). This system images the scene from a circular loci of viewpoints in addition to the camera's real viewpoint.

     
  Captured Images:

Images of a conical and cylindrical object captured by the system shown above. The top and all sides of each object are captured in just one image. These images can now be used as texture maps.

     
  Using Captured Images as Texture Maps:

A conical and a cylindrical object texture mapped with the captured images shown above.

     
  Recovering Complete Geometry of Convex Objects:

Images of a toy head captured by the radial imaging system shown above, that includes a conical mirror. The object was moved along the optical axis in between the two images. The complete head is seen in each of the two images. Due to the specific motion of the object, the epipolar lines for these two images are radial. Hence, we can use stereo to recover the complete geometry of the toy head.

     
  Reconstructed Complete Geometry:

Views of the complete geometry of the toy head recovered from the two captured images shown above.

     

Videos

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  Siggraph 2006 Video:

This video shows a variety of radial imaging systems and their applications. (With narration)

     
  Family of Radial Imaging Systems:

This video shows the family of radial imaging systems that are made up of conical mirrors. (With narration)

     
  Reconstructing and Synthesizing 3D Textures:

This video shows how a radial imaging system with a cylindrical mirror can be used to reconstruct the geometry of a 3D texture from just a single image. The reconstructed 3D texture can then be used to synthesize novel 3D texture samples. (With narration)

     
  Sampling and Estimating BRDFs:

This video shows how a radial imaging system with a cylindrical mirror can be used to sample and estimate the BRDF of an isotropic material by capturing just one image. (With narration)

     
  Reconstructing Faces:

This video shows how a radial imaging system with a conical mirror can be used to recover face geometry from a single captured image. (With narration)

     
  Capturing Complete Texture Map and Geometry of Convex Objects:

This video shows how a radial imaging system with a conical mirror can capture the complete texture map of a convex object by taking just one image. Capturing two such images with parallax enables the recovery of the complete geometry of the object. (With narration)

     

Slides

SIGGRAPH 2006 presentation     With videos (zip file)

Cylindrical Mirror Stereo Project at Nara Institute of Science and Technology

Catadioptric Cameras for 360 Degree Imaging

Applications of 360 Degree Cameras

Catadioptric Stereo: Planar and Curved Mirrors

Non-Single Viewpoint Imaging: Raxels and Caustics