Polydioptric Cameras

A regular array of pinhole cameras forms a polydioptric camera.

A theoretical model for a camera that captures the plenoptic function in some part of the space is a surface S that has at every point a pinhole camera. We call this camera a polydioptric camera. A "plenoptic camera'' had been described by Adelson and Wang in 1992, but since no physical device can capture the true time-varying plenoptic function, we prefer the term polydioptric to emphasize the difference between the theoretical concept and the implementation. With a polydioptric camera we observe every point in the scene in view from many different viewpoints (theoretically, from every point on S) and thus we capture many rays emanating from that point. A parameterization for these general cameras has been introduced recently by Grossberg and Nayar in 2001. A polydioptric camera can be obtained if we arrange ordinary cameras very close to each other (Figs. 1 and 2). This camera has an additional property arising from the proximity of the individual cameras: it can form a very large number of orthographic images, in addition to the perspective ones. Indeed, consider a direction r in space and then consider in each individual camera the captured ray parallel to r. All these rays together, one from each camera, form an image with rays that are parallel. Furthermore, for different directions r a different orthographic image can be formed. For example, Fig. 2 shows that we can select one appropriate pixel in each camera to form an orthographic image that looks to one side (blue rays) or another (red rays). Fig. 3 shows all the captured rays, thus illustrating that each individual camera collects conventional pinhole images.

Design of Polydioptric Camera Polydioptric Camera capturing Orthographic Images Design of Polydioptric Camera capturing Perspective Images
Fig.1 : Design of a Polydioptric Camera

Fig.2: capturing Parallel Rays

Fig.3: and simultaneously capturing Pencils of Rays

Thus, a polydioptric camera has the unique property that it captures, simultaneously, a large number of perspective and affine images (projections). We will demonstrate that it also makes the structure from motion problem linear. A polydioptric spherical camera is therefore the ultimate camera since it combines the stability of full field of view motion estimation with linearity of the problem, as well as the ability to reconstruct scene models with minimal reconstruction errors since we can choose the viewpoints from the viewpoint manifold for the scene reconstruction to minimize reconstruction uncertainty.