6

Spatial Sampling

Spatial sampling describes how a 3D space is sampled by stereo pairs of images, without considering geometric or photometric complexities of 3D scenes. This chapter presents studies on spatial sampling for stereo panoramas which are a pair of panoramic images which only differ in the chosen value of the principal angle ω. Symmetric panoramas are a special case of stereo panoramas. Recall from our previous definition of symmetric panoramas that this is a pair of stereo panoramas whose associated principal angles sum to 360°.

6.1 Stereo Panoramas

Consider a stereo panorama EpR(R, f, ωR, γ) and EpL(R, f, ωL, γ), with 0° ≤ ωR < ωL ≤ 360°. Without loss of generality, we call the panorama that is associated with the smaller (larger) value of the principal angle the right (left) image.

In the symmetric case (i.e., ωR = ω and ωL = 360° − ω), we only consider ω between 0° and 180°. In order to reduce repetition, only the right image parameters will be referred to in the analysis and calculations throughout this chapter. The chapter will mostly consider stereo panoramas which are symmetric; non-symmetric cases are explicitly identified as such.

Section 6.2 is about sampling structures of stereo panoramic cameras, in which mainly the spatial distribution of samples will be discussed. Section 6.3 turns to sampling resolution and addresses the question how many samples can be acquired by a pair of stereo panoramas with image dimensions W × H. Section 6.4 computes different ...

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