9.1  Appendix. Occlusion-compatible scanning-order


The following summary presents only a concept which could not be fully verified at the time of writing the thesis.

Consider two 3D scene points P1 and P2, which are projected onto a target image (virtual view) at the same pixel position p, and onto the reference view at pixel positions p1′ and p2′ (see Figure 4.8). To perform an occlusion-compatible scanning order of the reference image, it is necessary to scan first the background point P1 and then the foreground P2. Hence, when projecting the 3D points P1 and P2 onto the reference view, it can be derived that

|M ′P2 - M ′C | < |M ′P1 - M ′C |,
(9.1)

which is equivalent to the same inequality using pixels in the reference image, thus

 ′  ′   ′ ′     ′ ′    ′ ′
|λ2p 2 - λee | < |λ1p1 - λee|,
(9.2)

where e′ corresponds to the epipole in the reference view. The points p1′ and p2′ are the projections of the background and foreground 3D points, respectively. Points p1′ and p2′ are therefore background and foreground pixels. By normalizing/dividing Equation (9.2) with the homogeneous scaling factor λe′, two cases can be distinguished. First, assuming λe′> 0, to perform the warping of background pixels p1 prior to foreground pixels p2, it is sufficient to scan the reference image from the border of the image towards the epipole e′. Second, in the case λe′< 0, the reference image should be scanned from the epipole towards the borders of the image.