]>Symmetric and Transitive Registration of Image Sequences : Figure 1
686875.fig.001a
(a)
686875.fig.001b
(b)
Figure 1: If two points ( 𝐴 1 and 𝐴 2 ) in two images ( 𝐼 1 and 𝐼 2 ) correspond, as sketched in (a), then the registration algorithm should associate the two points regardless of the order of images. This is the symmetry property. Let 𝐼 1 , 𝐼 2 , and 𝐼 3 represent images of the same deforming object taken at three-time points, and let 𝐴 1 , 𝐴 2 , and 𝐴 3 represent the location of the same physical point in the three images, as sketched in (b). If the registration algorithm, when applied to images 𝐼 1 and 𝐼 2 , associates points 𝐴 1 and 𝐴 2 , and, when applied to images 𝐼 2 and 𝐼 3 , associates points 𝐴 2 and 𝐴 3 , then it should, when applied to images 𝐼 1 and 𝐼 3 , associate points 𝐴 1 and 𝐴 3 . This is the transitivity property.