Fig. 1.

An illustration of a SyN geodesic path between images. The images in the top row are the original images, I and J, at the initialization of the method. After the SyN solution converges, (second row) these images deform in time along the series of diffeomorphisms that connect them. The deforming grids associated with these diffeomorphisms are shown in the bottom row. The maps, φ₁ and φ₂ are of equivalent length and map I and J to the mean shape between the images. The full path, φ and φ⁻¹, are found by joining the paths φ₁ and φ₂. The symmetric nature of this problem (proven in [40]) is due to the interchange-ability of the labels I and J in our problem formulation.