Fig. 4.

Geodesic paths (top to bottom) between two shapes in different pre-shape spaces, and the shape space S. The labeled arrows point to regions where noticeable changes in the shape along the path in S compared to the path in $\mathcal{C}∕\left({\mathbb{S}}^1\times \mathrm{SO}\left(2\right)\right)$ are observed. In the column $\mathcal{Q}$, s_tart, and s_end are the end-points of the shape respectively.