Fig. 6.

Examples of the completion process in SE(2) via time integration with negative exponential distribution (Row 1) and Gamma distribution (Row 2). Column (a) presents the negative exponential distribution with α = 0.05 and Gamma distribution with α = 0.05 and k = 3, Column (b) shows the contour plots of the 2D projection of the explicit completion kernel. Column (c) gives the 3D “ink propagation” for filling the gaps between two group elements $g=\left(51,2,\frac{29}{24}\pi \right)$ and $g^{\prime }=\left(51,100,\frac{19}{24}\pi \right)$, where the Gamma distribution gives better propagation and avoids singularities at the origin as shown in (d).