\psi_r(p_i - p_j) + \frac{1}{N}\sum_{i=1}^N \int_{\mathbb R^d} \omega(x) \psi_a(p_i- x) {\mathop{}\!\mathrm{d}}x,$$ where the $N$ points $p_1,\ldots,p_N \in \mathbb R^d$ represent point masses that should approximate a given image $\omega$, which is assumed to be a compactly supported absolutely continuous probability measure. The associated particle gradient flow $\partial_t p \in - \partial_p \mathcal E_N$ is of the form , where $\mu(t)$ is the sum of Dirac measures at the $p_j(t)$. The minimizer of $\mathcal E_N$ places the $N$ points in an optimal way in the sense that points are concentrated on large values of the image $\omega$, but they are not too densely distributed. This behavior results from the balance between the second (attraction) term with the first (repulsion) term in the energy . It is shown that the energy functional is continuous and coercive, and, for $d=1$, it is possible to calculate its minimizers explicitly. In the two or higher dimensional settings, minimizers have been approximated numerically. In [@grpost11] the data function $\omega$ was also considered on other sets than $\mathbb R^d$, such as $\mathbb T^d$ or $\mathbb S^2$, and kernels $\psi_a, \psi_r$ other than the Euclidean distance were used. When the number $N$ of particles is taken to $\infty$, 