\mathbb{N}^{0}$ as a counter for accumulated label changes of $e$ during the iteration, as described in [@amrehn2018ideal], with . is initialized with $1$ for scribbles, i.e. , and $0$ otherwise.

Iterations are performed utilizing local state transition rule $\delta$: starting from initial seeds, labels are propagated based on local intensity features $\mathbf{c}$. At each discrete time step $t$, each node $f$ attempts to conquer its direct neighbors. A node $e$ is conquered if $$\begin{aligned}
    \mathbf{\Theta}_f^t\cdot\operatorname{g}(\mathbf{c}_e,\mathbf{c}_f)&>\mathbf{\Theta}_e^t\,,\ \text{where}\label{eq:growcutisconquered}\\
    \operatorname{g}(\mathbf{c}_e,\mathbf{c}_f) &= 1 - \frac{\Vert\mathbf{c}_e-\mathbf{c}_f\Vert_2}{\max_{j,k}\Vert\mathbf{c}_j-\mathbf{c}_k\Vert_2}\end{aligned}$$ If node $e$ is conquered, the automaton’s state set is updated $$\mbox{$\mathbf{Q}_e^{t+1}=((\mathbf{p}_e,\mathbf{\ell}_f^t),\mathbf{\Theta}_f^t\cdot\operatorname{g}(c_e,c_f),\mathbf{c}_e,\mathbf{h}_e^t+1)$},
\label{eq:growcutupdatestate}$$ The process is guaranteed to converge with positive and bounded node strengths monotonously decreasing

Interactive Segmentation Prototypes {#sec:sgmentation_prototypes}
-----------------------------------

Three interactive segmentation prototypes with different were implemented for usability testing. The segmentation technique applied in all prototypes is based on the approach as described in **Sec.**\[sec:segmentation\_method\]. allows for efficient and parallelizable computation of image segmentations while providing an acceptable accuracy from only few initial seed points. It is therefore well suited for an integration into a highly interactive system.

All three user interfaces provided include an *undo* button to reverse the effects of the user’s latest action. A *finish* button is used to define the stopping 