Piecewise-constant Mumford–Shah problem
= Piecewise-constant Mumford–Shah problem
{title2=$\min_{\nabla u=0}\{\|u-g\|_2^2+\beta\mathcal H^1(J_u)\}$}
The infinite gradient-weight limit restricts to <SBV space> <image signals> with $\nabla u=0$ almost everywhere. Their energy is fidelity plus jump length, represented by constants on a <Caccioppoli partition>. Internal perimeter is counted once by $\tfrac12\sum_i\operatorname{Per}(E_i;\Omega)$; adjacent equal-valued regions can be merged.