Segmentation overfitting without an edge penalty
= Segmentation overfitting without an edge penalty
Removing the jump-length cost from the <Mumford–Shah functional> lets finer piecewise-constant partitions reduce squared fidelity without charging for their proliferating <image edges>. For <continuous> data on a compact image domain, fine-cell averages converge in squared error while the ordinary within-cell <gradient> is zero. A finite interface penalty makes that geometry costly.