stylistic:style_transfer, structural:reformatting
Variational methods

The functional value is the sum of the total length of the segmentation curve K {\displaystyle K}, the smoothness of the approximation u {\displaystyle u}, and its distance to the original image f {\displaystyle f}. The weight of the smoothness penalty is adjusted by μ > 0 {\displaystyle \mu >0}. The Potts model is often called piecewise constant Mumford-Shah model as it can be seen as the degenerate case μ → ∞ {\displaystyle \mu \to \infty }. The optimization problems are known to be NP-hard in general but near-minimizing strategies work well in practice. Classical algorithms are graduated non-convexity and Ambrosio-Tortorelli approximation.