The Mumford-Shah functional balances smooth approximation to data with the length of an edge set. For a bounded planar domain 
, bounded real data 
,
a relatively closed set 
of finite length, and 
, a normalization
is
 |
The term 
is Hausdorff measure. Removing redundant pieces
of 
gives its reduced representative, the support of length
measure restricted to 
. The Mumford-Shah conjecture
describes the geometry of this set for minimizers.
