More novel forms of these filters, such as opening and closing by reconstruction [12, 13], use a specified structuring element to initiate the reconstruction.
Opening by reconstruction of an image g is defined as the reconstruction of g from an transformed (usually an erosion) g:
where g is a grey-scale image, 
is an erosion
operation, 
is a morphological reconstruction of g and
is a morphological reconstruction.
Contrary to the morphological opening, the opening by reconstruction allows one to preserve the shape of the components that are not removed by the erosion.