pmumfordshahmerging

Performs priority region merging based on Mumford-Shah criterion.

Synopsis

Description

pmumfordshahmerging merges connected regions of the input image rg_in if the difference between the energy variation of the region defined by Mumford and Shah is lower than the specified threshold.

Two regions are connected if there exists a link between the related nodes in the input graph gr_in.

The principle of the algorithm is as follows:

For each region of the input region map rg_in:
If the difference between the criterion value of the two connected regions ≤ threshold
then merge them into one region.

The algorithm uses the priority merging that consists in merging regions with the lower difference.

The output region map reg_out defines the new regions and the output graph gr_out defines the new relationship between regions.

The energy variation (DE) is calculated as follows :

     Card(R1)*Card(R2)*(mean(R1)-mean(R2))²-2*alpha*boundary(R1,R2)
dE = ------------------------------------------------------------------------
                        Card(R1)+Card(R2)

where alpha is a parameter;
mean(R1) is the mean of the region R1;
boundary is the length of the boundary between R1 and R2;
and Card(R1) is the number of pixels in the region R1.

Negative values mean that energy that results from the merging of R1 and R2 is lower than the sum of the energy of the two regions.

Parameters

number specifies the number of allowed merging. If number = -1 then all possible merging are done.
alpha specifies the importance given to the boundary of the regions rather than the inner mean difference. Values are positive values and can be greater than 2000.
threshold specifies the maximum energy difference allowed between two regions to decide to merge them. Values can be positive or negative values. A typical value is 0.

Inputs

rg_in: a region map.
gr_in: a graph.
im_in: a grayscale image.

Outputs

rg_out: a region map.
gr_out: a graph.

Result

Returns the number of merging.

Examples

Merges regions yielded by a quadtree splitting process:

   puniformityquadtree 0.9 tangram.pan a.pan
   prg2gr a.pan b.pan
   pmumfordshahmerging -1 5 1  a.pan b.pan tangram.pan c.pan d.pan

C++ prototype

Errc PMumfordshahMerging( const Reg2d &rg_in, const Graph2d &gr_in, const Img2duc &im_in, Reg2d &rg_out, Graph2d &gr_out, long number, double alpha, float threshold );

Version française

Fusion prioritaire de régions selon la variation d'énergie de Mumford Shah.

Author: Laurent Quesnel