Geometric moments of regions.

The operator moments_region_central calculates the central moments (I1, I2, I3, I4).

 Calculation: Then the moments Ii  are defined by:

	I1 = MU20 MU02 - MU11^2  
	I2 = ( MU30 MU03 - MU21  MU12 )^2
		 -4( MU30 MU12 - MU21^2)( MU21  MU03 - MU12^2)  
	I3 =  MU20 ( MU21 MU03- MU12^2 )- MU11 (MU30 MU03 
             - MU21  MU12 ) +  MU02 (MU30 MU12 - MU21^2)  
   	I4 = MU30^2 MU02^3 - 6 MU30 MU21  MU11 MU02^2 +
             6 MU30 MU12  MU02 (2 MU11^2 - MU20  MU02 )  
             + MU30 MU03 (6 MU20  MU11  MU02 -8 MU11^3) +
             9{ MU21 ^2} MU20 MU02^2 - 18 MU21  MU12  MU20  MU11  MU02   
             +6 MU21  MU03  MU20 (2 MU11^2 - MU20  MU02 )+
             9 MU12^2 MU20^2 MU02 -
             6 MU12  MU03  MU11 MU20^2 + MU03^2 MU20^3  

If more than one region is passed the results are stored in tuples, the index of a value in the tuple corresponding to the index of a region in the input.

In case of empty region all parameters have the value 0.0 if no other behavior was set (see set_system).

If Z is the area of the region the mean runtime complexity is O(sqrt(Z)).

The operator moments_region_central returns the value 2 (H_MSG_TRUE) if the input is not empty. The behavior in case of empty input (no input regions available) is set via the operator set_system('no_object_result',<Result>). The behavior in case of empty region (the region is the empty set) is set via set_system('empty_region_result',<Result>). If necessary an exception handling is raised.

moments_region_central is reentrant and automatically parallelized (on tuple level).

threshold, regiongrowing, connection

moments_region_2nd

elliptic_axis

Region processing