moments_norm ( Regions : : : M11, M20, M02 )

Geometric moments of regions.

The operator moments_norm calculates the scaled moments (M20, M02) and the procut of inertia of the axes through the center parallel to the coordinate axes (M11).

Calculation: Z0 and S0 are the coordinates of the
            center of a region R with the area F.
            Then the moments Mij are defined by:

                    Mij = 1/F^2 * SUMME ( (Z0 - Z)^i (S0 - S)^j ),

            wherein Z and S run throug all pixels of the region R.

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).


Parameters

Regions (input_object)
region(-array) -> object
Regions to be examined.

M11 (output_control)
real(-array) -> real
Product of inertia of the axes through the center parallel to the coordinate axes.

M20 (output_control)
real(-array) -> real
Moment of 2nd order (line-dependent).

M02 (output_control)
real(-array) -> real
Moment of 2nd order (column-dependent).


Complexity

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


Result

The operator moments_norm returns the value 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 is raised.


Possible Predecessors

threshold__, regiongrowing__, connection


Alternatives

moments


See also

elliptic_axis



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