moments ( Regions : : : M11, M20, M02, Ia, Ib )

Geometric moments of regions.

The operator moments calculates the moments (M20, M02) and the product of inertia of the axes through the center parallel to the coordinate axes (M11). Furthermore the main axes of inertia (Ia, Ib) are calculated.

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 = SUMME ( (Z0 - Z)^i (S0 - S)^j ),

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

            Furthermore, h = (M20 + M02) / 2.

            Then Ia and Ib are defined by:

                    Ia = h + sqrt ( h^2 - M20 x M02 + M11^2)
                    Ib = h - sqrt ( h^2 - M20 x M02 + M11^2)

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).

Ia (output_control)
real(-array) -> real
The one main axis of inertia.

Ib (output_control)
real(-array) -> real
The other main axis of inertia.


Complexity

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


Result

The operator moments 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 (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_norm


See also

elliptic_axis



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