Geometric moments of regions.

The operator moments_region_2nd 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 = SUM ( (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).

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

The operator moments_region_2nd 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 (region is the empty set) is set via set_system('empty_region_result',<Result>). If necessary an exception handling is raised.

moments_region_2nd is reentrant and automatically parallelized (on tuple level).

threshold, regiongrowing, connection

moments_region_2nd_invar

elliptic_axis

Foundation