Geometric moments of regions.
The operator moments_region_2nd_invar 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).
|
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). | |
If F is the area of the region the mean runtime complexity is O(sqrt(F)).
The operator moments_region_2nd_invar 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_2nd_invar is reentrant and automatically parallelized (on tuple level).
threshold, regiongrowing, connection
Region processing
