fit_surface_second_orderFitSurfaceSecondOrderFitSurfaceSecondOrderfit_surface_second_orderfit_surface_second_order🔗

Short description🔗

fit_surface_second_orderFitSurfaceSecondOrderFitSurfaceSecondOrderfit_surface_second_orderfit_surface_second_order — Calculate gray value moments and approximation by a second order surface.

Signature🔗

fit_surface_second_order( region Regions, image Image, string Algorithm, integer Iterations, real ClippingFactor, out real Alpha, out real Beta, out real Gamma, out real Delta, out real Epsilon, out real Zeta )

Description🔗

The operator fit_surface_second_orderFitSurfaceSecondOrder calculates the gray value moments and the parameters of the approximation of the gray values by a second order surface. The calculation is done by minimizing the distance between the gray values and the surface. A second order surface is described by the following formula:

\[\begin{eqnarray*} \textrm{Image}(r,c) & = & \textrm{Alpha}(r - r_{center})^2\\ & + & \textrm{Beta}(c - c_{center})^2\\ & + & \textrm{Gamma}(r - r_{center})*(c - c_{center})\\ & + & \textrm{Delta}(r - r_{center})\\ & + & \textrm{Epsilon}(c - c_{center})\\ & + & \textrm{Zeta} \end{eqnarray*}\]

\(r_{center}\) and \(c_{center}\) are the center coordinates of the intersection of the input region with the full image domain. By the minimization process the parameters from Alphaalphaalpha to Zetazetazeta is calculated.

The algorithm used for the fitting can be selected via Algorithmalgorithmalgorithm:

'regression'"regression" Standard ‘least squares’ fitting.
'huber'"huber" Weighted ‘least squares’ fitting, where the impact of outliers is decreased based on the approach of Huber.
'tukey'"tukey" Weighted ‘least squares’ fitting, where outliers are ignored based on the approach of Tukey.

The parameter ClippingFactorclippingFactorclipping_factor (a scaling factor for the standard deviation) controls the amount of damping outliers: The smaller the value chosen for ClippingFactorclippingFactorclipping_factor the more outliers are detected. The detection of outliers is repeated. The parameter Iterationsiterationsiterations specifies the number of iterations. If 'regression'"regression" is set for Algorithmalgorithmalgorithm Iterationsiterationsiterations is ignored.

Attention🔗

Note that the operator fit_surface_second_orderFitSurfaceSecondOrder only considers the given Regionsregionsregions and ignores any previously set domain of the input image Imageimageimage.

Execution information🔗

Execution information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Automatically parallelized on internal data level.

Parameters🔗

Regionsregionsregions (input_object) region(-array) → objectHObjectHRegionHObjectHobject

Regions to be checked.

Imageimageimage (input_object) singlechannelimage → object (byte / uint2 / direction / cyclic / real)

Corresponding gray values.

Algorithmalgorithmalgorithm (input_control) string → (string)HTuple (HString)HTuple (string)strHtuple (char*)

Algorithm for the fitting.

Default: 'regression'"regression"
List of values: 'huber', 'regression', 'tukey'"huber", "regression", "tukey"

Iterationsiterationsiterations (input_control) integer → (integer)HTuple (Hlong)HTuple (int / long)intHtuple (Hlong)

Maximum number of iterations (unused for ‘regression’).

Default: 55
Restriction: Iterations >= 0

ClippingFactorclippingFactorclipping_factor (input_control) real → (real)HTuple (double)HTuple (double)floatHtuple (double)

Clipping factor for the elimination of outliers.

Default: 2.02.0
List of values: 1.0, 1.5, 2.0, 2.5, 3.01.0, 1.5, 2.0, 2.5, 3.0
Restriction: ClippingFactor > 0

Alphaalphaalpha (output_control) real(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Parameter Alpha of the approximating surface.

Betabetabeta (output_control) real(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Parameter Beta of the approximating surface.

Gammagammagamma (output_control) real(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Parameter Gamma of the approximating surface.

Deltadeltadelta (output_control) real(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Parameter Delta of the approximating surface.

Epsilonepsilonepsilon (output_control) real(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Parameter Epsilon of the approximating surface.

Zetazetazeta (output_control) real(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Parameter Zeta of the approximating surface.

Result🔗

The operator fit_surface_second_orderFitSurfaceSecondOrder returns the value 2 (H_MSG_TRUE) if an image with the defined gray values (byte) is entered and the parameters are correct. If necessary an exception is raised.

Combinations with other operators🔗

Combinations

Possible successors

gen_image_surface_second_orderGenImageSurfaceSecondOrder

Module🔗

Foundation