fit_surface_first_orderfit_surface_first_orderFitSurfaceFirstOrderfit_surface_first_orderFitSurfaceFirstOrderFitSurfaceFirstOrder (Operator)

Name

fit_surface_first_orderfit_surface_first_orderFitSurfaceFirstOrderfit_surface_first_orderFitSurfaceFirstOrderFitSurfaceFirstOrder — Calculate gray value moments and approximation by a first order surface (plane).

Signature

Description

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

ImageImageImageImageImageimage(r,c) =  AlphaAlphaAlphaAlphaAlphaalpha(r - r_center) +
                        BetaBetaBetaBetaBetabeta(c - c_center) +
                        GammaGammaGammaGammaGammagamma

r_center and c_center are the center coordinates of intersection of the input region with the full image domain. By the minimization process the parameters from AlphaAlphaAlphaAlphaAlphaalpha to GammaGammaGammaGammaGammagamma is calculated.

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

'regression'

Standard 'least squares' line fitting.

'huber'

Weighted 'least squares' fitting, where the impact of outliers is decreased based on the approach of Huber.

'tukey'

Weighted 'least squares' fitting, where outliers are ignored based on the approach of Tukey.

The parameter ClippingFactorClippingFactorClippingFactorClippingFactorClippingFactorclippingFactor (a scaling factor for the standard deviation) controls the amount of damping outliers: The smaller the value chosen for ClippingFactorClippingFactorClippingFactorClippingFactorClippingFactorclippingFactor the more outliers are detected. The detection of outliers is repeated. The parameter IterationsIterationsIterationsIterationsIterationsiterations specifies the number of iterations. In the modus 'regression' this value is ignored.

Attention

Note that the operator fit_surface_first_orderfit_surface_first_orderFitSurfaceFirstOrderfit_surface_first_orderFitSurfaceFirstOrderFitSurfaceFirstOrder only considers the given RegionsRegionsRegionsRegionsRegionsregions and ignores any previously set domain of the input image ImageImageImageImageImageimage.

Parallelization

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

Parameters

Result

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

Possible Successors

gen_image_surface_first_ordergen_image_surface_first_orderGenImageSurfaceFirstOrdergen_image_surface_first_orderGenImageSurfaceFirstOrderGenImageSurfaceFirstOrder

See also

moments_gray_planemoments_gray_planeMomentsGrayPlanemoments_gray_planeMomentsGrayPlaneMomentsGrayPlane, fit_surface_second_orderfit_surface_second_orderFitSurfaceSecondOrderfit_surface_second_orderFitSurfaceSecondOrderFitSurfaceSecondOrder

Module

Foundation