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fit_surface_first_orderfit_surface_first_orderFitSurfaceFirstOrderFitSurfaceFirstOrderfit_surface_first_order (Operator)

Name

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

Signature

fit_surface_first_order(Regions, Image : : Algorithm, Iterations, ClippingFactor : Alpha, Beta, Gamma)

Herror fit_surface_first_order(const Hobject Regions, const Hobject Image, const char* Algorithm, const Hlong Iterations, double ClippingFactor, double* Alpha, double* Beta, double* Gamma)

Herror T_fit_surface_first_order(const Hobject Regions, const Hobject Image, const Htuple Algorithm, const Htuple Iterations, const Htuple ClippingFactor, Htuple* Alpha, Htuple* Beta, Htuple* Gamma)

void FitSurfaceFirstOrder(const HObject& Regions, const HObject& Image, const HTuple& Algorithm, const HTuple& Iterations, const HTuple& ClippingFactor, HTuple* Alpha, HTuple* Beta, HTuple* Gamma)

HTuple HImage::FitSurfaceFirstOrder(const HRegion& Regions, const HString& Algorithm, Hlong Iterations, double ClippingFactor, HTuple* Beta, HTuple* Gamma) const

double HImage::FitSurfaceFirstOrder(const HRegion& Regions, const HString& Algorithm, Hlong Iterations, double ClippingFactor, double* Beta, double* Gamma) const

double HImage::FitSurfaceFirstOrder(const HRegion& Regions, const char* Algorithm, Hlong Iterations, double ClippingFactor, double* Beta, double* Gamma) const

double HImage::FitSurfaceFirstOrder(const HRegion& Regions, const wchar_t* Algorithm, Hlong Iterations, double ClippingFactor, double* Beta, double* Gamma) const   ( Windows only)

HTuple HRegion::FitSurfaceFirstOrder(const HImage& Image, const HString& Algorithm, Hlong Iterations, double ClippingFactor, HTuple* Beta, HTuple* Gamma) const

double HRegion::FitSurfaceFirstOrder(const HImage& Image, const HString& Algorithm, Hlong Iterations, double ClippingFactor, double* Beta, double* Gamma) const

double HRegion::FitSurfaceFirstOrder(const HImage& Image, const char* Algorithm, Hlong Iterations, double ClippingFactor, double* Beta, double* Gamma) const

double HRegion::FitSurfaceFirstOrder(const HImage& Image, const wchar_t* Algorithm, Hlong Iterations, double ClippingFactor, double* Beta, double* Gamma) const   ( Windows only)

static void HOperatorSet.FitSurfaceFirstOrder(HObject regions, HObject image, HTuple algorithm, HTuple iterations, HTuple clippingFactor, out HTuple alpha, out HTuple beta, out HTuple gamma)

HTuple HImage.FitSurfaceFirstOrder(HRegion regions, string algorithm, int iterations, double clippingFactor, out HTuple beta, out HTuple gamma)

double HImage.FitSurfaceFirstOrder(HRegion regions, string algorithm, int iterations, double clippingFactor, out double beta, out double gamma)

HTuple HRegion.FitSurfaceFirstOrder(HImage image, string algorithm, int iterations, double clippingFactor, out HTuple beta, out HTuple gamma)

double HRegion.FitSurfaceFirstOrder(HImage image, string algorithm, int iterations, double clippingFactor, out double beta, out double gamma)

def fit_surface_first_order(regions: HObject, image: HObject, algorithm: str, iterations: int, clipping_factor: float) -> Tuple[Sequence[float], Sequence[float], Sequence[float]]

def fit_surface_first_order_s(regions: HObject, image: HObject, algorithm: str, iterations: int, clipping_factor: float) -> Tuple[float, float, float]

Description

The operator fit_surface_first_orderfit_surface_first_orderFitSurfaceFirstOrderFitSurfaceFirstOrderfit_surface_first_order 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:

and are the center coordinates of intersection of the input region with the full image domain. By the minimization process the parameters from AlphaAlphaAlphaalphaalpha to GammaGammaGammagammagamma is calculated.

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

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

Attention

Note that the operator fit_surface_first_orderfit_surface_first_orderFitSurfaceFirstOrderFitSurfaceFirstOrderfit_surface_first_order only considers the given RegionsRegionsRegionsregionsregions and ignores any previously set domain of the input image ImageImageImageimageimage.

Execution Information

Parameters

RegionsRegionsRegionsregionsregions (input_object)  region(-array) → objectHRegionHObjectHObjectHobject

Regions to be checked.

ImageImageImageimageimage (input_object)  singlechannelimage → objectHImageHObjectHObjectHobject (byte / uint2 / direction / cyclic / real)

Corresponding gray values.

AlgorithmAlgorithmAlgorithmalgorithmalgorithm (input_control)  string → HTuplestrHTupleHtuple (string) (string) (HString) (char*)

Algorithm for the fitting.

Default: 'regression' "regression" "regression" "regression" "regression"

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

IterationsIterationsIterationsiterationsiterations (input_control)  integer → HTupleintHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Maximum number of iterations (unused for 'regression').

Default: 5

Restriction: Iterations >= 0

ClippingFactorClippingFactorClippingFactorclippingFactorclipping_factor (input_control)  real → HTuplefloatHTupleHtuple (real) (double) (double) (double)

Clipping factor for the elimination of outliers.

Default: 2.0

List of values: 1.0, 1.5, 2.0, 2.5, 3.0

Restriction: ClippingFactor > 0

AlphaAlphaAlphaalphaalpha (output_control)  real(-array) → HTupleSequence[float]HTupleHtuple (real) (double) (double) (double)

Parameter Alpha of the approximating surface.

BetaBetaBetabetabeta (output_control)  real(-array) → HTupleSequence[float]HTupleHtuple (real) (double) (double) (double)

Parameter Beta of the approximating surface.

GammaGammaGammagammagamma (output_control)  real(-array) → HTupleSequence[float]HTupleHtuple (real) (double) (double) (double)

Parameter Gamma of the approximating surface.

Result

The operator fit_surface_first_orderfit_surface_first_orderFitSurfaceFirstOrderFitSurfaceFirstOrderfit_surface_first_order returns the value 2 ( H_MSG_TRUE) if an image with the defined gray values ('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_orderGenImageSurfaceFirstOrderGenImageSurfaceFirstOrdergen_image_surface_first_order

See also

moments_gray_planemoments_gray_planeMomentsGrayPlaneMomentsGrayPlanemoments_gray_plane, fit_surface_second_orderfit_surface_second_orderFitSurfaceSecondOrderFitSurfaceSecondOrderfit_surface_second_order

Module

Foundation

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