fit_surface_second_order fit_surface_second_order FitSurfaceSecondOrder FitSurfaceSecondOrder fit_surface_second_order (Operator)
Name
fit_surface_second_order fit_surface_second_order FitSurfaceSecondOrder FitSurfaceSecondOrder fit_surface_second_order
— Calculate gray value moments and approximation by a second order surface.
Signature
Herror fit_surface_second_order (const Hobject Regions , const Hobject Image , const char* Algorithm , const Hlong Iterations , double ClippingFactor , double* Alpha , double* Beta , double* Gamma , double* Delta , double* Epsilon , double* Zeta )
Herror T_fit_surface_second_order (const Hobject Regions , const Hobject Image , const Htuple Algorithm , const Htuple Iterations , const Htuple ClippingFactor , Htuple* Alpha , Htuple* Beta , Htuple* Gamma , Htuple* Delta , Htuple* Epsilon , Htuple* Zeta )
void FitSurfaceSecondOrder (const HObject& Regions , const HObject& Image , const HTuple& Algorithm , const HTuple& Iterations , const HTuple& ClippingFactor , HTuple* Alpha , HTuple* Beta , HTuple* Gamma , HTuple* Delta , HTuple* Epsilon , HTuple* Zeta )
HTuple HImage ::FitSurfaceSecondOrder (const HRegion& Regions , const HString& Algorithm , Hlong Iterations , double ClippingFactor , HTuple* Beta , HTuple* Gamma , HTuple* Delta , HTuple* Epsilon , HTuple* Zeta ) const
double HImage ::FitSurfaceSecondOrder (const HRegion& Regions , const HString& Algorithm , Hlong Iterations , double ClippingFactor , double* Beta , double* Gamma , double* Delta , double* Epsilon , double* Zeta ) const
double HImage ::FitSurfaceSecondOrder (const HRegion& Regions , const char* Algorithm , Hlong Iterations , double ClippingFactor , double* Beta , double* Gamma , double* Delta , double* Epsilon , double* Zeta ) const
double HImage ::FitSurfaceSecondOrder (const HRegion& Regions , const wchar_t* Algorithm , Hlong Iterations , double ClippingFactor , double* Beta , double* Gamma , double* Delta , double* Epsilon , double* Zeta ) const
(Windows only)
HTuple HRegion ::FitSurfaceSecondOrder (const HImage& Image , const HString& Algorithm , Hlong Iterations , double ClippingFactor , HTuple* Beta , HTuple* Gamma , HTuple* Delta , HTuple* Epsilon , HTuple* Zeta ) const
double HRegion ::FitSurfaceSecondOrder (const HImage& Image , const HString& Algorithm , Hlong Iterations , double ClippingFactor , double* Beta , double* Gamma , double* Delta , double* Epsilon , double* Zeta ) const
double HRegion ::FitSurfaceSecondOrder (const HImage& Image , const char* Algorithm , Hlong Iterations , double ClippingFactor , double* Beta , double* Gamma , double* Delta , double* Epsilon , double* Zeta ) const
double HRegion ::FitSurfaceSecondOrder (const HImage& Image , const wchar_t* Algorithm , Hlong Iterations , double ClippingFactor , double* Beta , double* Gamma , double* Delta , double* Epsilon , double* Zeta ) const
(Windows only)
static void HOperatorSet .FitSurfaceSecondOrder (HObject regions , HObject image , HTuple algorithm , HTuple iterations , HTuple clippingFactor , out HTuple alpha , out HTuple beta , out HTuple gamma , out HTuple delta , out HTuple epsilon , out HTuple zeta )
HTuple HImage .FitSurfaceSecondOrder (HRegion regions , string algorithm , int iterations , double clippingFactor , out HTuple beta , out HTuple gamma , out HTuple delta , out HTuple epsilon , out HTuple zeta )
double HImage .FitSurfaceSecondOrder (HRegion regions , string algorithm , int iterations , double clippingFactor , out double beta , out double gamma , out double delta , out double epsilon , out double zeta )
HTuple HRegion .FitSurfaceSecondOrder (HImage image , string algorithm , int iterations , double clippingFactor , out HTuple beta , out HTuple gamma , out HTuple delta , out HTuple epsilon , out HTuple zeta )
double HRegion .FitSurfaceSecondOrder (HImage image , string algorithm , int iterations , double clippingFactor , out double beta , out double gamma , out double delta , out double epsilon , out double zeta )
def fit_surface_second_order (regions : HObject, image : HObject, algorithm : str, iterations : int, clipping_factor : float) -> Tuple[Sequence[float], Sequence[float], Sequence[float], Sequence[float], Sequence[float], Sequence[float]]
def fit_surface_second_order_s (regions : HObject, image : HObject, algorithm : str, iterations : int, clipping_factor : float) -> Tuple[float, float, float, float, float, float]
Description
The operator fit_surface_second_order fit_surface_second_order FitSurfaceSecondOrder FitSurfaceSecondOrder FitSurfaceSecondOrder fit_surface_second_order
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:
and
are the center
coordinates of the intersection of the input region with the full image
domain.
By the minimization process the parameters from Alpha Alpha Alpha Alpha alpha alpha
to
Zeta Zeta Zeta Zeta zeta zeta
is calculated.
The algorithm used for the fitting can be selected via
Algorithm Algorithm Algorithm Algorithm algorithm algorithm
:
'regression' "regression" "regression" "regression" "regression" "regression"
Standard 'least squares' fitting.
'huber' "huber" "huber" "huber" "huber" "huber"
Weighted 'least squares' fitting, where the impact of outliers
is decreased based on the approach of Huber.
'tukey' "tukey" "tukey" "tukey" "tukey" "tukey"
Weighted 'least squares' fitting, where outliers
are ignored based on the approach of Tukey.
The parameter ClippingFactor ClippingFactor ClippingFactor ClippingFactor clippingFactor clipping_factor
(a scaling factor for the standard
deviation) controls the amount of damping outliers: The smaller the
value chosen for ClippingFactor ClippingFactor ClippingFactor ClippingFactor clippingFactor clipping_factor
the more outliers are
detected. The detection of outliers is repeated. The parameter
Iterations Iterations Iterations Iterations iterations iterations
specifies the number of iterations. If
'regression' "regression" "regression" "regression" "regression" "regression" is set for Algorithm Algorithm Algorithm Algorithm algorithm algorithm
Iterations Iterations Iterations Iterations iterations iterations
is ignored.
Attention
Note that the operator fit_surface_second_order fit_surface_second_order FitSurfaceSecondOrder FitSurfaceSecondOrder FitSurfaceSecondOrder fit_surface_second_order
only considers
the given Regions Regions Regions Regions regions regions
and ignores any previously set domain
of the input image Image Image Image Image image image
.
Execution Information
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
Regions Regions Regions Regions regions regions
(input_object) region(-array) →
object HRegion HObject HRegion Hobject
Regions to be checked.
Image Image Image Image image image
(input_object) singlechannelimage →
object HImage HObject HImage Hobject (byte / uint2 / direction / cyclic / real)
Corresponding gray values.
Algorithm Algorithm Algorithm Algorithm algorithm algorithm
(input_control) string →
HTuple str HTuple Htuple (string) (string ) (HString ) (char* )
Algorithm for the fitting.
Default value:
'regression'
"regression"
"regression"
"regression"
"regression"
"regression"
List of values: 'huber' "huber" "huber" "huber" "huber" "huber" , 'regression' "regression" "regression" "regression" "regression" "regression" , 'tukey' "tukey" "tukey" "tukey" "tukey" "tukey"
Iterations Iterations Iterations Iterations iterations iterations
(input_control) integer →
HTuple int HTuple Htuple (integer) (int / long) (Hlong ) (Hlong )
Maximum number of iterations (unused for 'regression').
Default value: 5
Restriction: Iterations >= 0
ClippingFactor ClippingFactor ClippingFactor ClippingFactor clippingFactor clipping_factor
(input_control) real →
HTuple float HTuple Htuple (real) (double ) (double ) (double )
Clipping factor for the elimination of outliers.
Default value: 2.0
List of values: 1.0, 1.5, 2.0, 2.5, 3.0
Restriction: ClippingFactor > 0
Alpha Alpha Alpha Alpha alpha alpha
(output_control) real(-array) →
HTuple Sequence[float] HTuple Htuple (real) (double ) (double ) (double )
Parameter Alpha of the approximating surface.
Beta Beta Beta Beta beta beta
(output_control) real(-array) →
HTuple Sequence[float] HTuple Htuple (real) (double ) (double ) (double )
Parameter Beta of the approximating surface.
Gamma Gamma Gamma Gamma gamma gamma
(output_control) real(-array) →
HTuple Sequence[float] HTuple Htuple (real) (double ) (double ) (double )
Parameter Gamma of the approximating surface.
Delta Delta Delta Delta delta delta
(output_control) real(-array) →
HTuple Sequence[float] HTuple Htuple (real) (double ) (double ) (double )
Parameter Delta of the approximating surface.
Epsilon Epsilon Epsilon Epsilon epsilon epsilon
(output_control) real(-array) →
HTuple Sequence[float] HTuple Htuple (real) (double ) (double ) (double )
Parameter Epsilon of the approximating surface.
Zeta Zeta Zeta Zeta zeta zeta
(output_control) real(-array) →
HTuple Sequence[float] HTuple Htuple (real) (double ) (double ) (double )
Parameter Zeta of the approximating surface.
Result
The operator fit_surface_second_order fit_surface_second_order FitSurfaceSecondOrder FitSurfaceSecondOrder FitSurfaceSecondOrder fit_surface_second_order
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.
Possible Successors
gen_image_surface_second_order gen_image_surface_second_order GenImageSurfaceSecondOrder GenImageSurfaceSecondOrder GenImageSurfaceSecondOrder gen_image_surface_second_order
See also
moments_gray_plane moments_gray_plane MomentsGrayPlane MomentsGrayPlane MomentsGrayPlane moments_gray_plane
,
fit_surface_first_order fit_surface_first_order FitSurfaceFirstOrder FitSurfaceFirstOrder FitSurfaceFirstOrder fit_surface_first_order
Module
Foundation