fit_surface_second

fit_surface_second_order ( Regions, Image : : Algorithm, Iterations, ClippingFactor : Alpha, Beta, Gamma, Delta, Epsilon, Zeta )

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

The operator 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:

Image(r,c) =  Alpha(r-r_center)**2 +
                        Beta(c-c_center)**2 + 
                        Gamma(r- r_center)*(c-c_center) +
                        Delta(r- r_center) + 
                        Epsilon(c- c_center) +  
                        Zeta

r_center and c_center are the coordinates of the center of the input region. By the minimization process the parameters from Alpha to Zeta is calculated.

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

'regression':
Standard 'least squares' 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 the impact of outliers
is decreased based on the approach of Tukey.

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

Parameters

`Regions` (input_object)	region(-array) `->` object
Regions to be checked.

`Image` (input_object)	image `->` object : byte / uint2 / direction / cyclic / real
Corresponding gray values.

`Algorithm` (input_control)	string `->` string
Algorithm for the fitting.
Default value: 'regression'
List of values: 'regression', 'tukey', 'huber'

`Iterations` (input_control)	integer `->` integer
Maximum number of iterations (unused for 'regression').
Default value: 5
Restriction: `Iterations >= 0`

`ClippingFactor` (input_control)	real `->` real
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` (output_control)	real(-array) `->` real
Parameter Alpha of the approximating surface.

`Beta` (output_control)	real(-array) `->` real
Parameter Beta of the approximating surface.

`Gamma` (output_control)	real(-array) `->` real
Parameter Gamma of the approximating surface.

`Delta` (output_control)	real(-array) `->` real
Parameter Deltaa of the approximating surface.

`Epsilon` (output_control)	real(-array) `->` real
Parameter Epsilon of the approximating surface.

`Zeta` (output_control)	real(-array) `->` real
Parameter Zeta of the approximating surface.

Result

The operator 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 handling is raised.

Parallelization Information

fit_surface_second_order is reentrant and automatically parallelized (on tuple level).

Module

Image filters