fit_line_contour_xld (Operator)

Name

fit_line_contour_xld — Approximation of XLD contours by line segments.

Synopsis

fit_line_contour_xld(Contours : : Algorithm, MaxNumPoints, ClippingEndPoints, Iterations, ClippingFactor : RowBegin, ColBegin, RowEnd, ColEnd, Nr, Nc, Dist)

Description

fit_line_contour_xld approximates the XLD contours Contours by line segments. It does not perform a segmentation of the input contours. Thus, one has to make sure that each contour corresponds to one and only one line segment. The operator returns for each contour the start point (RowBegin, ColBegin), the end point (RowEnd, ColEnd), and the regression line to the contour given by the normal vector (Nr, Nc) of the line and its distance Dist from the origin, i.e., the line equation is given by r *Nr + c * Nc - Dist = 0 .

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

'regression':
Standard 'least squares' line fitting.

'huber':
Weighted 'least squares' line fitting, where the impact of outliers
is decreased based on the approach of Huber (see below).

'tukey':
Weighted 'least squares' line fitting, where the impact of outliers
is decreased based on the approach of Tukey (see below).

'drop':
Weighted 'least squares' line fitting, where outliers are
eliminated.

'gauss':
Weighted 'least squares' line fitting, where the impact of outliers
is decreased based on the mean value and the standard deviation of
the distances of all contour points from the approximating line.

For 'huber', 'tukey', and 'drop' a robust error statistics is used to estimate the standard deviation of the distances from the contour points without outliers from the approximating line. 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. Note that in the approach of Tukey ('tukey'), the outliers are removed before performing the approximation and all other points are weighted, whereas in the approach of Huber ('huber'), the outliers still have a small influence. Particularly, for outliers the optimization is influenced linearly and for points with a smaller distance it is influenced quadratically. In practice, the approach of Tukey is recommended.

To reduce the computational load, the fitting of lines can be restricted to a subset of the contour points: If a value other than -1 is assigned to MaxNumPoints, only up to MaxNumPoints points - uniformly distributed over the contour - are used.

The start point and the end point of a line segment is determined by projecting the first and the last point of the corresponding contour to the approximating line. Due to artefacts in the pre-processing the start and end points of a contour might be faulty. Therefore, it is possible to exclude ClippingEndPoints points at the beginning and at the end of a contour from the line fitting. However, they are still used for the determination of the start point and the end point of the line segment.

The minimun necessary number of contour points for fitting a line is two. Therefore, it is required that the number of contour points is at least 2 + 2*ClippingEndPoints .

Parameters

Contours (input_object)	xld_cont(-array) → object
Input contours.

Algorithm (input_control)	string → (string)
Algorithm for the fitting of lines.
Default value: 'tukey'
List of values: 'regression', 'huber', 'tukey', 'gauss', 'drop'

MaxNumPoints (input_control)	integer → (integer)
Maximum number of contour points used for the computation (-1 for all points).
Default value: -1
Restriction: MaxNumPoints >= 2

ClippingEndPoints (input_control)	integer → (integer)
Number of points at the beginning and at the end of the contours to be ignored for the fitting.
Default value: 0
Restriction: ClippingEndPoints >= 0

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 (typical: 1.0 for 'huber' and 'drop' and 2.0 for 'tukey').
Default value: 2.0
List of values: 1.0, 1.5, 2.0, 2.5, 3.0
Restriction: ClippingFactor > 0

RowBegin (output_control)	line.begin.y(-array) → (real)
Row coordinates of the starting points of the line segments.

ColBegin (output_control)	line.begin.x(-array) → (real)
Column coordinates of the starting points of the line segments.

RowEnd (output_control)	line.end.y(-array) → (real)
Row coordinates of the end points of the line segments.

ColEnd (output_control)	line.end.x(-array) → (real)
Column coordinates of the end points of the line segments.

Nr (output_control)	number(-array) → (real)
Line parameter: Row coordinate of the normal vector

Nc (output_control)	number(-array) → (real)
Line parameter: Column coordinate of the normal vector

Dist (output_control)	number(-array) → (real)
Line parameter: Distance of the line from the origin

Example

read_image (Image, 'mreut')
edges_sub_pix (Image, Edges, 'lanser2', 0.5, 20, 40)
gen_polygons_xld (Edges, Polygons, 'ramer', 2)
split_contours_xld (Polygons, Contours, 'polygon', 1, 5)
fit_line_contour_xld (Contours, 'regression', -1, 0, 5, 2, RowBegin, \
                      ColBegin, RowEnd, ColEnd, Nr, Nc)

Result

fit_line_contour_xld returns 2 (H_MSG_TRUE) if all parameter values are correct, and line segments could be fitted to the input contours. If the input is empty the behaviour can be set via set_system('no_object_result',<Result>). If necessary, an exception is raised. If the parameter ClippingFactor is chosen too small, i.e., all points are classified as outliers, the error 3264 is raised.

Parallelization Information

fit_line_contour_xld is reentrant and processed without parallelization.

Possible Predecessors

gen_contours_skeleton_xld, lines_gauss, lines_facet, edges_sub_pix, smooth_contours_xld

Possible Successors

disp_line, select_lines, line_orientation

See also

regress_contours_xld, get_regress_params_xld

Module

Foundation