# dist_ellipse_contour_xld (Operator)

## Name

dist_ellipse_contour_xld — Compute the distance of contours to an ellipse.

## Description

dist_ellipse_contour_xld determines the distance between the contours in Contours and an ellipse specified by the center (Row, Column), the orientation of the main axis Phi, the length of the larger half axis Radius1, and the length of the smaller half axis Radius2. Different measures for the distance of a contour point to the ellipse are available (Mode):

'geometric'

The underlying distance measure is the geometric distance between a point on the contour and the ellipse. This measure is also called orthogonal or Euclidean distance.

'algebraic'

The distance is measured by the algebraic distance , where the parameters a - f describing the ellipse are normalized in order to obtain Radius2 as distance of the center of the ellipse. This measure shows a high curvature bias: Near points of high curvature on the ellipse (like the poles on the main axis) the distance is smaller than near points with low curvature.

'focpoints'

The distance is measured by the deviation , where are the focal points and a corresponds to Radius1. This measure shows a low curvature bias: Near points of high curvature on the ellipse (like the poles on the main axis) the distance is larger than near points with low curvature.

'bisec'

The distance is measured by the distance between X and the intersection of the angular bisector of the two lines through X and the focal points with the ellipse. This is a good approximation of the orthogonal distance from X to the ellipse. The accuracy of the approximation depends on both the aspect ratio of the ellipse and the distance.

The operator returns the minimum absolute distance MinDist, the maximum absolute distance MaxDist, the average absolute distance AvgDist, and the standard deviation of the absolute distances SigmaDist of all contour points.

To reduce the computational load, the computation of the distances 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. Due to artifacts 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 computation.

## Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Processed without parallelization.

## Parameters

Contours (input_object)  xld_cont(-array) object

Input contours.

Mode (input_control)  string (string)

Method for the determination of the distances.

Default: 'geometric'

List of values: 'algebraic', 'bisec', 'focpoints', 'geometric'

MaxNumPoints (input_control)  integer (integer)

Maximum number of contour points used for the computation (-1 for all points).

Default: -1

Restriction: MaxNumPoints >= 3

ClippingEndPoints (input_control)  integer (integer)

Number of points at the beginning and the end of the contours to be ignored for the computation of distances.

Default: 0

Restriction: ClippingEndPoints >= 0

Row (input_control)  ellipse.center.y (real)

Row coordinate of the center of the ellipse.

Column (input_control)  ellipse.center.x (real)

Column coordinate of the center of the ellipse.

Orientation of the main axis in radian.

Restriction: Phi >= 0 && Phi <= 6.283185307

Length of the larger half axis.

Length of the smaller half axis.

MinDist (output_control)  real(-array) (real)

Minimum distance.

MaxDist (output_control)  real(-array) (real)

Maximum distance.

AvgDist (output_control)  real(-array) (real)

Mean distance.

Standard deviation of the distance.

## Example (HDevelop)

find_caltab (Image, CalPlate, 'caltab_big.descr', 3, 112, 5)
reduce_domain (Image, CalPlate, ImageReduced)
edges_sub_pix (ImageReduced, Edges, 'lanser2', 0.5, 20, 40)
select_contours_xld (Edges, EdgesClosed, 'closed', 0, 2.0, 0, 0)
select_contours_xld (EdgesClosed, EdgesMarks, 'contour_length', 20, 100, \
0, 0)
fit_ellipse_contour_xld (EdgesMarks, 'fitzgibbon', -1, 2, 0, 200, 3, 2.0, \
EndPhi, PointOrder)
for i := 0 to |Row|-1 by 1
select_obj (EdgesMarks, ObjectSelected, i+1)
dist_ellipse_contour_xld (ObjectSelected, 'bisec', -1, 0, Row[i], \