elliptic_axis_xld — Parameters of the equivalent ellipse of contours or polygons.
elliptic_axis_xld calculates the radii and the
orientations of the ellipses having the same orientation and the same
aspect ratio as the input contours or polygons.
The length of the major radius
Ra and the minor radius
Rb as well as the
orientation of the main axis with regard to the horizontal
Phi) are determined. The angle is indicated in radians.
It is assumed that the contours or polygons are closed. If this is
not the case
elliptic_axis_xld will artificially close the
contours or polygons.
If the moments , and are
normalized and passed to the area (see
Rb are calculated as:
Phi is defined by:
It should be noted that
elliptic_axis_xld only returns
useful results if the contour or polygon encloses a region in the
plane. In particular, the contour or polygon must not intersect
itself. This is particularly important if open contours or polygons
are passed because they are closed automatically, which can produce
a self-intersection. To test whether the contours or polygons
test_self_intersection_xld can be
used. If the contour or polygon intersects itself, useful values
for the ellipse parameters can be calculated with
If more than one contour or polygon is passed, the results are stored
in tuples in the same order as the respective contours or polygons in
Contours or polygons to be examined.
Ra >= 0.0
Rb >= 0.0 && Rb <= Ra
Angle between the major axis and the x axis (radians).
- pi / 2 < Phi && Phi <= pi / 2
If N is the number of contour or polygon points, the runtime complexity is O(N).
elliptic_axis_xld returns TRUE if the input is not empty.
If the input is empty the behavior can be set via
necessary, an exception is raised.
R. Haralick, L. Shapiro “Computer and Robot Vision” Addison-Wesley, 1992, pp. 73-75