smallest_circle — Smallest surrounding circle of a region.
smallest_circle determines the smallest
surrounding circle of a region, i.e., the circle with the smallest
area of all circles containing the region. For this circle the
Column) and the radius
Radius) are calculated. The operator is applied when,
for example, the location and size of circular objects (e.g.,
coins) which, however, are not homogeneous inside or have broken
edges due to bad segmentation, has to be determined. The output of
the operator is selected in such a way that it can be used as input
for the operators
In the documentation of this chapter (Regions / Features), you can find an image illustrating regions with varying outer and inner radii.
If several regions are passed in
tuples are returned as output parameter. In case of empty region
all parameters have the value 0.0 if no other behavior was set (see
Internally, the calculation is based on the center coordinates of
the region pixels. To take into account that pixels are not just
infinitely small points but have a certain area, the calculated
radius is enlarged by 0.5 before it is returned in
Radius. This, in most cases, gives acceptable results.
However, in the worst case (pixel diagonal) this enlargement is not
sufficient. If one wants to ensure that the border of the input
region completely lies within the circle, one had to enlarge the
radius by instead of 0.5. Consequently,
the value returned in
Radius must be corrected by
. However, this would also be only
an upper bound, i.e., the circle with the corrected radius would be
slightly too big in most cases.
Regions to be examined.
Line index of the center.
Column index of the center.
Radius of the surrounding circle.
Radius >= 0
read_image(Image,'fabrik') regiongrowing(Image,Regions,5,5,6,100) select_shape(Regions,SelectedRegions,'area','and',100,2000) smallest_circle(SelectedRegions,Row,Column,Radius) gen_circle(Circles,Row,Column,Radius) dev_display (Circles)
If F is the area of the region, then the mean runtime complexity is O(sqrt(F).
smallest_circle returns the value TRUE
if the input is not empty. The behavior in case of empty input (no input regions available)
is set via the operator
The behavior in case of empty region (the region is the empty set) is set via
If necessary an exception is raised.