For scenes where the input object is a composition of a general oval in combination with a linear element (LE, that is,
a point, P, or a line, L) of the plane incident to it, in an arbitrary mutual arrangement of them (an external LE, an
internal LE, or an LE belonging to the contour of the oval), on the material of model numerical realizations, procedural
approaches for the problem of projectively-invariant description of such a composition are considered. The proposed
processing algorithms use previously obtained theoretical assertions (theorems). For an oval with a specific internal
point, intP, these theorems guarantee the presence of a triad of external projectively-invariant elliptic points (ET):
E1, E2, and E3. For an oval combined with a line, extL (external position), they guarantee the presence of two pairs of
invariant points generating a pair of stable interior points, C1 and C2. It is shown how to convert an arbitrarily
organized composition of the “oval + LE” type to a composition of the “oval + intP + extL + T-polar” type, suitable for
calculating its projectively-invariant map, which is not solely based on a fixed set of invariant points of the contour,
but represents an integral description of the original composition (in the form of a wurf map). We implement this
universal algorithmic approach as a result of introducing the developed criteria for the deterministic selection of the
ET pair specifying the extL and the only intP from the C1-C2 pair - for specifying the external invariant T-polar curve.
Key words:
linear element of a plane, elliptic points, wurf, projectively-invariant mapping, criteria for choosing basis points
DOI: 10.1134/S0235009219010104
Cite:
Nikolaev P. P.
Raspoznavanie proektivno preobrazovannykh ploskikh figur. xii. o novykh metodakh proektivno invariantnogo opisaniya ovalov v kompozitsii s lineinym elementom ploskosti
[Recognition of projectively transformed planar figures xii. on new methods for projectively-invariant description of ovals in composition with a linear element of a plane].
Sensornye sistemy [Sensory systems].
2019.
V. 33(1).
P. 15-29 (in Russian). doi: 10.1134/S0235009219010104
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