On the basis of numerical simulations performed, we state and discuss approaches and procedures for projectively-
invariant description of ovals, which use our previously developed theory and technique of ht-contours in the problem of
nding eight invariant points on a gure contour, given that the curve shows either axial or radial implicit symmetry. It
is demonstrated that a similar octet of stable contour points can be obtained by introducing subsidiary structures of
ht-polar lines and notes of the developed theory, including those for curves showing no symmetry features and being de
ned along with an a priori selected point on the plane of the gure (either inside or outside of its contour). The
detected octet, {Ci}, allows computing a compact descriptor of the oval shape on the wurf plane. This descriptor can be
used for low-costidenti cation of a curve with respect to the projective equivalence class. Using the examples of ovals
of two types of symmetry, we consider some new iterative schemes for detecting their basic elements (the positions of
the centers or the axes), the adequate localization of which ensures computation of {Ci}. The key stages of curve
recognition procedures (successively engaged schemes of analysis, search, and representation) do not exceed the o(n)
threshold of the algorithm complexity, which shows high potentials of their use in systems of automatic analysis of
object geometry. We outline the aspects of the suggested theory, further development of which might turn the developed
heuristic methods into universal schemes for description of smooth planar curves.

*Key words:*
projective invariant, wurf mapping, symmetry elements, ht-contour, descriptor octet {Ci}, theorems on the number and the
properties of invariant points of an oval

*Cite:*
Nikolayev P. P..
Raspoznavanie proektivno preobrazovannykh ploskikh figur. xi. novye metody poiska proektivno invariantnykh tochek ovala
[Recognition of projectively transformed planar gures. xi. a new methods for detecting projectively-invariant points of an oval].
*Sensornye sistemy* [Sensory systems].
2017.
V. 31(4).
P. 343-362
(in Russian).

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