We consider the formulation of the problem of affine-invariant recognition of axisymmetric smoothly convex bodies
obtained by rotating an oval, O, of explicit axial symmetry and registered in orthographic projection at different
angles to the axis of rotation, A, of the body in the scene. Using model numerical examples for six ovals-generators O
(having one, two, and three axes), the results of detecting the a axis are shown. The detection is based on the
developed procedure Rot, which gives an estimate of the position of a on the sensory projection of the body. In the
space of the scene, the occluding contour, c, of the body, in its general form, is a nonplanar oval curve considered as
the body boundary on the planar optical projection. From the detected input projection with the axis a, whose position
is calculated on the basis of the Rot algorithm, four parameters being affine invariants of the body for a given viewing
angle (the angle between the optical axis of the camera and the axis A) are estimated. The descriptor (a special curve
in the 4D parameter space) is interpolated by a sequence of 11 viewing angles in the reference stage for each body (the
set of their forms is defined), which allows us to identify the body for an arbitrary viewing angle (using a single
projection). The peculiarities of the Rot scheme, versions of its implementation, and the idea of constructing a more
complex descriptor suitable for identifying the body in the projective way of registration (a camera obscura model) are
contour of ovaloid of revolution, affine invariant, body registration angle, symmetry plane, symmetry axis, affine and
central plane projections, descriptor
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