• 2021 (Vol.35)

Projectively invariant description of non-planar smooth figures. 2. On recognition of ovaloids of revolution

© 2018 P. P. Nikolaev

Institute for Information Transmission Problems 127051 Moscow, B. Karetny per., 19, Russia

Received 04 May 2018

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 also discussed.

Key words: contour of ovaloid of revolution, affine invariant, body registration angle, symmetry plane, symmetry axis, affine and central plane projections, descriptor

DOI: 10.1134/S023500921804008X

Cite: Nikolaev P. P. Proektivno invariantnoe opisanie neploskikh gladkikh figur. 2. o racpoznavanii ovaloidov vrashcheniya [Projectively invariant description of non-planar smooth figures. 2. on recognition of ovaloids of revolution]. Sensornye sistemy [Sensory systems]. 2018. V. 32(4). P. 342-355 (in Russian). doi: 10.1134/S023500921804008X

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