REGULAR VIRTUAL COORDINATE SYSTEM OF COORDINATES OVER THE FIELD OF MOVING VISUAL LANDMARKS

Abstract

The problem objects tracing in respect to large sample of visual landmarks whose position, shape, and optical properties change over time is considered. A Regular Virtual Coordinate System (RVCS) based on visual landmarks triangulation is proposed. RVCS is created using a linear iterative algorithm to relax initial triangulation to the quasi equilibrium state – shagreen, in which the grid nodes are located close to centers of their surroundings. It is shown that shagreen has a dense boundary with strongly elongated cells and the central core with almost regular triangles. We proposed to use the shagreen core as a virtual barycentric mesh because its geometry is regular and resistant to random displacements of visual landmarks, while correctly mirror affinity transformations. The use of RVCS allows to minimize the amount of information for representing the object trajectory while maintaining the accuracy of its localization close to the maximum achievable when using all available landmarks. It is shown that due to its global instability of the shagreen with random structure the triangulations with less then 100 vertices should be relaxed by no more then T = 10 – 20 simple iterations. This process can be represented by single linear operator which in special case T = 2t is created by t matrix multiplications. In addition, shagreen indicates the smooth trend for rough landscape, which increases the reliability of the estimation of local normals.