A Method of Describing Objects in a Scene of a Robot Vision System by Means of Fuzzy Delaunay Triangulation Using an Adaptive Mesh
Abstract
The paper considers a method for representing a set of information objects (scenes) in the field of view of an intelligent robot, based on the fuzzy Delaunay triangulation due to locally regular refinement of the original (coarse) triangular mesh using multiple half-divisions of the sides of the original triangles and building on its basis four congruent triangles with four times smaller area. This approach to refinement allows you to build regular, grids and the corresponding triangulation of these midpoints, consisting of both equilateral and arbitrary triangles, depending on how the individual information objects are distributed in the space of the study area. The arising problem of refining and rearranging border triangles is simplified due to the fact that the process of splitting them is carried out by analogy with adjacent initial triangles. The described method can be modified in order to grind an already finished mesh as a whole or its individual zones. In this case, the stage of constructing a rough triangulation is skipped and a half division is carried out on the material of the already finished mesh. Thus, there is no need to check the Delaunay condition at each step. With such a refinement, only a local rearrangement of the cells can occur. The advantage of this approach is that there is no need to regenerate the entire mesh. Note also that the considered procedure for bringing the triangulation in accordance with the Delaunay condition can significantly reduce the computer time spent on rebuilding the mesh, since the condition is not checked for all mesh elements. In the process of describing the context of the image under study, the centers of gravity of flat information objects are determined, which act as the initial ones for a rough division into triangles according to the Delaunay rules. The proposed approach makes it possible to significantly simplify the computational procedures for identifying elements of fuzzy images.
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