Program Systems: Theory and Applications, 2024 Volume 15, Issue 4,Pages 55–77(Mi ps456)
Mathematic Modeling
Mathematical modeling with constraints and research of the optimal configuration of an optical stereo system consisting of two flat mirrors and videocamera
Abstract:
The paper continues a series of studies devoted to mathematical modeling
and optimization of optical stereo system configuration, consists of video camera and two
flat mirrors. In previous work, we developed a model that takes into account various
constraints on the configuration of such a system: the size of the stereo base, the size
of the mirrors, overall dimensions of the optical system, the absence of double reflection
of light rays, preventing the situation when the video camera is reflected in the mirrors.
A conditional optimization problem is formulated, the perimeter of the rectangle that
bounds the optical system is chosen as the objective function.
In this work we added a set of constraints to the model that define the configuration
of the working area, which is formed by the intersection of the fields of view of two
virtual cameras. The corresponding changes were made to the program for the numerical
solution of the constrained optimization problem using the SciPy package. The results
obtained expand the theory of computer vision and can be used in the creation and
research of computer vision systems for robotic systems and non-destructive testing
systems.
Key words and phrases:machine vision, optical devices, mathematical modeling, stereovision, optimization, catoptric system.