Analytical review of software-algorithmic methods of processing of measuring information about geometrical parameters of objects in images

Abstract

The paper considers software-algorithmic methods and computational aspects of operations of transformation of coordinates of points in the plane. These procedures include: finding new rectangular coordinates of a vector when rotating it (or a coordinate system) by some angle in the image plane; transforming vector coordinates from a rectangular coordinate system to a polar one and vice versa. In this case vector coordinates correspond to coordinates of some object point on the image. This point can be an element of the object contour or its centre of mass. Transformations of coordinates of these points allow describing translational motion of the centre of mass and rotational motion of the object around the centre of mass. Accordingly, the considered coordinate transformations are used in determination of geometrical parameters of these objects, analytical description of object motion parameters on the basis of affine transformations, development of new methods of image transformation, coding and compression on the basis of intellectual technologies (fractals, artificial neural networks). Execution of coordinate transformation operations requires multiple multiplication operations and calculation of values of transcendental functions (direct and inverse trigonometric functions, square roots). Methods of calculating these functions are considered and analysed: tabular methods; approximation methods; tabular-algorithmic methods; iterative methods. The main attention is paid to tabular-algorithmic methods of calculating polar coordinates, determining the distance and linear dimensions of objects, their angular position on the basis of square root and arctangent functions. The iterative method «digit by digit» (Cordic method) for calculating affine transformations and transition between rectangular and polar coordinate systems is also considered.

Keywords

• geometric parameters
• image
• iterative cordic method