## Appendix A  
In this Appendix, we reproduce the basic ideas of the DGI approach and necessary formulas that are necessary for understanding the proposed algorithm outlined in Section 3. In the book of [PERSON] (1984), it was shown that the well-known [PERSON]'s theorem can be _generalized_ and propagated for a set of _random_ points having _discrete_ coordinates (\(x_{k}\), \(y_{k}\)) (\(k=1,2,3,\dots,\)\(n\)). Let us consider the square of the distance connecting an arbitrary point \(M(x,y)\) with the \(k\)th point (\(x_{k}\), \(y_{k}\)) belonging to two given sets. \[l_{k}^{2}=\left(x-x_{k}\right)^{2}+\left(y-y_{k}\right)^{2}. \tag{1}\]  
We require that  
\[\frac{1}{n}\sum_{k=1}^{n}l_{k}^{2}=I^{2}\equiv const. \tag{2}\]  
Inserting Equation (1) into (2), we obtain  
\[ \begin{array}{l}\left(x-\left\langle x\right\rangle\right)^{2}+\left(y- \left\langle y\right\rangle\right)^{2}=I^{2}-R^{2},\\ \left\langle x^{p}\right\rangle=\frac{1}{n}\sum_{k=1}^{n}x_{k}^{p},\ \left\langle y^{p}\right\rangle= \frac{1}{n}\sum_{k=1}^{n}y_{k}^{p},\ R^{2}=\left\langle\Delta x^{2}\right\rangle +\left\langle\Delta y^{2}\right\rangle,\\ \left\langle\Delta V^{2}\right\rangle=\left\langle V^{2}\right\rangle-\left\langle V \right\rangle^{2}.\end{array}  \tag{3}\]  
As one can notice from Equation (3) that the set of circles can exist if the invariant \(I^{2}\geq R^{2}\), where the equality sign corresponds to a circle with zero radius; it is convenient to consider the invariant circle with radius \(I^{2}=2R^{2}\). From another point of view, the requirement of Equation (2) can be considered as the reduction of the given set of points to the continuous circle with four statistical parameters (\(<\)\(x^{p}\)\(>\), \(<\)\(y^{p}\)\(>\); \(p=1\), \(2\)). However, for practical purposes this simplest requirement in Equation (2) is _not_ sufficient and, therefore, it makes sense to consider other geometrical combinations. In order to reduce the curve with eight statistical parameters, we consider another combination that is more complex in comparison with Equation (1). \[ \begin{array}{l}L_{k}^{(2)}=C^{2}(y-y_{k})^{2}-2B(x-x_{k})\cdot(y-y_{k})+A^ {2}(x-x_{k})^{2},\\ k=1,2,\dots,n\end{array}  \tag{4}\]  
The quadratic form in Equation (4) contains five statistical parameters (\(<\)\(x^{p}\)\(>\), \(<\)\(y^{p}\)\(>\), \(p=1\), \(2\); \(<\)\(xy\)\(>\)) and three unknown parameters (\(A\), \(B\), \(C\)). We subordinate this combination to the following requirement:  
\[\frac{1}{n}\sum_{k=1}^{n}L_{k}^{(2)}=I^{2}\equiv const. \tag{5}\]Inserting Equation (A4) into (A5), after simple algebraic manipulations, one can obtain  
\[ \begin{array}{l}C^{2}(y-\langle y\rangle)^{2}-2B(y-\langle y\rangle)\cdot(x- \langle x\rangle)+A^{2}(x-\langle x\rangle)^{2}+E^{2}\equiv I^{2},\\ E^{2}=C^{2}\big{\langle}\Delta y^{2}\big{\rangle}-2B\langle\Delta x\Delta y \rangle+A^{2}\big{\langle}\Delta x^{2}\big{\rangle}.\end{array} \] (A6)  
As before, we put \(I^{2}=2E^{2}\). In order to find three unknown parameters (\(A\), \(B\), \(C\)), it is convenient to use the obvious parameterization for the variables (\(x\), \(y\)) relative to the angle \(\varphi\). \[ \begin{array}{l}y=\langle y\rangle+A\cos(\varphi-\alpha),\\ x=\langle x\rangle+C\cos(\varphi),\,0\leq\varphi\leq 2\pi.\end{array} \] (A7)  
Excluding the parameter \(\varphi\) from Equation (A7) and identifying expression (A6) with expression (A8),  
\[ \begin{array}{l}C^{2}\Big{\langle}(\Delta y)^{2}\Big{\rangle}-2 AC\cos\alpha \langle(\Delta x)\cdot(\Delta y)\rangle+A^{2}\Big{\langle}(\Delta x)^{2} \Big{\rangle}\equiv A^{2}C^{2}-B^{2},\\ E^{2}=C^{2}\big{\langle}\Delta y^{2}\big{\rangle}-2 AC\cos\alpha\langle\Delta x \Delta y\rangle+A^{2}\big{\langle}\Delta x^{2}\big{\rangle}=A^{2}C^{2}\sin^{ 2}\alpha,\end{array} \] (A8)  
we obtain  
\[\cos\alpha=\frac{B}{AC},\,E^{2}=A^{2}C^{2}-B^{2}.\] (A9)  
In order to decrease the number of unknown parameters, we find from Equation (A7) the values of \(A\) and \(C\) from the obvious conditions. \[