Given two sets of points P={p;|ie 1,2...n}, Q={9;\i 1,2...n} with both n elements. After the transformation of p, the new P should match with Q as much as possible. n arg min 11 fe(Pi) 9i|l? i=1 Where foby parametrized transformation on a point applied. In this homework we are interested in the translation and scaling of sets of points in 2D. fe(Pi) = sp+ tx sp? +ty, Hey i fe 1) 2) a) Find a system of linear equations, where @ = {s,1,,ty) for all i fo(P) = 9 b) Looking at the system of linear equations, -when is this system of linear equations solveble? Describe two sets of points with a minimum number of points that leads to the system of linear equations. -how can the compatibility conditions be interpreted geometrically? c) In genera, Procrustean analysis is applied to sets of points which lead to a system of linear equations for more equitions than unknowns and unsatisfied compatibility conditions. How can we minimize the objective function described above? arg min life(Pi) 9i| i=1 d) Verify the formula on a numerical example. Use sets of points with exactly 3 points. Choose the points in a way that the compatibility conditions in your derived system of linear equations from a) are not fullfilled. Draw a 2D coordinate system after the transformation. Since you may not get nice numbers, the drawing can be approximately correct