please do this carefully and clearly. show steps of how you solve this problem and print out the result also.

# Import library import numpy as #(2 points) # # Function register_Arun_3D # Input: Two 3x matrices of points to register: fixed dataset F of N points and moving dataset M of N points # Output: R = 3x3 rotation matrix, t = 3x1 column vector # such that M = ReF+t # Note: the operator @ is used for matrix multiplication. def register_Arun_3D(F, M): # Ensure the matrices F and have the same shape: same dimension and same amount of points to register if F. ----- != M. ------ #(5 points) raise Exception("The datasets do not have the same size") # Ensure the points have 3D coordinates num_rows, num_cols = #(5 points) if num_rows = 3: raise Exception("The datasets do not have a 3xN size") # (i) Find R # Step 1, Arun's algorithm # Find centroids of F and M column wise centroid_F = np.(F, axis=1) #(3 points) centroid_M = (M, axis=1) #(3 points) # Ensure F and M have same centroid ...reshape(-1, 1) (5 points) Mc = ..reshape(-1, 1) #(5 points) FC = # Step 2. Arun's algorithm #Calculate the 3x3 matrix H H = @ np. >#(6 points) # Step 3, Arun's algorithm # Find the SVD of H U, S, Vt = (H) #17 points) # Step 4, Arun's algorithm # Calculate X X- T@T #(5 points) # Step 5, Arun's algorithm R = X # Calculate, det (x), the determinant of X if - ---(x) #(6 points) # Step 3, Arun's algorithm # Find the SVD of H U, S, Vt = (H) #17 points) # Step 4, Arun's algorithm # Calculate X X- T@T #(5 points) # Step 5, Arun's algorithm R = X # Calculate, det (x), the determinant of X if - ---(x)