Scipy optimize unable to find the correct results

I am trying to use scipy.optimize.minimize to fit parameters for a multivariate function, however, regardless of how many noise free data points I am providing to the optimizer, the optimizer could not converge to a correct (or close) answer.

I wonder if there is a mistake in the way I am using the optimizer but I have been scratching my head to find the mistake. I would appreciate any advice or guesses, thanks!

import numpy as np  from scipy.optimize import minimize  import math    def get_transform(ai,aj,ak,x,y,z):        i,j,k = 0, 1, 2      si, sj, sk = math.sin(ai), math.sin(aj), math.sin(ak)      ci, cj, ck = math.cos(ai), math.cos(aj), math.cos(ak)      cc, cs = ci*ck, ci*sk      sc, ss = si*ck, si*sk      M = np.identity(4)      M[i, i] = cj*ck      M[i, j] = sj*sc-cs      M[i, k] = sj*cc+ss      M[j, i] = cj*sk      M[j, j] = sj*ss+cc      M[j, k] = sj*cs-sc      M[k, i] = -sj      M[k, j] = cj*si      M[k, k] = cj*ci      M[0, 3] = x      M[1, 3] = y      M[2, 3] = z            return M    def camera_intrinsic(fx, ppx, fy, ppy):      K = np.zeros((3, 3), dtype='float64')      K[0, 0], K[0, 2] = fx, ppx      K[1, 1], K[1, 2] = fy, ppy        K[2, 2] = 1        return K    def apply_transform(p, matrix):      rotation = matrix[0:3,0:3]          T = np.array([matrix[0][3],matrix[1][3],matrix[2][3]])      transformed = (np.dot(rotation, p.T).T)+T      return transformed    def project(points_3D,internal_calibration):      points_3D = points_3D.T      projections_2d = np.zeros((2, points_3D.shape[1]), dtype='float32')      camera_projection = (internal_calibration).dot(points_3D)      projections_2d[0, :] = camera_projection[0, :]/camera_projection[2, :]      projections_2d[1, :] = camera_projection[1, :]/camera_projection[2, :]        return projections_2d.T            def error(x):      global points,pixels      transform = get_transform(x[0],x[1],x[2],x[3],x[4],x[5])      points_transfered = apply_transform(points, transform)      internal_calibration = camera_intrinsic(x[6],x[7],x[8],x[9])      projected = project(points_transfered,internal_calibration)      # print(((projected-pixels)**2).mean())      return ((projected-pixels)**2).mean()      def generate(points, x):        transform = get_transform(x[0],x[1],x[2],x[3],x[4],x[5])      points_transfered = apply_transform(points, transform)      internal_calibration = camera_intrinsic(x[6],x[7],x[8],x[9])      projected = project(points_transfered,internal_calibration)      return projected      points = np.random.rand(100,3)  x_initial = np.random.rand(10)  pixels = generate(points,x_initial)  x_guess = np.random.rand(10)  results = minimize(error,x_guess, method='nelder-mead', tol = 1e-15)  x = results.x  print(x_initial)  print(x)    

https://stackoverflow.com/questions/66057717/scipy-optimize-unable-to-find-the-correct-results February 05, 2021 at 12:49PM