My Portfolio

Part A

A.1: Shoot the Pictures

A.2: Recover Homographies

First we need to construct system of equations

selfie — Equations to construct system equations for point (x,y) to (u,v)

Then we will use normal equation to solve for h

A =
6.70000e+01 5.10000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.93630e+04 -1.47390e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.70000e+01 5.10000e+02 1.00000e+00 -3.39690e+04 -2.58570e+05
4.00000e+00 4.67000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.48000e+02 -1.10679e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.00000e+00 4.67000e+02 1.00000e+00 -1.87600e+03 -2.19023e+05
2.65000e+02 4.67000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.22960e+05 -2.16688e+05
0.00000e+00 0.00000e+00 0.00000e+00 2.65000e+02 4.67000e+02 1.00000e+00 -1.24285e+05 -2.19023e+05
2.35000e+02 5.02000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.02695e+05 -2.19374e+05
0.00000e+00 0.00000e+00 0.00000e+00 2.35000e+02 5.02000e+02 1.00000e+00 -1.17970e+05 -2.52004e+05
3.38000e+02 4.53000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.79478e+05 -2.40543e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.38000e+02 4.53000e+02 1.00000e+00 -1.53790e+05 -2.06115e+05
4.42000e+02 3.53000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.78018e+05 -2.22037e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.42000e+02 3.53000e+02 1.00000e+00 -1.57794e+05 -1.26021e+05
4.25000e+02 3.76000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.60100e+05 -2.30112e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.25000e+02 3.76000e+02 1.00000e+00 -1.61500e+05 -1.42880e+05
5.10000e+01 5.41000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.40250e+04 -1.48775e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.10000e+01 5.41000e+02 1.00000e+00 -2.73360e+04 -2.89976e+05
4.90000e+01 5.69000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.33770e+04 -1.55337e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.90000e+01 5.69000e+02 1.00000e+00 -2.74890e+04 -3.19209e+05
4.60000e+01 5.97000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.24660e+04 -1.61787e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.60000e+01 5.97000e+02 1.00000e+00 -2.70480e+04 -3.51036e+05
4.30000e+01 6.25000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.15670e+04 -1.68125e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.30000e+01 6.25000e+02 1.00000e+00 -2.63590e+04 -3.83125e+05
3.70000e+01 5.42000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.76800e+03 -1.43088e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.70000e+01 5.42000e+02 1.00000e+00 -1.98320e+04 -2.90512e+05
2.00000e+01 5.41000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.98000e+03 -1.34709e+05
0.00000e+00 0.00000e+00 0.00000e+00 2.00000e+01 5.41000e+02 1.00000e+00 -1.07000e+04 -2.89435e+05
2.60000e+01 5.14000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.63000e+03 -1.31070e+05
0.00000e+00 0.00000e+00 0.00000e+00 2.60000e+01 5.14000e+02 1.00000e+00 -1.33120e+04 -2.63168e+05
1.60000e+01 6.24000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.93600e+03 -1.53504e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.60000e+01 6.24000e+02 1.00000e+00 -9.79200e+03 -3.81888e+05
1.60000e+02 6.14000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.93600e+04 -2.27794e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.60000e+02 6.14000e+02 1.00000e+00 -9.69600e+04 -3.72084e+05
1.45000e+02 7.11000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.16200e+04 -2.53116e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.45000e+02 7.11000e+02 1.00000e+00 -1.00775e+05 -4.94145e+05
9.00000e+01 5.42000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.77200e+04 -1.66936e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.00000e+01 5.42000e+02 1.00000e+00 -4.83300e+04 -2.91054e+05
8.50000e+01 6.00000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.58400e+04 -1.82400e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.50000e+01 6.00000e+02 1.00000e+00 -5.02350e+04 -3.54600e+05
9.50000e+01 6.32000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.97350e+04 -1.97816e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.50000e+01 6.32000e+02 1.00000e+00 -5.90900e+04 -3.93104e+05
4.88000e+02 8.70000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.31352e+05 -5.90730e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.88000e+02 8.70000e+02 1.00000e+00 -4.21632e+05 -7.51680e+05
4.65000e+02 8.87000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.05505e+05 -5.82759e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.65000e+02 8.87000e+02 1.00000e+00 -4.08270e+05 -7.78786e+05
6.02000e+02 8.98000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.76784e+05 -7.11216e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.02000e+02 8.98000e+02 1.00000e+00 -5.42402e+05 -8.09098e+05
6.84000e+02 8.86000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.96448e+05 -7.72592e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.84000e+02 8.86000e+02 1.00000e+00 -6.11496e+05 -7.92084e+05
3.69000e+02 4.56000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.06640e+05 -2.55360e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.69000e+02 4.56000e+02 1.00000e+00 -1.69002e+05 -2.08848e+05
4.96000e+02 4.62000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.37280e+05 -3.14160e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.96000e+02 4.62000e+02 1.00000e+00 -2.29648e+05 -2.13906e+05
4.85000e+02 4.79000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.24465e+05 -3.20451e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.85000e+02 4.79000e+02 1.00000e+00 -2.32800e+05 -2.29920e+05
5.22000e+02 4.80000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.68010e+05 -3.38400e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.22000e+02 4.80000e+02 1.00000e+00 -2.51082e+05 -2.30880e+05
5.10000e+02 4.62000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.53940e+05 -3.20628e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.10000e+02 4.62000e+02 1.00000e+00 -2.36640e+05 -2.14368e+05
5.77000e+02 5.16000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.38520e+05 -3.92160e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.77000e+02 5.16000e+02 1.00000e+00 -2.98309e+05 -2.66772e+05
5.66000e+02 4.98000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.23368e+05 -3.72504e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.66000e+02 4.98000e+02 1.00000e+00 -2.82434e+05 -2.48502e+05
6.33000e+02 4.64000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.17161e+05 -3.79088e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.33000e+02 4.64000e+02 1.00000e+00 -2.94345e+05 -2.15760e+05
6.21000e+02 4.81000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.99905e+05 -3.87205e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.21000e+02 4.81000e+02 1.00000e+00 -2.99322e+05 -2.31842e+05
6.08000e+02 5.17000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.81536e+05 -4.09464e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.08000e+02 5.17000e+02 1.00000e+00 -3.14944e+05 -2.67806e+05
5.97000e+02 4.98000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.65063e+05 -3.87942e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.97000e+02 4.98000e+02 1.00000e+00 -2.98500e+05 -2.49000e+05
6.33000e+02 5.17000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.17161e+05 -4.22389e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.33000e+02 5.17000e+02 1.00000e+00 -3.28527e+05 -2.68323e+05
6.22000e+02 4.99000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.00710e+05 -4.01695e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.22000e+02 4.99000e+02 1.00000e+00 -3.11622e+05 -2.49999e+05
6.88000e+02 4.82000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.02688e+05 -4.22232e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.88000e+02 4.82000e+02 1.00000e+00 -3.32992e+05 -2.33288e+05
6.76000e+02 4.66000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.83388e+05 -4.02158e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.76000e+02 4.66000e+02 1.00000e+00 -3.15692e+05 -2.17622e+05
6.88000e+02 5.00000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.02000e+05 -4.37500e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.88000e+02 5.00000e+02 1.00000e+00 -3.45376e+05 -2.51000e+05
7.73000e+02 4.39000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.48264e+05 -4.24952e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.73000e+02 4.39000e+02 1.00000e+00 -3.39347e+05 -1.92721e+05
8.00000e+02 4.31000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.97600e+05 -4.29707e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.00000e+02 4.31000e+02 1.00000e+00 -3.45600e+05 -1.86192e+05
6.95000e+02 4.47000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.14380e+05 -3.95148e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.95000e+02 4.47000e+02 1.00000e+00 -3.12055e+05 -2.00703e+05
6.45000e+02 4.47000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.35995e+05 -3.71457e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.45000e+02 4.47000e+02 1.00000e+00 -2.88960e+05 -2.00256e+05
5.90000e+02 4.45000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.56070e+05 -3.43985e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.90000e+02 4.45000e+02 1.00000e+00 -2.63730e+05 -1.98915e+05
5.35000e+02 4.45000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.83595e+05 -3.19065e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.35000e+02 4.45000e+02 1.00000e+00 -2.38610e+05 -1.98470e+05
5.85000e+02 4.28000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.49280e+05 -3.28704e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.85000e+02 4.28000e+02 1.00000e+00 -2.51550e+05 -1.84040e+05
8.56000e+02 4.24000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.06504e+05 -4.49016e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.56000e+02 4.24000e+02 1.00000e+00 -3.62088e+05 -1.79352e+05
8.75000e+02 4.24000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.45000e+05 -4.57920e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.75000e+02 4.24000e+02 1.00000e+00 -3.70125e+05 -1.79352e+05
8.08000e+02 4.05000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.12848e+05 -4.07430e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.08000e+02 4.05000e+02 1.00000e+00 -3.26432e+05 -1.63620e+05
5.42000e+02 4.01000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.92408e+05 -2.90324e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.42000e+02 4.01000e+02 1.00000e+00 -2.18426e+05 -1.61603e+05
6.39000e+02 4.03000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.26536e+05 -3.32072e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.39000e+02 4.03000e+02 1.00000e+00 -2.57517e+05 -1.62409e+05
5.76000e+02 5.50000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.37184e+05 -4.17450e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.76000e+02 5.50000e+02 1.00000e+00 -3.18528e+05 -3.04150e+05
5.65000e+02 5.33000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.22620e+05 -3.98684e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.65000e+02 5.33000e+02 1.00000e+00 -3.02840e+05 -2.85688e+05
8.59000e+02 7.60000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.10540e+05 -8.05600e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.59000e+02 7.60000e+02 1.00000e+00 -6.68302e+05 -5.91280e+05
5.79000e+02 9.12000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.46409e+05 -7.03152e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.79000e+02 9.12000e+02 1.00000e+00 -5.26890e+05 -8.29920e+05
3.05000e+02 7.01000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.52195e+05 -3.49799e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.05000e+02 7.01000e+02 1.00000e+00 -2.11060e+05 -4.85092e+05
3.66000e+02 5.99000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.03862e+05 -3.33643e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.66000e+02 5.99000e+02 1.00000e+00 -2.17770e+05 -3.56405e+05
3.13000e+02 6.00000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.59317e+05 -3.05400e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.13000e+02 6.00000e+02 1.00000e+00 -1.86235e+05 -3.57000e+05
6.49000e+02 7.88000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.41915e+05 -6.57980e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.49000e+02 7.88000e+02 1.00000e+00 -5.15306e+05 -6.25672e+05
6.57000e+02 6.85000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.54508e+05 -5.78140e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.57000e+02 6.85000e+02 1.00000e+00 -4.53987e+05 -4.73335e+05
6.79000e+02 7.84000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.87335e+05 -6.78160e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.79000e+02 7.84000e+02 1.00000e+00 -5.37768e+05 -6.20928e+05
3.50000e+01 6.44000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.20500e+03 -1.69372e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.50000e+01 6.44000e+02 1.00000e+00 -2.20500e+04 -4.05720e+05
2.69000e+02 7.05000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.25623e+05 -3.29235e+05
0.00000e+00 0.00000e+00 0.00000e+00 2.69000e+02 7.05000e+02 1.00000e+00 -1.86686e+05 -4.89270e+05
6.70000e+02 5.06000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.73520e+05 -4.33136e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.70000e+02 5.06000e+02 1.00000e+00 -3.40360e+05 -2.57048e+05
6.83000e+02 5.97000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.94210e+05 -5.19390e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.83000e+02 5.97000e+02 1.00000e+00 -4.11166e+05 -3.59394e+05
7.84000e+02 4.46000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.67536e+05 -4.36634e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.84000e+02 4.46000e+02 1.00000e+00 -3.50448e+05 -1.99362e+05

b = 
2.89000e+02
5.07000e+02
2.37000e+02
4.69000e+02
4.64000e+02
4.69000e+02
4.37000e+02
5.02000e+02
5.31000e+02
4.55000e+02
6.29000e+02
3.57000e+02
6.12000e+02
3.80000e+02
2.75000e+02
5.36000e+02
2.73000e+02
5.61000e+02
2.71000e+02
5.88000e+02
2.69000e+02
6.13000e+02
2.64000e+02
5.36000e+02
2.49000e+02
5.35000e+02
2.55000e+02
5.12000e+02
2.46000e+02
6.12000e+02
3.71000e+02
6.06000e+02
3.56000e+02
6.95000e+02
3.08000e+02
5.37000e+02
3.04000e+02
5.91000e+02
3.13000e+02
6.22000e+02
6.79000e+02
8.64000e+02
6.57000e+02
8.78000e+02
7.92000e+02
9.01000e+02
8.72000e+02
8.94000e+02
5.60000e+02
4.58000e+02
6.80000e+02
4.63000e+02
6.69000e+02
4.80000e+02
7.05000e+02
4.81000e+02
6.94000e+02
4.64000e+02
7.60000e+02
5.17000e+02
7.48000e+02
4.99000e+02
8.17000e+02
4.65000e+02
8.05000e+02
4.82000e+02
7.92000e+02
5.18000e+02
7.79000e+02
5.00000e+02
8.17000e+02
5.19000e+02
8.05000e+02
5.01000e+02
8.76000e+02
4.84000e+02
8.63000e+02
4.67000e+02
8.75000e+02
5.02000e+02
9.68000e+02
4.39000e+02
9.97000e+02
4.32000e+02
8.84000e+02
4.49000e+02
8.31000e+02
4.48000e+02
7.73000e+02
4.47000e+02
7.17000e+02
4.46000e+02
7.68000e+02
4.30000e+02
1.05900e+03
4.23000e+02
1.08000e+03
4.23000e+02
1.00600e+03
4.04000e+02
7.24000e+02
4.03000e+02
8.24000e+02
4.03000e+02
7.59000e+02
5.53000e+02
7.48000e+02
5.36000e+02
1.06000e+03
7.78000e+02
7.71000e+02
9.10000e+02
4.99000e+02
6.92000e+02
5.57000e+02
5.95000e+02
5.09000e+02
5.95000e+02
8.35000e+02
7.94000e+02
8.44000e+02
6.91000e+02
8.65000e+02
7.92000e+02
2.63000e+02
6.30000e+02
4.67000e+02
6.94000e+02
8.56000e+02
5.08000e+02
8.70000e+02
6.02000e+02
9.79000e+02
4.47000e+02

H = 
7.99289e-01 1.64371e-02 2.25349e+02
-7.55456e-02 9.20842e-01 4.11003e+01
-1.62101e-04 1.26245e-05 1.00000e+00

A = 3.64000e+02 5.73000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.55164e+05 -4.01673e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.64000e+02 5.73000e+02 1.00000e+00 -2.09300e+05 -3.29475e+05
3.87000e+02 5.71000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.79801e+05 -4.12833e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.87000e+02 5.71000e+02 1.00000e+00 -2.21751e+05 -3.27183e+05
3.62000e+02 5.86000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.53038e+05 -4.09614e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.62000e+02 5.86000e+02 1.00000e+00 -2.12132e+05 -3.43396e+05
3.89000e+02 5.85000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.81247e+05 -4.22955e+05
0.00000e+00 0.00000e+00 0.00000e+00 3.89000e+02 5.85000e+02 1.00000e+00 -2.27176e+05 -3.41640e+05
4.25000e+02 8.01000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.24275e+05 -6.11163e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.25000e+02 8.01000e+02 1.00000e+00 -3.40850e+05 -6.42402e+05
4.65000e+02 7.75000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.73395e+05 -6.22325e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.65000e+02 7.75000e+02 1.00000e+00 -3.61770e+05 -6.02950e+05
4.25000e+02 7.81000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.24275e+05 -5.95903e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.25000e+02 7.81000e+02 1.00000e+00 -3.31925e+05 -6.09961e+05
4.67000e+02 7.95000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.75468e+05 -6.39180e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.67000e+02 7.95000e+02 1.00000e+00 -3.72666e+05 -6.34410e+05
7.72000e+02 7.98000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.80080e+05 -9.09720e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.72000e+02 7.98000e+02 1.00000e+00 -6.42304e+05 -6.63936e+05
8.02000e+02 7.29000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.43152e+05 -8.57304e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.02000e+02 7.29000e+02 1.00000e+00 -6.08718e+05 -5.53311e+05
8.15000e+02 6.17000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.69850e+05 -7.34230e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.15000e+02 6.17000e+02 1.00000e+00 -5.15895e+05 -3.90561e+05
7.44000e+02 6.07000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.19888e+05 -6.68914e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.44000e+02 6.07000e+02 1.00000e+00 -4.61280e+05 -3.76340e+05
7.72000e+02 6.09000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.76220e+05 -6.91215e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.72000e+02 6.09000e+02 1.00000e+00 -4.80956e+05 -3.79407e+05
8.73000e+02 5.40000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.10173e+06 -6.81480e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.73000e+02 5.40000e+02 1.00000e+00 -4.77531e+05 -2.95380e+05
1.61000e+02 8.31000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.48470e+04 -4.37937e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.61000e+02 8.31000e+02 1.00000e+00 -1.30088e+05 -6.71448e+05
4.40000e+01 7.08000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.90520e+04 -3.06564e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.40000e+01 7.08000e+02 1.00000e+00 -3.03160e+04 -4.87812e+05
4.70000e+01 6.40000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.03510e+04 -2.77120e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.70000e+01 6.40000e+02 1.00000e+00 -2.95160e+04 -4.01920e+05
1.77000e+02 5.63000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.50490e+04 -3.02331e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.77000e+02 5.63000e+02 1.00000e+00 -9.94740e+04 -3.16406e+05
4.09000e+02 5.21000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.03478e+05 -3.86582e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.09000e+02 5.21000e+02 1.00000e+00 -2.15134e+05 -2.74046e+05
9.90000e+01 5.43000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.68270e+04 -2.56839e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.90000e+01 5.43000e+02 1.00000e+00 -5.37570e+04 -2.94849e+05
4.47000e+02 5.59000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.47766e+05 -4.34902e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.47000e+02 5.59000e+02 1.00000e+00 -2.51214e+05 -3.14158e+05
4.62000e+02 5.58000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.67290e+05 -4.43610e+05
0.00000e+00 0.00000e+00 0.00000e+00 4.62000e+02 5.58000e+02 1.00000e+00 -2.59182e+05 -3.13038e+05

b = 7.01000e+02
5.75000e+02
7.23000e+02
5.73000e+02
6.99000e+02
5.86000e+02
7.23000e+02
5.84000e+02
7.63000e+02
8.02000e+02
8.03000e+02
7.78000e+02
7.63000e+02
7.81000e+02
8.04000e+02
7.98000e+02
1.14000e+03
8.32000e+02
1.17600e+03
7.59000e+02
1.19000e+03
6.33000e+02
1.10200e+03
6.20000e+02
1.13500e+03
6.23000e+02
1.26200e+03
5.47000e+02
5.27000e+02
8.08000e+02
4.33000e+02
6.89000e+02
4.33000e+02
6.28000e+02
5.37000e+02
5.62000e+02
7.42000e+02
5.26000e+02
4.73000e+02
5.43000e+02
7.78000e+02
5.62000e+02
7.95000e+02
5.61000e+02

H = 
6.36105e-01 1.04294e-02 3.88828e+02
-1.43650e-01 8.60686e-01 7.24843e+01
-2.77276e-04 -9.20088e-06 1.00000e+00

A = 9.18000e+02 6.33000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.25096e+05 -3.62076e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.18000e+02 6.33000e+02 1.00000e+00 -5.54472e+05 -3.82332e+05
9.76000e+02 5.13000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.16832e+05 -3.24216e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.76000e+02 5.13000e+02 1.00000e+00 -4.81168e+05 -2.52909e+05
1.02600e+03 5.19000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.92550e+05 -3.50325e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.02600e+03 5.19000e+02 1.00000e+00 -5.10948e+05 -2.58462e+05
1.00400e+03 5.26000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.58624e+05 -3.45056e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.00400e+03 5.26000e+02 1.00000e+00 -5.06016e+05 -2.65104e+05
1.02800e+03 4.77000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.96984e+05 -3.23406e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.02800e+03 4.77000e+02 1.00000e+00 -4.71852e+05 -2.18943e+05
1.04600e+03 4.76000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.25924e+05 -3.30344e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.04600e+03 4.76000e+02 1.00000e+00 -4.80114e+05 -2.18484e+05
9.43000e+02 4.50000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.69572e+05 -2.71800e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.43000e+02 4.50000e+02 1.00000e+00 -4.07376e+05 -1.94400e+05
9.44000e+02 4.68000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.70176e+05 -2.82672e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.44000e+02 4.68000e+02 1.00000e+00 -4.21968e+05 -2.09196e+05
1.14600e+03 4.86000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.90442e+05 -3.77622e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.14600e+03 4.86000e+02 1.00000e+00 -5.38620e+05 -2.28420e+05
1.14700e+03 5.09000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.90072e+05 -3.94984e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.14700e+03 5.09000e+02 1.00000e+00 -5.62030e+05 -2.49410e+05
1.16100e+03 4.82000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.16029e+05 -3.80298e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.16100e+03 4.82000e+02 1.00000e+00 -5.42187e+05 -2.25094e+05
1.16300e+03 5.03000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.18770e+05 -3.97370e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.16300e+03 5.03000e+02 1.00000e+00 -5.65218e+05 -2.44458e+05
1.19700e+03 4.71000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.77949e+05 -3.84807e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.19700e+03 4.71000e+02 1.00000e+00 -5.47029e+05 -2.15247e+05
1.19900e+03 4.93000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -9.80782e+05 -4.03274e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.19900e+03 4.93000e+02 1.00000e+00 -5.73122e+05 -2.35654e+05
1.13500e+03 6.84000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.66005e+05 -5.21892e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.13500e+03 6.84000e+02 1.00000e+00 -7.34345e+05 -4.42548e+05
1.09800e+03 6.57000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.04834e+05 -4.81581e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.09800e+03 6.57000e+02 1.00000e+00 -6.85152e+05 -4.09968e+05
7.64000e+02 7.01000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.23172e+05 -2.96523e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.64000e+02 7.01000e+02 1.00000e+00 -5.17992e+05 -4.75278e+05
8.21000e+02 6.67000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.95722e+05 -3.21494e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.21000e+02 6.67000e+02 1.00000e+00 -5.26261e+05 -4.27547e+05
8.25000e+02 6.44000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.00950e+05 -3.12984e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.25000e+02 6.44000e+02 1.00000e+00 -5.09025e+05 -3.97348e+05
7.92000e+02 6.35000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.58776e+05 -2.87655e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.92000e+02 6.35000e+02 1.00000e+00 -4.83912e+05 -3.87985e+05
7.88000e+02 6.59000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.53812e+05 -2.95891e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.88000e+02 6.59000e+02 1.00000e+00 -4.99592e+05 -4.17806e+05
1.07600e+03 5.40000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.72568e+05 -3.87720e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.07600e+03 5.40000e+02 1.00000e+00 -5.56292e+05 -2.79180e+05
1.02800e+03 5.52000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.93900e+05 -3.72600e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.02800e+03 5.52000e+02 1.00000e+00 -5.42784e+05 -2.91456e+05
1.03000e+03 5.85000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -6.96280e+05 -3.95460e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.03000e+03 5.85000e+02 1.00000e+00 -5.74740e+05 -3.26430e+05
7.04000e+02 3.61000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.59776e+05 -1.33209e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.04000e+02 3.61000e+02 1.00000e+00 -2.30912e+05 -1.18408e+05
8.79000e+02 3.66000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.80813e+05 -2.00202e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.79000e+02 3.66000e+02 1.00000e+00 -3.04134e+05 -1.26636e+05
5.45000e+02 3.41000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.02460e+05 -6.41080e+04
0.00000e+00 0.00000e+00 0.00000e+00 5.45000e+02 3.41000e+02 1.00000e+00 -1.60230e+05 -1.00254e+05
5.10000e+02 3.29000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.49700e+04 -4.83630e+04
0.00000e+00 0.00000e+00 0.00000e+00 5.10000e+02 3.29000e+02 1.00000e+00 -1.41270e+05 -9.11330e+04
6.68000e+02 3.71000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.20440e+05 -1.22430e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.68000e+02 3.71000e+02 1.00000e+00 -2.24448e+05 -1.24656e+05
6.78000e+02 3.55000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.31198e+05 -1.21055e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.78000e+02 3.55000e+02 1.00000e+00 -2.16960e+05 -1.13600e+05
6.18000e+02 4.22000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.68714e+05 -1.15206e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.18000e+02 4.22000e+02 1.00000e+00 -2.38548e+05 -1.62892e+05
5.80000e+02 5.73000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.29920e+05 -1.28352e+05
0.00000e+00 0.00000e+00 0.00000e+00 5.80000e+02 5.73000e+02 1.00000e+00 -3.19000e+05 -3.15150e+05
7.37000e+02 6.03000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.93326e+05 -2.39994e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.37000e+02 6.03000e+02 1.00000e+00 -4.25986e+05 -3.48534e+05
6.84000e+02 5.95000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.33244e+05 -2.02895e+05
0.00000e+00 0.00000e+00 0.00000e+00 6.84000e+02 5.95000e+02 1.00000e+00 -3.91248e+05 -3.40340e+05
5.63000e+02 3.58000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.17667e+05 -7.48220e+04
0.00000e+00 0.00000e+00 0.00000e+00 5.63000e+02 3.58000e+02 1.00000e+00 -1.76219e+05 -1.12054e+05

b = 5.72000e+02
6.04000e+02
6.32000e+02
4.93000e+02
6.75000e+02
4.98000e+02
6.56000e+02
5.04000e+02
6.78000e+02
4.59000e+02
6.94000e+02
4.59000e+02
6.04000e+02
4.32000e+02
6.04000e+02
4.47000e+02
7.77000e+02
4.70000e+02
7.76000e+02
4.90000e+02
7.89000e+02
4.67000e+02
7.90000e+02
4.86000e+02
8.17000e+02
4.57000e+02
8.18000e+02
4.78000e+02
7.63000e+02
6.47000e+02
7.33000e+02
6.24000e+02
4.23000e+02
6.78000e+02
4.82000e+02
6.41000e+02
4.86000e+02
6.17000e+02
4.53000e+02
6.11000e+02
4.49000e+02
6.34000e+02
7.18000e+02
5.17000e+02
6.75000e+02
5.28000e+02
6.76000e+02
5.58000e+02
3.69000e+02
3.28000e+02
5.47000e+02
3.46000e+02
1.88000e+02
2.94000e+02
1.47000e+02
2.77000e+02
3.30000e+02
3.36000e+02
3.41000e+02
3.20000e+02
2.73000e+02
3.86000e+02
2.24000e+02
5.50000e+02
3.98000e+02
5.78000e+02
3.41000e+02
5.72000e+02
2.09000e+02
3.13000e+02

H = 1.61645e+00 -3.01759e-02 -6.31980e+02
2.58307e-01 1.40031e+00 -2.46859e+02
4.73816e-04 2.02956e-05 1.00000e+00

A = 8.71000e+02 4.40000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.97882e+05 -1.50480e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.71000e+02 4.40000e+02 1.00000e+00 -3.91950e+05 -1.98000e+05
8.70000e+02 4.75000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.96670e+05 -1.61975e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.70000e+02 4.75000e+02 1.00000e+00 -4.22820e+05 -2.30850e+05
9.95000e+02 4.79000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.61680e+05 -2.22256e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.95000e+02 4.79000e+02 1.00000e+00 -4.86555e+05 -2.34231e+05
1.19400e+03 8.19000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.68936e+05 -5.27436e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.19400e+03 8.19000e+02 1.00000e+00 -9.81468e+05 -6.73218e+05
1.25000e+03 8.21000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.70000e+05 -5.71416e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.25000e+03 8.21000e+02 1.00000e+00 -1.02875e+06 -6.75683e+05
1.16900e+03 8.18000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.25949e+05 -5.07978e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.16900e+03 8.18000e+02 1.00000e+00 -9.58580e+05 -6.70760e+05
1.22300e+03 8.20000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.21856e+05 -5.51040e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.22300e+03 8.20000e+02 1.00000e+00 -1.00653e+06 -6.74860e+05
8.49000e+02 4.41000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.71680e+05 -1.41120e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.49000e+02 4.41000e+02 1.00000e+00 -3.82050e+05 -1.98450e+05
8.49000e+02 4.77000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.70831e+05 -1.52163e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.49000e+02 4.77000e+02 1.00000e+00 -4.12614e+05 -2.31822e+05
7.00000e+02 4.07000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.15500e+05 -6.71550e+04
0.00000e+00 0.00000e+00 0.00000e+00 7.00000e+02 4.07000e+02 1.00000e+00 -2.87000e+05 -1.66870e+05
6.55000e+02 3.19000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.79450e+04 -3.79610e+04
0.00000e+00 0.00000e+00 0.00000e+00 6.55000e+02 3.19000e+02 1.00000e+00 -2.08945e+05 -1.01761e+05
6.46000e+02 3.76000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.04140e+04 -4.09840e+04
0.00000e+00 0.00000e+00 0.00000e+00 6.46000e+02 3.76000e+02 1.00000e+00 -2.44834e+05 -1.42504e+05
6.32000e+02 4.13000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.81440e+04 -3.79960e+04
0.00000e+00 0.00000e+00 0.00000e+00 6.32000e+02 4.13000e+02 1.00000e+00 -2.61648e+05 -1.70982e+05
6.28000e+02 4.87000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.52640e+04 -4.28560e+04
0.00000e+00 0.00000e+00 0.00000e+00 6.28000e+02 4.87000e+02 1.00000e+00 -3.08976e+05 -2.39604e+05
6.27000e+02 5.62000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -5.20410e+04 -4.66460e+04
0.00000e+00 0.00000e+00 0.00000e+00 6.27000e+02 5.62000e+02 1.00000e+00 -3.58017e+05 -3.20902e+05
6.24000e+02 6.39000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.92960e+04 -5.04810e+04
0.00000e+00 0.00000e+00 0.00000e+00 6.24000e+02 6.39000e+02 1.00000e+00 -4.05600e+05 -4.15350e+05
6.95000e+02 5.94000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.07725e+05 -9.20700e+04
0.00000e+00 0.00000e+00 0.00000e+00 6.95000e+02 5.94000e+02 1.00000e+00 -4.19780e+05 -3.58776e+05
9.64000e+02 5.92000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.15484e+05 -2.55152e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.64000e+02 5.92000e+02 1.00000e+00 -5.79364e+05 -3.55792e+05
9.16000e+02 5.91000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.52660e+05 -2.27535e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.16000e+02 5.91000e+02 1.00000e+00 -5.48684e+05 -3.54009e+05
9.99000e+02 8.18000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.59540e+05 -3.76280e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.99000e+02 8.18000e+02 1.00000e+00 -8.24175e+05 -6.74850e+05
8.14000e+02 8.09000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.23036e+05 -2.21666e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.14000e+02 8.09000e+02 1.00000e+00 -6.69108e+05 -6.64998e+05
7.72000e+02 8.08000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -1.78332e+05 -1.86648e+05
0.00000e+00 0.00000e+00 0.00000e+00 7.72000e+02 8.08000e+02 1.00000e+00 -6.34584e+05 -6.64176e+05
1.17400e+03 5.20000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.39620e+05 -3.27600e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.17400e+03 5.20000e+02 1.00000e+00 -6.24568e+05 -2.76640e+05
1.17200e+03 5.57000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -7.38360e+05 -3.50910e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.17200e+03 5.57000e+02 1.00000e+00 -6.65696e+05 -3.16376e+05
1.25700e+03 3.74000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -8.92470e+05 -2.65540e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.25700e+03 3.74000e+02 1.00000e+00 -4.96515e+05 -1.47730e+05
1.00700e+03 3.50000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.81346e+05 -1.67300e+05
0.00000e+00 0.00000e+00 0.00000e+00 1.00700e+03 3.50000e+02 1.00000e+00 -3.66548e+05 -1.27400e+05
8.89000e+02 3.46000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.21818e+05 -1.25252e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.89000e+02 3.46000e+02 1.00000e+00 -3.16484e+05 -1.23176e+05
9.62000e+02 7.55000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.07888e+05 -3.20120e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.62000e+02 7.55000e+02 1.00000e+00 -7.32082e+05 -5.74555e+05
8.66000e+02 7.50000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -2.84914e+05 -2.46750e+05
0.00000e+00 0.00000e+00 0.00000e+00 8.66000e+02 7.50000e+02 1.00000e+00 -6.59026e+05 -5.70750e+05
9.41000e+02 7.34000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -3.81105e+05 -2.97270e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.41000e+02 7.34000e+02 1.00000e+00 -7.00104e+05 -5.46096e+05
9.77000e+02 7.09000e+02 1.00000e+00 0.00000e+00 0.00000e+00 0.00000e+00 -4.30857e+05 -3.12669e+05
0.00000e+00 0.00000e+00 0.00000e+00 9.77000e+02 7.09000e+02 1.00000e+00 -7.00509e+05 -5.08353e+05

b = 3.42000e+02
4.50000e+02
3.41000e+02
4.86000e+02
4.64000e+02
4.89000e+02
6.44000e+02
8.22000e+02
6.96000e+02
8.23000e+02
6.21000e+02
8.20000e+02
6.72000e+02
8.23000e+02
3.20000e+02
4.50000e+02
3.19000e+02
4.86000e+02
1.65000e+02
4.10000e+02
1.19000e+02
3.19000e+02
1.09000e+02
3.79000e+02
9.20000e+01
4.14000e+02
8.80000e+01
4.92000e+02
8.30000e+01
5.71000e+02
7.90000e+01
6.50000e+02
1.55000e+02
6.04000e+02
4.31000e+02
6.01000e+02
3.85000e+02
5.99000e+02
4.60000e+02
8.25000e+02
2.74000e+02
8.22000e+02
2.31000e+02
8.22000e+02
6.30000e+02
5.32000e+02
6.30000e+02
5.68000e+02
7.10000e+02
3.95000e+02
4.78000e+02
3.64000e+02
3.62000e+02
3.56000e+02
4.24000e+02
7.61000e+02
3.29000e+02
7.61000e+02
4.05000e+02
7.44000e+02
4.41000e+02
7.17000e+02

H = 1.19818e+00 -3.20533e-02 -6.41696e+02
1.00595e-01 1.13039e+00 -7.49931e+01
1.63442e-04 -1.51922e-05 1.00000e+00

A.3: Warp the Images

target coordinate:
      [[   0,    0],
       [   0,  852],
       [1279,    0],
       [1279,  852]]

target coordinate: 
      [[  0,   0],
       [  0, 479],
       [639,   0],
       [639, 479]]

Analysis

Visual Difference

By comparing image warped using nearest-neighbor and using bilinear interpolation, we can see using nearest-neighbor interpolation the warped image's edge is less smooth, you can see obvious pixels on the edges or where sharp color transitions happens. bilinear interpolation will produce warped image with more smoothed color transitions and edges.

Runtime Difference

The runtime for bilinear interpolation is slower than nearest-neighbor interpolation. bilinear interpolation for track image cost 0.2 sec and nearest-neighbor cost 0.1 sec. bilinear interpolation for sunflower image cost 4.3 sec and nearest-neighbor cost 18 sec.

Extra Rectification Image

A.4: Blend the Images into a Mosaic

Step 1:

Select Correspondence point

Step 2:

Warp the image, here I chose to nearest neighbor warping

Step 3:

Apply Blending mask, I used alpha mask. using function ndimage.distance_transform_edt to get a matrix shows each pixels's distance to edges in a image

Then, Alpha = logical(dtrans1>dtrans2)

Finally, apply gaussian blur to alpah mask to blur edges.

Step 4:

Overlay masked images on gloabl canvas

Other panarama

Set 2

Set 3

Set 4

Part B: FEATURE MATCHING for AUTOSTITCHING

B.1: Harris Corner Detection

Interest points are located where the corner strength f_HM(x,y) is a local maximum in a 3 × 3 neighbourhood, and above a threshold t = f_HM.max() * 0.01.

Adaptive Non-Maximal Suppression

First calculate minimum suppression radius r_i for each interest x_i

We use a value crobust = 0.9, which ensures that a neighbour must have significantly higher strength for suppression to take place. We select the n_ip = 500 interest points with the largest values of r_i.

we can see after ANMS we drastically reduce number of features in the image but features are much still well distributed across the image

B.2: Feature Descriptor Extraction

For each interst points, take 40 by 40 patch around that interst point. Then gaussian blur the patch. Finally we sample a 8 × 8 patch of pixels around the sub-pixel location of the interest point, using a spacing of s =5 pixels. Also bias/gain-normalize each descriptor.

Center Image Feature Descriptors

Side Image Feature Descriptors

B.3: Feature Matching

Feature-Space Outlier Rejection

1-NN: L2 of the closest match

2-NN: L2 of the second-closest match

if 1-NN/2-NN > threshold: keep the correspondence (interest pt, 1-NN)

here I use threshold = 0.3

B.4: RANSAC for Robust Homography

best_T=None 
best_inlier_count=0 
for iteration in range(N): 
    sample=randomly_sample_4_correspondences(all_correspondences)
    #Fitmodeltosample 
    T=get_T(sample) 
    #Count inliers using the fitted model 
    inlier_count=count_inliers(T,all_correspondences,threshold) 
    #Keepbestmodel 
    if inlier_count>best_inlier_count: 
    best_inlier_count=inlier_count 
    best_T=T 
return best_T

I used threshold = 2 to clssify if a correspondence is inlier. Finally I use output homography H to warp images using nearest-neighbor interpolation.

Other autostiching mosaic

Conclusion

By comparing mosaic constructed using manual selected correspondence versus mosaic constructed using autostiching. We can see they can achieve similar effect after blending to reduce boundary effect. autostiching usually can't produce exact same moasic as manual correspondence.