How to ignore certain values (e.g. NaNs) when curve fitting?-CodePudding

take a look at the image below. On the left, you see a plot by plt.imshow of a 2D array called img_roi. On the right, I first identify the maximum and then cut along the vertical, i.e.

centre = np.unravel_index(np.argmax(img_roi, axis=None), img_roi.shape)
x_profile = img_roi[:, centre[1]]

I then fit a normal distribution to that curve. As can be seen, since every second pixel is off by a certain factor, the fit doesn't look good, even though the curve is clearly Gaussian.

For completeness, the data is

x_profile = [ 1.50000000e 00 -7.00000000e-01 -2.70000000e 00  2.80000000e 00
  3.00000000e-01  5.00000000e-01  2.50000000e 00  1.10000000e 00
 -1.00000000e-01  8.10000000e 00  6.90000000e 00  7.53000000e 01
  2.14000000e 01  2.31000000e 02  4.68000000e 01  4.84900000e 02
  8.91000000e 01  7.47500000e 02  1.16400000e 02  8.62900000e 02
  1.13100000e 02  7.01300000e 02  8.74000000e 01  4.46700000e 02
  4.70000000e 01  2.01900000e 02  1.69000000e 01  4.68000000e 01
  7.50000000e 00  1.60000000e 00  3.50000000e 00  4.20000000e 00
  4.00000000e-01  9.10000000e 00  7.10542736e-15  5.50000000e 00
  2.60000000e 00  5.00000000e-01  2.50000000e 00  1.40000000e 00]

My goal is to fit a Gaussian by using the bright pixel values only, without losing information that they are not neighbors but second-nearest neighbors.

I know that there are some "easy" fixes, e.g.: Taking every second pixel, fitting, and then re-scaling.

x_profile_squish = x_profile[::2] - Fit to this

What doesn't work is setting the "not so bright" pixels to zero. I could scale them to match the bright ones, but that misses the point. It's clear how to do the Gaussian fit.

Question Is there a way to set every second pixel to empty or some value that Python simply discards when doing a fit? Or is there another way to tell scipy to ignore certain values when fitting?

Edit: Here is the full 2D data (it is quite large)

img_roi = [[ 3.10000000e 00  1.60000000e 00 -3.90000000e 00  4.10000000e 00
  -4.10000000e 00  3.10000000e 00  4.00000000e-01 -6.00000000e-01
   1.60000000e 00 -2.00000000e-01 -3.00000000e-01  3.00000000e-01
   3.00000000e-01  1.30000000e 00  9.00000000e-01  2.70000000e 00
  -1.80000000e 00 -6.00000000e-01  3.50000000e 00  2.00000000e 00
   1.30000000e 00 -7.00000000e-01  9.00000000e-01  7.10542736e-15
  -4.00000000e-01 -3.00000000e-01  3.00000000e-01  2.50000000e 00
  -2.20000000e 00  7.00000000e-01  2.40000000e 00 -9.00000000e-01
   7.00000000e-01  6.00000000e-01  2.70000000e 00  7.00000000e-01
   1.50000000e 00  1.40000000e 00  1.30000000e 00  9.00000000e-01]
 [ 7.00000000e-01  2.10000000e 00  1.30000000e 00  1.20000000e 00
   7.00000000e-01 -1.30000000e 00  3.20000000e 00 -3.90000000e 00
   2.50000000e 00 -2.40000000e 00  3.00000000e-01  1.70000000e 00
   6.00000000e-01  1.30000000e 00 -9.00000000e-01  1.00000000e-01
   1.00000000e 00  3.00000000e 00  2.00000000e-01  2.00000000e 00
   1.10000000e 00  2.00000000e-01 -1.00000000e-01  1.20000000e 00
   1.20000000e 00  6.00000000e-01  5.00000000e-01  9.00000000e-01
  -4.00000000e-01  7.00000000e-01 -1.00000000e-01 -9.00000000e-01
   3.10000000e 00  4.00000000e-01  1.10000000e 00  6.00000000e-01
   2.00000000e-01  3.00000000e-01 -1.00000000e-01  3.00000000e-01]
 [-3.30000000e 00 -3.00000000e-01 -2.00000000e-01  7.00000000e-01
   1.40000000e 00  4.00000000e-01  1.40000000e 00 -6.00000000e-01
   5.00000000e-01 -5.00000000e-01  2.20000000e 00  2.00000000e-01
   1.60000000e 00  3.00000000e-01 -2.60000000e 00  4.00000000e-01
   9.00000000e-01  3.10000000e 00 -5.00000000e-01  2.00000000e-01
   1.70000000e 00  8.00000000e-01 -1.50000000e 00  7.10542736e-15
   6.00000000e-01 -3.00000000e-01  1.70000000e 00 -1.10000000e 00
   1.10000000e 00 -1.00000000e-01  1.10000000e 00  2.00000000e-01
   2.60000000e 00  1.00000000e-01 -6.00000000e-01  3.00000000e-01
   3.50000000e 00  5.30000000e 00  4.10000000e 00  4.90000000e 00]
 [-4.00000000e-01 -2.00000000e-01  7.00000000e-01  1.40000000e 00
   8.00000000e-01  1.40000000e 00  6.00000000e-01  3.30000000e 00
  -4.00000000e-01  1.40000000e 00 -4.00000000e-01  3.20000000e 00
   1.10000000e 00  2.70000000e 00  8.00000000e-01  1.50000000e 00
   4.00000000e-01  1.50000000e 00 -4.40000000e 00  1.60000000e 00
   3.00000000e-01  3.90000000e 00 -4.00000000e-01  2.00000000e 00
  -9.00000000e-01  1.00000000e-01  2.00000000e-01  2.80000000e 00
   5.00000000e-01 -3.00000000e-01  8.00000000e-01 -3.00000000e-01
   5.20000000e 00  2.80000000e 00  5.70000000e 00  3.10000000e 00
   4.60000000e 00 -6.00000000e-01  9.60000000e 00  1.30000000e 00]
 [ 7.00000000e-01  7.00000000e-01  5.00000000e-01  2.30000000e 00
  -2.40000000e 00  7.00000000e-01  8.00000000e-01  2.00000000e-01
   3.20000000e 00  1.00000000e-01  1.00000000e-01 -2.00000000e-01
   1.40000000e 00  1.00000000e 00 -4.20000000e 00  8.00000000e-01
   4.00000000e-01  3.30000000e 00  5.00000000e-01  4.00000000e-01
  -4.00000000e-01 -4.00000000e-01 -4.00000000e-01 -3.00000000e-01
   1.00000000e 00  8.00000000e-01  3.70000000e 00  7.00000000e-01
   9.00000000e-01 -6.00000000e-01  1.20000000e 00  6.20000000e 00
   1.10000000e 00  4.70000000e 00 -1.00000000e-01  9.90000000e 00
   1.80000000e 00  1.31000000e 01 -5.00000000e-01  8.70000000e 00]
 [-6.00000000e-01  1.30000000e 00  9.00000000e-01  8.00000000e-01
   0.00000000e 00 -6.00000000e-01  1.40000000e 00  6.00000000e-01
   1.80000000e 00  1.60000000e 00  5.20000000e 00  3.70000000e 00
  -8.00000000e-01  3.00000000e-01 -3.70000000e 00 -8.00000000e-01
   5.00000000e-01  3.10000000e 00  3.00000000e-01 -2.00000000e-01
   6.00000000e-01  2.20000000e 00 -9.00000000e-01  1.00000000e 00
  -7.00000000e-01  1.20000000e 00  2.00000000e 00  2.00000000e-01
   3.60000000e 00  1.90000000e 00  8.50000000e 00 -2.00000000e-01
   7.60000000e 00  1.30000000e 00  1.48000000e 01  3.80000000e 00
   1.24000000e 01  3.00000000e-01  1.33000000e 01  2.60000000e 00]
 [ 1.00000000e-01  3.00000000e-01  1.50000000e 00  6.00000000e-01
   3.00000000e-01  5.00000000e-01  1.40000000e 00  3.20000000e 00
  -4.60000000e 00  9.00000000e-01  1.10000000e 00  4.00000000e-01
   1.60000000e 00 -1.00000000e-01  5.00000000e-01  2.20000000e 00
   6.00000000e-01  2.00000000e 00  1.10000000e 00  7.00000000e-01
   2.00000000e 00  0.00000000e 00 -2.90000000e 00 -5.00000000e-01
   7.00000000e-01  3.20000000e 00  7.00000000e-01  2.60000000e 00
  -1.70000000e 00  4.30000000e 00  1.20000000e 00  5.00000000e 00
   1.80000000e 00  9.00000000e 00  1.60000000e 00  1.36000000e 01
   8.00000000e-01  2.18000000e 01  2.50000000e 00  2.26000000e 01]
 [ 5.40000000e 00 -6.00000000e-01 -2.00000000e-01  4.00000000e-01
  -2.00000000e-01 -2.00000000e-01 -6.00000000e-01  2.00000000e 00
   1.00000000e 00  8.00000000e-01  4.00000000e-01  4.10000000e 00
  -4.00000000e-01  3.10000000e 00 -2.70000000e 00  3.00000000e 00
   1.10000000e 00  2.80000000e 00  2.40000000e 00  4.00000000e-01
   2.90000000e 00 -1.70000000e 00 -7.00000000e-01  9.00000000e-01
   1.10000000e 00  7.00000000e-01  2.30000000e 00  1.70000000e 00
   5.00000000e-01 -3.10000000e 00  7.00000000e-01  2.70000000e 00
   4.90000000e 00  2.20000000e 00  1.17000000e 01  7.00000000e 00
   1.53000000e 01  2.60000000e 00  2.80000000e 01  4.40000000e 00]
 [ 3.30000000e 00 -1.00000000e-01  5.00000000e-01 -6.00000000e-01
   2.80000000e 00  1.90000000e 00  2.10000000e 00  5.00000000e-01
   2.30000000e 00 -8.00000000e-01  3.20000000e 00  4.10000000e 00
   1.00000000e 00 -9.00000000e-01  1.50000000e 00  8.00000000e-01
   1.30000000e 00  3.20000000e 00 -6.00000000e-01  3.00000000e-01
   2.30000000e 00  1.00000000e-01  3.60000000e 00  1.20000000e 00
   1.00000000e-01 -2.00000000e-01  1.00000000e 00  8.00000000e-01
   1.60000000e 00  1.90000000e 00 -1.00000000e-01  6.70000000e 00
  -6.00000000e-01  1.37000000e 01  6.00000000e-01  1.55000000e 01
   6.80000000e 00  2.90000000e 01  4.10000000e 00  2.77000000e 01]
 [-6.00000000e-01  2.00000000e 00  3.00000000e-01  4.00000000e-01
   0.00000000e 00  6.00000000e-01  1.50000000e 00  2.80000000e 00
   1.40000000e 00  1.70000000e 00  1.00000000e-01  2.50000000e 00
  -3.00000000e-01  3.00000000e 00  2.40000000e 00  2.60000000e 00
   6.00000000e 00  1.70000000e 00  4.00000000e 00  1.00000000e 00
   1.00000000e-01  9.00000000e-01 -3.00000000e-01 -1.40000000e 00
   1.03000000e 01  3.10000000e 00  1.11000000e 01  8.00000000e-01
   8.20000000e 00  6.00000000e-01  9.20000000e 00  1.00000000e 00
   1.29000000e 01  6.00000000e-01  1.79000000e 01  4.90000000e 00
   2.35000000e 01  5.30000000e 00  2.31000000e 01  7.40000000e 00]
 [ 1.00000000e-01  2.50000000e 00  2.80000000e 00  4.10000000e 00
  -3.00000000e 00 -8.00000000e-01  2.90000000e 00 -3.00000000e-01
   2.40000000e 00 -1.00000000e-01  3.20000000e 00  2.90000000e 00
  -5.00000000e-01  7.00000000e-01 -4.00000000e-01  6.50000000e 00
  -3.00000000e-01  4.30000000e 00  1.20000000e 00  4.60000000e 00
  -6.00000000e-01  3.20000000e 00  2.50000000e 00  1.97000000e 01
   4.40000000e 00  2.58000000e 01  4.80000000e 00  3.30000000e 01
   1.00000000e-01  2.34000000e 01  0.00000000e 00  1.72000000e 01
   3.60000000e 00  2.74000000e 01 -2.00000000e-01  3.04000000e 01
   5.70000000e 00  3.94000000e 01  5.00000000e 00  3.15000000e 01]
 [ 2.60000000e 00  3.60000000e 00 -4.00000000e-01  2.60000000e 00
   5.00000000e-01  2.30000000e 00  2.30000000e 00  7.00000000e-01
   4.00000000e-01  1.20000000e 00  9.00000000e-01  0.00000000e 00
   5.20000000e 00  1.60000000e 00  5.30000000e 00  2.90000000e 00
   5.90000000e 00  5.00000000e-01  6.00000000e-01  3.50000000e 00
   8.00000000e-01  3.40000000e 00  2.31000000e 01  5.10000000e 00
   5.82000000e 01  1.01000000e 01  7.56000000e 01  7.70000000e 00
   6.34000000e 01  8.50000000e 00  4.76000000e 01  7.50000000e 00
   4.03000000e 01  6.00000000e 00  4.40000000e 01  3.90000000e 00
   4.30000000e 01  3.40000000e 00  4.10000000e 01  9.70000000e 00]
 [ 3.00000000e-01  5.00000000e-01 -4.10000000e 00  1.00000000e-01
  -6.00000000e-01  2.90000000e 00  2.10000000e 00  3.00000000e-01
   3.10000000e 00 -4.00000000e-01 -1.10000000e 00  4.50000000e 00
   1.90000000e 00  2.90000000e 00  1.70000000e 00  4.10000000e 00
  -1.00000000e-01  5.60000000e 00  1.50000000e 00  2.50000000e 00
   1.30000000e 00  2.47000000e 01  1.17000000e 01  7.51000000e 01
   1.50000000e 01  1.15200000e 02  2.28000000e 01  1.30900000e 02
   1.29000000e 01  1.09500000e 02  1.21000000e 01  7.60000000e 01
   1.13000000e 01  6.12000000e 01  6.30000000e 00  5.38000000e 01
   4.20000000e 00  4.44000000e 01  4.70000000e 00  4.59000000e 01]
 [ 9.00000000e-01  4.00000000e-01  1.80000000e 00  5.00000000e-01
   2.00000000e-01  5.00000000e-01 -3.00000000e-01  5.00000000e-01
   8.00000000e-01  2.30000000e 00  1.80000000e 00  2.80000000e 00
   1.20000000e 00  3.00000000e 00  4.90000000e 00 -1.00000000e-01
   5.20000000e 00  4.00000000e-01  1.30000000e 00  3.70000000e 00
   2.45000000e 01  1.48000000e 01  8.45000000e 01  3.01000000e 01
   1.60100000e 02  3.88000000e 01  2.24200000e 02  3.32000000e 01
   2.21900000e 02  2.77000000e 01  1.59000000e 02  2.22000000e 01
   1.14200000e 02  1.60000000e 01  8.95000000e 01  1.01000000e 01
   5.86000000e 01  1.03000000e 01  5.06000000e 01  5.00000000e 00]
 [ 3.10000000e 00  2.00000000e-01  6.00000000e-01 -1.20000000e 00
   3.50000000e 00  4.00000000e-01  2.00000000e 00  3.00000000e-01
  -3.00000000e-01  1.10000000e 00  1.50000000e 00  9.00000000e-01
   1.00000000e 00  4.40000000e 00  2.50000000e 00 -2.00000000e-01
   2.90000000e 00  2.00000000e-01  1.90000000e 00  1.76000000e 01
   1.19000000e 01  8.60000000e 01  2.25000000e 01  2.11800000e 02
   4.67000000e 01  3.03900000e 02  4.53000000e 01  3.38200000e 02
   3.98000000e 01  2.85500000e 02  2.98000000e 01  2.05900000e 02
   2.00000000e 01  1.42400000e 02  1.32000000e 01  9.68000000e 01
   1.12000000e 01  5.57000000e 01  6.40000000e 00  4.90000000e 01]
 [-4.00000000e 00  0.00000000e 00 -2.90000000e 00  3.00000000e 00
   4.00000000e-01  3.10000000e 00  1.40000000e 00  8.00000000e-01
  -1.10000000e 00  8.00000000e-01  1.30000000e 00  0.00000000e 00
   4.10000000e 00  2.10000000e 00  5.30000000e 00  2.80000000e 00
  -1.00000000e-01  1.30000000e 00  1.60000000e 01  1.42000000e 01
   7.20000000e 01  2.89000000e 01  2.05000000e 02  5.11000000e 01
   3.58600000e 02  7.71000000e 01  4.28900000e 02  7.63000000e 01
   4.32700000e 02  5.68000000e 01  3.30600000e 02  4.14000000e 01
   2.33900000e 02  3.12000000e 01  1.50400000e 02  1.80000000e 01
   8.39000000e 01  9.40000000e 00  5.02000000e 01  6.70000000e 00]
 [ 1.60000000e 00  5.00000000e-01  6.00000000e-01  5.00000000e-01
   6.00000000e-01  1.00000000e 00  2.00000000e 00  6.00000000e-01
  -6.00000000e-01  3.00000000e-01  1.20000000e 00  8.00000000e-01
   2.30000000e 00  1.00000000e-01  3.40000000e 00  6.00000000e-01
   1.90000000e 00  4.60000000e 00  6.70000000e 00  5.37000000e 01
   1.62000000e 01  1.82300000e 02  5.04000000e 01  3.82500000e 02
   6.97000000e 01  5.40600000e 02  7.82000000e 01  5.44800000e 02
   7.65000000e 01  4.89900000e 02  5.67000000e 01  3.57800000e 02
   3.81000000e 01  2.19400000e 02  2.04000000e 01  1.48500000e 02
   1.32000000e 01  6.97000000e 01  6.10000000e 00  4.51000000e 01]
 [ 1.00000000e-01 -2.90000000e 00 -4.00000000e-01 -3.90000000e 00
   3.30000000e 00  8.00000000e-01 -9.00000000e-01  4.00000000e-01
   5.00000000e-01  1.80000000e 00  2.90000000e 00  1.00000000e-01
   9.00000000e-01 -1.60000000e 00 -9.00000000e-01  1.30000000e 00
   4.30000000e 00  6.00000000e 00  3.76000000e 01  2.17000000e 01
   1.44300000e 02  4.89000000e 01  3.33400000e 02  8.32000000e 01
   5.66200000e 02  1.09800000e 02  6.62000000e 02  1.16500000e 02
   6.38900000e 02  8.49000000e 01  4.89100000e 02  6.72000000e 01
   3.42200000e 02  4.13000000e 01  2.06000000e 02  2.02000000e 01
   1.09900000e 02  1.01000000e 01  4.38000000e 01  4.80000000e 00]
 [ 1.00000000e-01  7.00000000e-01 -3.30000000e 00  0.00000000e 00
   1.90000000e 00  2.20000000e 00  1.30000000e 00  7.10542736e-15
   7.00000000e-01  0.00000000e 00 -3.70000000e 00 -9.00000000e-01
   1.80000000e 00  3.80000000e 00  2.60000000e 00  2.50000000e 00
   3.10000000e 00  1.96000000e 01  9.80000000e 00  9.64000000e 01
   2.91000000e 01  2.77500000e 02  6.83000000e 01  5.17200000e 02
   8.77000000e 01  6.69000000e 02  1.14300000e 02  7.31000000e 02
   7.97000000e 01  6.14700000e 02  6.81000000e 01  4.53100000e 02
   4.72000000e 01  2.86100000e 02  3.10000000e 01  1.53000000e 02
   1.61000000e 01  6.66000000e 01  6.10000000e 00  3.09000000e 01]
 [ 3.30000000e 00 -9.00000000e-01  8.00000000e-01  6.00000000e-01
  -3.60000000e 00  1.10000000e 00 -2.00000000e-01  1.30000000e 00
   1.40000000e 00  3.00000000e-01  1.60000000e 00  1.00000000e-01
   0.00000000e 00 -5.00000000e-01  1.20000000e 00  6.00000000e-01
   8.40000000e 00  6.40000000e 00  5.73000000e 01  2.63000000e 01
   1.93700000e 02  6.28000000e 01  4.26900000e 02  9.50000000e 01
   6.18500000e 02  1.27700000e 02  7.38200000e 02  1.29800000e 02
   6.68100000e 02  9.69000000e 01  5.17600000e 02  6.49000000e 01
   3.69900000e 02  5.00000000e 01  2.18600000e 02  2.18000000e 01
   9.12000000e 01  9.20000000e 00  3.50000000e 01  2.50000000e 00]
 [ 8.00000000e-01 -2.90000000e 00  1.30000000e 00  2.50000000e 00
   1.50000000e 00 -5.80000000e 00  1.60000000e 00 -1.00000000e-01
   5.00000000e-01 -9.00000000e-01  4.00000000e-01 -6.00000000e-01
   1.80000000e 00  3.00000000e-01  2.70000000e 00  7.20000000e 00
   3.00000000e-01  2.53000000e 01  1.51000000e 01  1.14600000e 02
   3.40000000e 01  2.82100000e 02  6.08000000e 01  5.11400000e 02
   9.37000000e 01  6.59200000e 02  1.05600000e 02  7.09900000e 02
   9.21000000e 01  5.78900000e 02  6.34000000e 01  4.09200000e 02
   4.77000000e 01  2.77700000e 02  2.03000000e 01  1.27500000e 02
   1.08000000e 01  5.07000000e 01  7.00000000e 00  1.34000000e 01]
 [-3.10000000e 00  5.00000000e-01 -8.00000000e-01 -1.00000000e-01
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  -4.00000000e-01  1.60000000e 00  1.00000000e-01 -4.00000000e-01
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   5.34100000e 02  1.15000000e 02  6.15400000e 02  1.13100000e 02
   5.86700000e 02  9.07000000e 01  4.21400000e 02  5.94000000e 01
   2.93800000e 02  3.84000000e 01  1.50200000e 02  1.29000000e 01
   6.51000000e 01  5.70000000e 00  1.63000000e 01  2.00000000e 00]
 [ 1.10000000e 00  9.00000000e-01 -1.00000000e-01  1.40000000e 00
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   4.00000000e-01  2.11000000e 01  1.01000000e 01  8.35000000e 01
   2.32000000e 01  2.22400000e 02  4.82000000e 01  3.86300000e 02
   7.43000000e 01  4.94700000e 02  7.49000000e 01  5.27900000e 02
   6.54000000e 01  4.16900000e 02  4.92000000e 01  2.88200000e 02
   3.27000000e 01  1.70000000e 02  1.68000000e 01  7.52000000e 01
   7.10000000e 00  2.23000000e 01  2.70000000e 00  5.00000000e 00]
 [-4.00000000e-01  1.70000000e 00  1.50000000e 00  1.20000000e 00
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   1.10000000e 00  6.00000000e-01  1.60000000e 00  5.00000000e-01
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   1.01200000e 02  3.35000000e 01  2.30600000e 02  5.66000000e 01
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   3.59600000e 02  5.39000000e 01  2.44500000e 02  3.76000000e 01
   1.66200000e 02  1.88000000e 01  7.38000000e 01  9.60000000e 00
   2.49000000e 01 -6.00000000e-01  5.70000000e 00  3.70000000e 00]
 [-3.90000000e 00 -1.40000000e 00  6.00000000e-01 -4.30000000e 00
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   4.00000000e 01  2.86700000e 02  4.98000000e 01  2.74100000e 02
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   9.00000000e-01  6.40000000e 00 -2.00000000e-01  1.30000000e 00]
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   4.00000000e-01  6.30000000e 00  3.00000000e-01 -5.00000000e-01
   2.00000000e 00  1.70000000e 00  1.90000000e 00 -3.00000000e-01
   1.70000000e 00  8.00000000e-01  2.10000000e 00  4.50000000e 00]
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   2.00000000e-01 -3.00000000e 00 -6.00000000e-01  5.00000000e-01
  -4.00000000e-01  9.00000000e-01  5.00000000e 00  3.20000000e 00
   5.10000000e 00 -1.00000000e-01  9.50000000e 00  1.50000000e 00
   1.03000000e 01  2.70000000e 00  1.25000000e 01  5.00000000e-01
   9.90000000e 00  1.00000000e 00  1.00000000e-01  1.20000000e 00
   6.00000000e-01  3.00000000e 00  8.00000000e-01  9.00000000e-01
   1.30000000e 00  1.70000000e 00 -4.30000000e 00  2.00000000e-01
   3.00000000e-01  3.30000000e 00 -1.40000000e 00 -2.40000000e 00
   3.30000000e 00  2.20000000e 00  4.50000000e 00  1.50000000e 00]
 [ 5.00000000e-01  4.00000000e-01 -5.00000000e-01  1.00000000e-01
   9.00000000e-01  8.00000000e-01  1.80000000e 00 -1.00000000e-01
   2.00000000e-01  3.00000000e-01  2.20000000e 00  5.70000000e 00
   3.00000000e-01  4.20000000e 00  3.00000000e-01  1.59000000e 01
   6.00000000e-01  1.37000000e 01  1.60000000e 00  1.19000000e 01
   1.70000000e 00  8.50000000e 00  4.00000000e-01  3.70000000e 00
   1.00000000e-01  9.00000000e-01  2.00000000e-01 -7.00000000e-01
   1.80000000e 00  7.00000000e-01  1.80000000e 00  0.00000000e 00
   3.00000000e 00 -1.00000000e-01  1.70000000e 00  5.00000000e-01
   1.60000000e 00  1.50000000e 00  3.00000000e-01  3.80000000e 00]
 [ 3.10000000e 00 -4.00000000e-01  7.00000000e-01 -4.00000000e-01
   6.00000000e-01  1.60000000e 00  6.00000000e-01 -1.10000000e 00
  -4.00000000e-01  8.00000000e-01  1.00000000e 00  1.40000000e 00
   7.00000000e-01 -3.00000000e-01  9.70000000e 00  2.10000000e 00
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   1.58000000e 01  6.00000000e-01  1.12000000e 01  1.80000000e 00
   8.00000000e 00 -3.00000000e 00  4.00000000e 00  2.20000000e 00
   3.90000000e 00  1.00000000e 00  4.40000000e 00  1.00000000e-01
  -1.00000000e-01  6.00000000e-01  0.00000000e 00  1.90000000e 00
   4.30000000e 00  3.00000000e 00  5.20000000e 00 -2.00000000e-01]
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   1.00000000e 00  3.10000000e 00  3.00000000e-01 -5.00000000e-01
   1.80000000e 00 -5.00000000e-01 -7.00000000e-01  3.30000000e 00
  -3.70000000e 00  4.70000000e 00  1.70000000e 00  9.90000000e 00
  -5.00000000e-01  1.18000000e 01  2.20000000e 00  1.34000000e 01
   1.20000000e 00  1.32000000e 01  1.20000000e 00  9.10000000e 00
   3.00000000e 00  9.00000000e 00  3.60000000e 00  7.10000000e 00
   1.10000000e 00  5.20000000e 00  2.70000000e 00  6.10000000e 00
   2.10000000e 00  4.50000000e 00  2.00000000e 00  7.60000000e 00
   1.00000000e 00  5.20000000e 00  1.90000000e 00  9.30000000e 00]
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   1.00000000e-01  8.00000000e-01 -3.70000000e 00  4.00000000e-01
   4.00000000e-01  4.50000000e 00  2.20000000e 00  8.00000000e-01
  -1.00000000e-01 -2.00000000e-01  1.50000000e 00  2.10000000e 00
   4.20000000e 00  3.40000000e 00  1.04000000e 01  1.60000000e 00
   9.80000000e 00  3.20000000e 00  1.07000000e 01  2.80000000e 00
   1.01000000e 01  1.30000000e 00  9.40000000e 00  5.10000000e 00
   6.90000000e 00  1.70000000e 00  4.70000000e 00  1.00000000e 00
   3.80000000e 00  2.20000000e 00  5.20000000e 00  1.20000000e 00
   9.40000000e 00  5.00000000e-01  4.10000000e 00  2.40000000e 00]
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  -2.40000000e 00  1.40000000e 00  3.40000000e 00  1.80000000e 00
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   3.80000000e 00  1.08000000e 01  1.00000000e-01  1.37000000e 01
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   3.70000000e 00  4.30000000e 00  5.00000000e-01  4.00000000e 00
  -2.00000000e-01  4.70000000e 00  2.70000000e 00  4.30000000e 00]
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   4.20000000e 00  1.10000000e 00  1.00000000e-01  1.90000000e 00
   7.10542736e-15  0.00000000e 00  4.60000000e 00  0.00000000e 00
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   4.40000000e 00 -7.00000000e-01 -1.00000000e-01  7.00000000e-01]
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   5.00000000e-01 -1.00000000e-01 -4.00000000e-01 -1.00000000e-01
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   2.20000000e 00  4.50000000e 00  1.30000000e 00 -1.10000000e 00
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   6.00000000e 00  3.70000000e 00  1.30000000e 00  2.80000000e 00
   1.20000000e 00  1.80000000e 00  0.00000000e 00  1.40000000e 00]
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  -8.00000000e-01 -6.00000000e-01  2.00000000e-01  1.10000000e 00
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   3.20000000e 00  5.30000000e 00  1.80000000e 00  3.10000000e 00
  -2.40000000e 00  5.00000000e-01  8.00000000e-01  3.60000000e 00]
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   3.10000000e 00  1.00000000e-01 -1.20000000e 00 -2.00000000e-01]]

CodePudding user response：

I have found a related post that describes a solution that is applicable to scipy.optimize.leastsq routines. I first set the irrelevant data points to nan and then mask them using mask = ~np.isnan(img_roi).

This is sufficient for the purpose described above.

Link to answer: https://stackoverflow.com/a/30791245/12460839

CodePudding user response：

No need to throw away your data. You can get pretty close, and find true 2D parameters of fit:

import numpy as np
from scipy.optimize import curve_fit


modulator = np.zeros_like(img_roi)
modulator[0::2, 1::2] = 1
modulator[1::2, 0::2] = 1
modulator = modulator.ravel()


def gaussian(xy: np.ndarray, a: float, b: float, c: float, d: float, e: float, f: float) -> np.ndarray:
    x, y = xy
    return a * np.exp(-b*(x - c)**2) * np.exp(-d*(y - e)**2) * (1   f*modulator)


xy = np.stack(
    np.meshgrid(
        np.arange(img_roi.shape[0]),
        np.arange(img_roi.shape[1]),
        copy=False,
    )
).reshape((2, -1))

initial = (100, 0.01, 20, 0.01, 20, 1)

res, _ = curve_fit(
    f=gaussian,
    xdata=xy,
    ydata=img_roi.ravel(),
    p0=initial,
)

yfit = gaussian(xy, *res).reshape(img_roi.shape)

print(res)
print(img_roi[13:25, 25:30])
print(yfit[13:25, 25:30])

[1.20827916e 02 2.74206593e-02 2.68145375e 01 3.84558433e-02
 1.87491210e 01 5.22361058e 00]
[[ 38.8 224.2  33.2 221.9  27.7]
 [303.9  45.3 338.2  39.8 285.5]
 [ 77.1 428.9  76.3 432.7  56.8]
 [540.6  78.2 544.8  76.5 489.9]
 [109.8 662.  116.5 638.9  84.9]
 [669.  114.3 731.   79.7 614.7]
 [127.7 738.2 129.8 668.1  96.9]
 [659.2 105.6 709.9  92.1 578.9]
 [115.  615.4 113.1 586.7  90.7]
 [494.7  74.9 527.9  65.4 416.9]
 [ 66.2 391.   76.2 359.6  53.9]
 [286.7  49.8 274.1  41.2 200.2]]
[[ 30.97021507 207.15496225  33.86447586 202.9835828   29.73550831]
 [288.61537124  49.84088629 315.58735551  48.83726443 277.10898205]
 [ 64.29949346 430.08933303  70.3084767  421.42883179  61.73602987]
 [513.78112515  88.72468062 561.79553397  86.93807457 493.29792788]
 [ 98.14351263 656.46672494 107.31532239 643.24777146  94.23077074]
 [672.39975922 116.11647639 735.23756183 113.77829497 645.59282483]
 [110.13018257 736.64369995 120.4221831  721.81026143 105.73956146]
 [646.94545859 111.72078222 707.40447938 109.47111477 621.15332492]
 [ 90.85353635 607.70520491  99.34407565 595.46813862  87.23142799]
 [457.61315794  79.02505425 500.37849939  77.43376489 439.36924019]
 [ 55.10208456 368.56929224  60.25154196 361.14759036  52.90529917]
 [237.9688182   41.09475097 260.20772804  40.26724581 228.48158325]]

You can even establish "corrected" data views that remove the modulating checkerboard:

corrected_orig = img_roi / (1   res[5]*modulator.reshape(img_roi.shape))
corrected_fit = (gaussian(xy, *res) / (1   res[5]*modulator)).reshape(img_roi.shape)