Fitting a 2D pixel matrix over "time" steps (or some other independent quantity)

linfit2dpix.py

import numpy as np

# create dummy two-dimensional (3x3) data that represents
# per-pixel measured quantities taken at various "time steps"
# (say, 4 of such steps):
pixel_maps = np.asarray([
    [
        [0, 0, 0],
        [2, 2, 2],
        [3, 3, 3],
    ],
    [
        [1, 1, 1],
        [2, 2, 2],
        [2, 2, 2],
    ],
    [
        [2, 2, 2],
        [2, 2, 2],
        [1, 1, 1],
    ],
    [
        [3, 3, 3],
        [2, 2, 2],
        [0, 0, 0],
    ]
])
pixel_maps_for_fit = np.stack(pixel_maps, axis = 0)

# associate with each of the 2D pixel maps a corresponding
# "time" step value (the independent variable over which
# each pixel's data will fit)
time_steps = np.asarray([0, 0.5, 1, 1.5])

# reshape the pixel map data into a form that polyfit can take,
# see: https://numpy.org/doc/stable/reference/generated/numpy.polyfit.html
# summary:
# y-coordinates of the sample points can contain several data sets of sample
# points sharing the same x-coordinates if the data is re-shaped as a 2D-array
# that contains one dataset per column
pixel_maps_for_fit = pixel_maps_for_fit.reshape(len(pixel_maps_for_fit), -1)

# perform the linear regression over each time step for each individual "pixel"
slopes, intercepts = np.polyfit(time_steps, pixel_maps_for_fit, deg = 1)

print(slopes)
# prints:
# [
#   4.00000000e+00  4.00000000e+00  4.00000000e+00 
#   -1.13194253e-15 -1.13194253e-15 -1.13194253e-15
#   -4.00000000e+00 -4.00000000e+00 -4.00000000e+00
# ]

print(intercepts)
# prints:
# [
#   1.12255857e-16 1.12255857e-16 1.12255857e-16
#   2.00000000e+00 2.00000000e+00 2.00000000e+00
#   3.00000000e+00 3.00000000e+00 3.00000000e+00
# ]