I am trying to study the relationship between two parameters say
B for an image.
For a single scene S1, I take 20 images back-to-back where all 20 images will have different values of parameter
A. Now for each of 20 images I calculate parameter
B. Thus, I have 20 pairs of type
Now I plot all 20
(A, B) points.
I repeat the same experiment for different scenes and get curves which look similar. This is how all the curves look like: Example curve
I want to establish a formula linking parameters
B. I decided to use curve-fitting (using Python) and tried to fit a polynomial curve
ax^3 + bx^2 + cx + d. This curve fits very well most of the time, but for each graph I get different values of
d. The values vary too much.
Next, I tried fitting a logarithmic curve
a + b * log(x). This time, the curve does not always fit very well to the points and I get values of
a varying from 7 to 9 and values of
b varying from 1 to 3.
Basically my question is how should I go about establishing a formula between
B so that for a given image if I have value of parameter
A, I can get a fair estimate of parameter
Following are sample data points for parameter
A = [0.9937759763768161, 0.9929152405279837, 0.9931066175878016, 0.9931907432668384, 0.9423758456906559, 0.9423108644829163, 0.8950448401371942, 0.891681991390553, 0.8465614087427353, 0.805345556595838, 0.7662998080069015, 0.7314247255399298, 0.6984452544936371, 0.6367965670718196, 0.5836881571632964, 0.4988198092947567, 0.4194923476465984, 0.33213924154453156, 0.22415360562956688, 0.11320564921875846] B = [7.1924877201252109, 7.2179850206954717, 7.2104191677025398, 7.2052736759243174, 7.3607976206941599, 7.3592349109473805, 7.4487191455800605, 7.4675352495474385, 7.5513534938320701, 7.5711664827868503, 7.5349750797299357, 7.4872747506190747, 7.3718597264801442, 7.2183573562424082, 7.0814398229980107, 6.7632755526248989, 6.4009932656267612, 5.8645747001035851, 4.9334148033003622, 3.3773511239822742]
The data points are in order with each other.