如何在numpy / scipy中获取插值数组值

Question

I was wondering how I could get the interpolated value of a 3D array. I am trying to get the value at for example position: (1.4, 2.3, 4.2) of a 3d array. How can I get the interpolated value?

counterX = 1.5 
counterY = 1.5 
counterZ = 1.5 

for x in range(0, length)
    for y in range(0, length)
        for z in range(0, length)
            value = img[counterX, counterY, counterZ]
        counterZ = 0
    counterY = 0

counterX, counterY and counterZ are float values rather than integers. However I cannot css them int(...) since my results need to be very exact. Therefore I thought interpolation would be the best solution.

Answer 1

I am not sure what is exactly your problem.

Would you like to create an interpolated array from some observed values ? Then I would personnally recommend to use a kriging model, pyKriging seems to do that but I never used it personnally.

Then you could create a function (using the prediction model built through kriging) taking 3 arguments counterX, counterY and counterZ and just evaluate the prediction in any positions.

Answer 2

Just go for trilinear Interpolation as described here: https://en.wikipedia.org/wiki/Trilinear_interpolation

For your example this would be:

C00 = (1,2,4)*0.6 + (2,2,4)*0.4
C01 = (1,3,4)*0.6 + (2,3,4)*0.4
C10 = (1,2,5)*0.6 + (2,2,5)*0.4
C11 = (1,3,5)*0.6 + (2,3,5)*0.4

C0 = C00*0.8 + C10*0.2
C1 = C01*0.8 + C11*0.2

C = C0*0.7 + C1*0.3