SIM(3) Alignment Scale

Problem

Compute the optimal scale of a SIM(3) alignment.

The least-squares scale that maps dst onto src without rotation is sum(dot(src_i, dst_i)) / sum(||dst_i||^2) over the 3D correspondences. Return it rounded to 4 decimal places, or 0.0 when the denominator is 0.

Hint

This is the scalar projection of src onto dst, which minimizes ||src - s * dst||^2.

Test cases

case 1

in: [[[1,0,0],[0,2,0]],[[1,0,0],[0,2,0]]]

expected: 1

case 2

in: [[[2,0,0]],[[1,0,0]]]

expected: 2

case 3

in: [[[0,0,0],[0,0,0]],[[1,1,1],[2,2,2]]]

expected: 0

case 4

in: [[[1,1,0]],[[2,0,0]]]

expected: 0.5

Starter codePython

def sim3_scale(src, dst):
    # Your code here
    pass

4 test cases · run your code against them in the editor