NeRF Depth Expectation

Problem

Compute the expected depth of a NeRF ray.

Using the same alpha and transmittance weights as volume rendering, with alpha_i = 1 - exp(-sigma_i * delta_i), return sum T_i * alpha_i * depth_i rounded to 4 decimal places.

Hint

Depth is the weighted average of sample positions with weights T_i * alpha_i.

Test cases

case 1

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

expected: 1.0972

case 2

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

expected: 0

case 3

in: [[100],[1],[5]]

expected: 5

case 4

in: [[0.5,0.5,0.5],[2,1,3],[1,2,3]]

expected: 1.4416

Starter codePython

def nerf_depth(deltas, sigmas, depths):
    # Your code here
    pass

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