NeRF Density Integration

Problem

Compute the per-sample weights of volume rendering: alpha_i = 1 - exp(-sigma_i * delta_i), transmittance T_i = prod_{j<i} (1 - alpha_j), and weight_i = T_i * alpha_i.

The signature is nerf_density_integration(sigmas, deltas). Return the list of weights.

Hint

The weights sum to the total opacity along the ray and are used to composite colors.

Test cases

case 1

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

expected: [0.6321205588,0.2325441579,0.0855482149]

case 2

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

expected: [0,0]

case 3

in: [[1],[2]]

expected: [0.8646647168]

case 4

in: [[2,0,1],[0.5,1,0.5]]

expected: [0.6321205588,0,0.144749281]

Starter codePython

import math
def nerf_density_integration(sigmas, deltas):
    # Your code here
    pass

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