deepatlas/metrics/lookup_tables.py

# Copyright 2018 Google Inc. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#      http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS-IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import math
import numpy as np
ENCODE_NEIGHBOURHOOD_3D_KERNEL = np.array([[[128, 64], [32, 16]], [[8, 4],
                                                                   [2, 1]]])

"""

lookup_tables.py

all of the lookup-tables functions are borrowed from DeepMind surface_distance repository

"""


# _NEIGHBOUR_CODE_TO_NORMALS is a lookup table.
# For every binary neighbour code
# (2x2x2 neighbourhood = 8 neighbours = 8 bits = 256 codes)
# it contains the surface normals of the triangles (called "surfel" for
# "surface element" in the following). The length of the normal
# vector encodes the surfel area.
#
# created using the marching_cube algorithm
# see e.g. https://en.wikipedia.org/wiki/Marching_cubes
# pylint: disable=line-too-long
_NEIGHBOUR_CODE_TO_NORMALS = [
    [[0, 0, 0]],
    [[0.125, 0.125, 0.125]],
    [[-0.125, -0.125, 0.125]],
    [[-0.25, -0.25, 0.0], [0.25, 0.25, -0.0]],
    [[0.125, -0.125, 0.125]],
    [[-0.25, -0.0, -0.25], [0.25, 0.0, 0.25]],
    [[0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[0.5, 0.0, -0.0], [0.25, 0.25, 0.25], [0.125, 0.125, 0.125]],
    [[-0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.125, 0.125, 0.125]],
    [[-0.25, 0.0, 0.25], [-0.25, 0.0, 0.25]],
    [[0.5, 0.0, 0.0], [-0.25, -0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[0.25, -0.25, 0.0], [0.25, -0.25, 0.0]],
    [[0.5, 0.0, 0.0], [0.25, -0.25, 0.25], [-0.125, 0.125, -0.125]],
    [[-0.5, 0.0, 0.0], [-0.25, 0.25, 0.25], [-0.125, 0.125, 0.125]],
    [[0.5, 0.0, 0.0], [0.5, 0.0, 0.0]],
    [[0.125, -0.125, -0.125]],
    [[0.0, -0.25, -0.25], [0.0, 0.25, 0.25]],
    [[-0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[0.0, -0.5, 0.0], [0.25, 0.25, 0.25], [0.125, 0.125, 0.125]],
    [[0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[0.0, 0.0, -0.5], [0.25, 0.25, 0.25], [-0.125, -0.125, -0.125]],
    [[-0.125, -0.125, 0.125], [0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[-0.125, -0.125, -0.125], [-0.25, -0.25, -0.25],
        [0.25, 0.25, 0.25], [0.125, 0.125, 0.125]],
    [[-0.125, 0.125, 0.125], [0.125, -0.125, -0.125]],
    [[0.0, -0.25, -0.25], [0.0, 0.25, 0.25], [-0.125, 0.125, 0.125]],
    [[-0.25, 0.0, 0.25], [-0.25, 0.0, 0.25], [0.125, -0.125, -0.125]],
    [[0.125, 0.125, 0.125], [0.375, 0.375, 0.375],
        [0.0, -0.25, 0.25], [-0.25, 0.0, 0.25]],
    [[0.125, -0.125, -0.125], [0.25, -0.25, 0.0], [0.25, -0.25, 0.0]],
    [[0.375, 0.375, 0.375], [0.0, 0.25, -0.25],
        [-0.125, -0.125, -0.125], [-0.25, 0.25, 0.0]],
    [[-0.5, 0.0, 0.0], [-0.125, -0.125, -0.125],
        [-0.25, -0.25, -0.25], [0.125, 0.125, 0.125]],
    [[-0.5, 0.0, 0.0], [-0.125, -0.125, -0.125], [-0.25, -0.25, -0.25]],
    [[0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.0, -0.25, 0.25], [0.0, 0.25, -0.25]],
    [[0.0, -0.5, 0.0], [0.125, 0.125, -0.125], [0.25, 0.25, -0.25]],
    [[0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.125, -0.125, 0.125], [-0.25, -0.0, -0.25], [0.25, 0.0, 0.25]],
    [[0.0, -0.25, 0.25], [0.0, 0.25, -0.25], [0.125, -0.125, 0.125]],
    [[-0.375, -0.375, 0.375], [-0.0, 0.25, 0.25],
        [0.125, 0.125, -0.125], [-0.25, -0.0, -0.25]],
    [[-0.125, 0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, 0.125], [-0.125, 0.125, 0.125]],
    [[-0.0, 0.0, 0.5], [-0.25, -0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[0.25, 0.25, -0.25], [0.25, 0.25, -0.25],
        [0.125, 0.125, -0.125], [-0.125, -0.125, 0.125]],
    [[0.125, -0.125, 0.125], [0.25, -0.25, 0.0], [0.25, -0.25, 0.0]],
    [[0.5, 0.0, 0.0], [0.25, -0.25, 0.25],
        [-0.125, 0.125, -0.125], [0.125, -0.125, 0.125]],
    [[0.0, 0.25, -0.25], [0.375, -0.375, -0.375],
        [-0.125, 0.125, 0.125], [0.25, 0.25, 0.0]],
    [[-0.5, 0.0, 0.0], [-0.25, -0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[0.25, -0.25, 0.0], [-0.25, 0.25, 0.0]],
    [[0.0, 0.5, 0.0], [-0.25, 0.25, 0.25], [0.125, -0.125, -0.125]],
    [[0.0, 0.5, 0.0], [0.125, -0.125, 0.125], [-0.25, 0.25, -0.25]],
    [[0.0, 0.5, 0.0], [0.0, -0.5, 0.0]],
    [[0.25, -0.25, 0.0], [-0.25, 0.25, 0.0], [0.125, -0.125, 0.125]],
    [[-0.375, -0.375, -0.375], [-0.25, 0.0, 0.25],
        [-0.125, -0.125, -0.125], [-0.25, 0.25, 0.0]],
    [[0.125, 0.125, 0.125], [0.0, -0.5, 0.0],
        [-0.25, -0.25, -0.25], [-0.125, -0.125, -0.125]],
    [[0.0, -0.5, 0.0], [-0.25, -0.25, -0.25], [-0.125, -0.125, -0.125]],
    [[-0.125, 0.125, 0.125], [0.25, -0.25, 0.0], [-0.25, 0.25, 0.0]],
    [[0.0, 0.5, 0.0], [0.25, 0.25, -0.25],
        [-0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.375, 0.375, -0.375], [-0.25, -0.25, 0.0],
        [-0.125, 0.125, -0.125], [-0.25, 0.0, 0.25]],
    [[0.0, 0.5, 0.0], [0.25, 0.25, -0.25], [-0.125, -0.125, 0.125]],
    [[0.25, -0.25, 0.0], [-0.25, 0.25, 0.0],
        [0.25, -0.25, 0.0], [0.25, -0.25, 0.0]],
    [[-0.25, -0.25, 0.0], [-0.25, -0.25, 0.0], [-0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.25, -0.25, 0.0], [-0.25, -0.25, 0.0]],
    [[-0.25, -0.25, 0.0], [-0.25, -0.25, 0.0]],
    [[-0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [-0.25, -0.25, 0.0], [0.25, 0.25, -0.0]],
    [[0.0, -0.25, 0.25], [0.0, -0.25, 0.25]],
    [[0.0, 0.0, 0.5], [0.25, -0.25, 0.25], [0.125, -0.125, 0.125]],
    [[0.0, -0.25, 0.25], [0.0, -0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[0.375, -0.375, 0.375], [0.0, -0.25, -0.25],
        [-0.125, 0.125, -0.125], [0.25, 0.25, 0.0]],
    [[-0.125, -0.125, 0.125], [-0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125], [-0.125, 0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [-0.25, 0.0, 0.25], [-0.25, 0.0, 0.25]],
    [[0.5, 0.0, 0.0], [-0.25, -0.25, 0.25],
        [-0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.0, 0.5, 0.0], [-0.25, 0.25, -0.25], [0.125, -0.125, 0.125]],
    [[-0.25, 0.25, -0.25], [-0.25, 0.25, -0.25],
        [-0.125, 0.125, -0.125], [-0.125, 0.125, -0.125]],
    [[-0.25, 0.0, -0.25], [0.375, -0.375, -0.375],
        [0.0, 0.25, -0.25], [-0.125, 0.125, 0.125]],
    [[0.5, 0.0, 0.0], [-0.25, 0.25, -0.25], [0.125, -0.125, 0.125]],
    [[-0.25, 0.0, 0.25], [0.25, 0.0, -0.25]],
    [[-0.0, 0.0, 0.5], [-0.25, 0.25, 0.25], [-0.125, 0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [-0.25, 0.0, 0.25], [0.25, 0.0, -0.25]],
    [[-0.25, -0.0, -0.25], [-0.375, 0.375, 0.375],
        [-0.25, -0.25, 0.0], [-0.125, 0.125, 0.125]],
    [[0.0, 0.0, -0.5], [0.25, 0.25, -0.25], [-0.125, -0.125, 0.125]],
    [[-0.0, 0.0, 0.5], [0.0, 0.0, 0.5]],
    [[0.125, 0.125, 0.125], [0.125, 0.125, 0.125],
        [0.25, 0.25, 0.25], [0.0, 0.0, 0.5]],
    [[0.125, 0.125, 0.125], [0.25, 0.25, 0.25], [0.0, 0.0, 0.5]],
    [[-0.25, 0.0, 0.25], [0.25, 0.0, -0.25], [-0.125, 0.125, 0.125]],
    [[-0.0, 0.0, 0.5], [0.25, -0.25, 0.25],
        [0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[-0.25, 0.0, 0.25], [-0.25, 0.0, 0.25],
        [-0.25, 0.0, 0.25], [0.25, 0.0, -0.25]],
    [[0.125, -0.125, 0.125], [0.25, 0.0, 0.25], [0.25, 0.0, 0.25]],
    [[0.25, 0.0, 0.25], [-0.375, -0.375, 0.375],
        [-0.25, 0.25, 0.0], [-0.125, -0.125, 0.125]],
    [[-0.0, 0.0, 0.5], [0.25, -0.25, 0.25], [0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.25, 0.0, 0.25], [0.25, 0.0, 0.25]],
    [[0.25, 0.0, 0.25], [0.25, 0.0, 0.25]],
    [[-0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [0.0, -0.25, 0.25], [0.0, 0.25, -0.25]],
    [[0.0, -0.5, 0.0], [0.125, 0.125, -0.125],
        [0.25, 0.25, -0.25], [-0.125, -0.125, 0.125]],
    [[0.0, -0.25, 0.25], [0.0, -0.25, 0.25], [0.125, -0.125, 0.125]],
    [[0.0, 0.0, 0.5], [0.25, -0.25, 0.25],
        [0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.0, -0.25, 0.25], [0.0, -0.25, 0.25],
        [0.0, -0.25, 0.25], [0.0, 0.25, -0.25]],
    [[0.0, 0.25, 0.25], [0.0, 0.25, 0.25], [0.125, -0.125, -0.125]],
    [[-0.125, 0.125, 0.125], [0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.125, 0.125, 0.125], [0.125, -0.125, 0.125],
        [-0.125, -0.125, 0.125], [0.125, 0.125, 0.125]],
    [[-0.0, 0.0, 0.5], [-0.25, -0.25, 0.25],
        [-0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[-0.0, 0.5, 0.0], [-0.25, 0.25, -0.25],
        [0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[0.0, -0.25, -0.25], [0.0, 0.25, 0.25], [0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, -0.125]],
    [[0.5, 0.0, -0.0], [0.25, -0.25, -0.25], [0.125, -0.125, -0.125]],
    [[-0.25, 0.25, 0.25], [-0.125, 0.125, 0.125],
        [-0.25, 0.25, 0.25], [0.125, -0.125, -0.125]],
    [[0.375, -0.375, 0.375], [0.0, 0.25, 0.25],
        [-0.125, 0.125, -0.125], [-0.25, 0.0, 0.25]],
    [[0.0, -0.5, 0.0], [-0.25, 0.25, 0.25], [-0.125, 0.125, 0.125]],
    [[-0.375, -0.375, 0.375], [0.25, -0.25, 0.0],
        [0.0, 0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[-0.125, 0.125, 0.125], [-0.25, 0.25, 0.25], [0.0, 0.0, 0.5]],
    [[0.125, 0.125, 0.125], [0.0, 0.25, 0.25], [0.0, 0.25, 0.25]],
    [[0.0, 0.25, 0.25], [0.0, 0.25, 0.25]],
    [[0.5, 0.0, -0.0], [0.25, 0.25, 0.25],
        [0.125, 0.125, 0.125], [0.125, 0.125, 0.125]],
    [[0.125, -0.125, 0.125], [-0.125, -0.125, 0.125], [0.125, 0.125, 0.125]],
    [[-0.25, -0.0, -0.25], [0.25, 0.0, 0.25], [0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, 0.125]],
    [[-0.25, -0.25, 0.0], [0.25, 0.25, -0.0], [0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.25, -0.25, 0.0], [0.25, 0.25, -0.0], [0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, 0.125]],
    [[-0.25, -0.0, -0.25], [0.25, 0.0, 0.25], [0.125, 0.125, 0.125]],
    [[0.125, -0.125, 0.125], [-0.125, -0.125, 0.125], [0.125, 0.125, 0.125]],
    [[0.5, 0.0, -0.0], [0.25, 0.25, 0.25],
        [0.125, 0.125, 0.125], [0.125, 0.125, 0.125]],
    [[0.0, 0.25, 0.25], [0.0, 0.25, 0.25]],
    [[0.125, 0.125, 0.125], [0.0, 0.25, 0.25], [0.0, 0.25, 0.25]],
    [[-0.125, 0.125, 0.125], [-0.25, 0.25, 0.25], [0.0, 0.0, 0.5]],
    [[-0.375, -0.375, 0.375], [0.25, -0.25, 0.0],
        [0.0, 0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[0.0, -0.5, 0.0], [-0.25, 0.25, 0.25], [-0.125, 0.125, 0.125]],
    [[0.375, -0.375, 0.375], [0.0, 0.25, 0.25],
        [-0.125, 0.125, -0.125], [-0.25, 0.0, 0.25]],
    [[-0.25, 0.25, 0.25], [-0.125, 0.125, 0.125],
        [-0.25, 0.25, 0.25], [0.125, -0.125, -0.125]],
    [[0.5, 0.0, -0.0], [0.25, -0.25, -0.25], [0.125, -0.125, -0.125]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, -0.125]],
    [[0.0, -0.25, -0.25], [0.0, 0.25, 0.25], [0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[-0.0, 0.5, 0.0], [-0.25, 0.25, -0.25],
        [0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[-0.0, 0.0, 0.5], [-0.25, -0.25, 0.25],
        [-0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.125, 0.125, 0.125], [0.125, -0.125, 0.125],
        [-0.125, -0.125, 0.125], [0.125, 0.125, 0.125]],
    [[-0.125, 0.125, 0.125], [0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[0.0, 0.25, 0.25], [0.0, 0.25, 0.25], [0.125, -0.125, -0.125]],
    [[0.0, -0.25, -0.25], [0.0, 0.25, 0.25], [0.0, 0.25, 0.25], [0.0, 0.25, 0.25]],
    [[0.0, 0.0, 0.5], [0.25, -0.25, 0.25],
        [0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.0, -0.25, 0.25], [0.0, -0.25, 0.25], [0.125, -0.125, 0.125]],
    [[0.0, -0.5, 0.0], [0.125, 0.125, -0.125],
        [0.25, 0.25, -0.25], [-0.125, -0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [0.0, -0.25, 0.25], [0.0, 0.25, -0.25]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.25, 0.0, 0.25], [0.25, 0.0, 0.25]],
    [[0.125, 0.125, 0.125], [0.25, 0.0, 0.25], [0.25, 0.0, 0.25]],
    [[-0.0, 0.0, 0.5], [0.25, -0.25, 0.25], [0.125, -0.125, 0.125]],
    [[0.25, 0.0, 0.25], [-0.375, -0.375, 0.375],
        [-0.25, 0.25, 0.0], [-0.125, -0.125, 0.125]],
    [[0.125, -0.125, 0.125], [0.25, 0.0, 0.25], [0.25, 0.0, 0.25]],
    [[-0.25, -0.0, -0.25], [0.25, 0.0, 0.25],
        [0.25, 0.0, 0.25], [0.25, 0.0, 0.25]],
    [[-0.0, 0.0, 0.5], [0.25, -0.25, 0.25],
        [0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[-0.25, 0.0, 0.25], [0.25, 0.0, -0.25], [-0.125, 0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.25, 0.25, 0.25], [0.0, 0.0, 0.5]],
    [[0.125, 0.125, 0.125], [0.125, 0.125, 0.125],
        [0.25, 0.25, 0.25], [0.0, 0.0, 0.5]],
    [[-0.0, 0.0, 0.5], [0.0, 0.0, 0.5]],
    [[0.0, 0.0, -0.5], [0.25, 0.25, -0.25], [-0.125, -0.125, 0.125]],
    [[-0.25, -0.0, -0.25], [-0.375, 0.375, 0.375],
        [-0.25, -0.25, 0.0], [-0.125, 0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [-0.25, 0.0, 0.25], [0.25, 0.0, -0.25]],
    [[-0.0, 0.0, 0.5], [-0.25, 0.25, 0.25], [-0.125, 0.125, 0.125]],
    [[-0.25, 0.0, 0.25], [0.25, 0.0, -0.25]],
    [[0.5, 0.0, 0.0], [-0.25, 0.25, -0.25], [0.125, -0.125, 0.125]],
    [[-0.25, 0.0, -0.25], [0.375, -0.375, -0.375],
        [0.0, 0.25, -0.25], [-0.125, 0.125, 0.125]],
    [[-0.25, 0.25, -0.25], [-0.25, 0.25, -0.25],
        [-0.125, 0.125, -0.125], [-0.125, 0.125, -0.125]],
    [[-0.0, 0.5, 0.0], [-0.25, 0.25, -0.25], [0.125, -0.125, 0.125]],
    [[0.5, 0.0, 0.0], [-0.25, -0.25, 0.25],
        [-0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [-0.25, 0.0, 0.25], [-0.25, 0.0, 0.25]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125], [-0.125, 0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [-0.125, 0.125, 0.125]],
    [[0.375, -0.375, 0.375], [0.0, -0.25, -0.25],
        [-0.125, 0.125, -0.125], [0.25, 0.25, 0.0]],
    [[0.0, -0.25, 0.25], [0.0, -0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[0.0, 0.0, 0.5], [0.25, -0.25, 0.25], [0.125, -0.125, 0.125]],
    [[0.0, -0.25, 0.25], [0.0, -0.25, 0.25]],
    [[-0.125, -0.125, 0.125], [-0.25, -0.25, 0.0], [0.25, 0.25, -0.0]],
    [[-0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.125, -0.125, 0.125]],
    [[-0.25, -0.25, 0.0], [-0.25, -0.25, 0.0]],
    [[0.125, 0.125, 0.125], [-0.25, -0.25, 0.0], [-0.25, -0.25, 0.0]],
    [[-0.25, -0.25, 0.0], [-0.25, -0.25, 0.0], [-0.125, -0.125, 0.125]],
    [[-0.25, -0.25, 0.0], [-0.25, -0.25, 0.0],
        [-0.25, -0.25, 0.0], [0.25, 0.25, -0.0]],
    [[0.0, 0.5, 0.0], [0.25, 0.25, -0.25], [-0.125, -0.125, 0.125]],
    [[-0.375, 0.375, -0.375], [-0.25, -0.25, 0.0],
        [-0.125, 0.125, -0.125], [-0.25, 0.0, 0.25]],
    [[0.0, 0.5, 0.0], [0.25, 0.25, -0.25],
        [-0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.125, 0.125, 0.125], [0.25, -0.25, 0.0], [-0.25, 0.25, 0.0]],
    [[0.0, -0.5, 0.0], [-0.25, -0.25, -0.25], [-0.125, -0.125, -0.125]],
    [[0.125, 0.125, 0.125], [0.0, -0.5, 0.0],
        [-0.25, -0.25, -0.25], [-0.125, -0.125, -0.125]],
    [[-0.375, -0.375, -0.375], [-0.25, 0.0, 0.25],
        [-0.125, -0.125, -0.125], [-0.25, 0.25, 0.0]],
    [[0.25, -0.25, 0.0], [-0.25, 0.25, 0.0], [0.125, -0.125, 0.125]],
    [[0.0, 0.5, 0.0], [0.0, -0.5, 0.0]],
    [[0.0, 0.5, 0.0], [0.125, -0.125, 0.125], [-0.25, 0.25, -0.25]],
    [[0.0, 0.5, 0.0], [-0.25, 0.25, 0.25], [0.125, -0.125, -0.125]],
    [[0.25, -0.25, 0.0], [-0.25, 0.25, 0.0]],
    [[-0.5, 0.0, 0.0], [-0.25, -0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[0.0, 0.25, -0.25], [0.375, -0.375, -0.375],
        [-0.125, 0.125, 0.125], [0.25, 0.25, 0.0]],
    [[0.5, 0.0, 0.0], [0.25, -0.25, 0.25],
        [-0.125, 0.125, -0.125], [0.125, -0.125, 0.125]],
    [[0.125, -0.125, 0.125], [0.25, -0.25, 0.0], [0.25, -0.25, 0.0]],
    [[0.25, 0.25, -0.25], [0.25, 0.25, -0.25],
        [0.125, 0.125, -0.125], [-0.125, -0.125, 0.125]],
    [[-0.0, 0.0, 0.5], [-0.25, -0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, 0.125], [-0.125, 0.125, 0.125]],
    [[-0.125, 0.125, 0.125], [0.125, -0.125, 0.125]],
    [[-0.375, -0.375, 0.375], [-0.0, 0.25, 0.25],
        [0.125, 0.125, -0.125], [-0.25, -0.0, -0.25]],
    [[0.0, -0.25, 0.25], [0.0, 0.25, -0.25], [0.125, -0.125, 0.125]],
    [[0.125, -0.125, 0.125], [-0.25, -0.0, -0.25], [0.25, 0.0, 0.25]],
    [[0.125, -0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.0, -0.5, 0.0], [0.125, 0.125, -0.125], [0.25, 0.25, -0.25]],
    [[0.0, -0.25, 0.25], [0.0, 0.25, -0.25]],
    [[0.125, 0.125, 0.125], [0.125, -0.125, 0.125]],
    [[0.125, -0.125, 0.125]],
    [[-0.5, 0.0, 0.0], [-0.125, -0.125, -0.125], [-0.25, -0.25, -0.25]],
    [[-0.5, 0.0, 0.0], [-0.125, -0.125, -0.125],
        [-0.25, -0.25, -0.25], [0.125, 0.125, 0.125]],
    [[0.375, 0.375, 0.375], [0.0, 0.25, -0.25],
        [-0.125, -0.125, -0.125], [-0.25, 0.25, 0.0]],
    [[0.125, -0.125, -0.125], [0.25, -0.25, 0.0], [0.25, -0.25, 0.0]],
    [[0.125, 0.125, 0.125], [0.375, 0.375, 0.375],
        [0.0, -0.25, 0.25], [-0.25, 0.0, 0.25]],
    [[-0.25, 0.0, 0.25], [-0.25, 0.0, 0.25], [0.125, -0.125, -0.125]],
    [[0.0, -0.25, -0.25], [0.0, 0.25, 0.25], [-0.125, 0.125, 0.125]],
    [[-0.125, 0.125, 0.125], [0.125, -0.125, -0.125]],
    [[-0.125, -0.125, -0.125], [-0.25, -0.25, -0.25],
        [0.25, 0.25, 0.25], [0.125, 0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[0.0, 0.0, -0.5], [0.25, 0.25, 0.25], [-0.125, -0.125, -0.125]],
    [[0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[0.0, -0.5, 0.0], [0.25, 0.25, 0.25], [0.125, 0.125, 0.125]],
    [[-0.125, -0.125, 0.125], [0.125, -0.125, -0.125]],
    [[0.0, -0.25, -0.25], [0.0, 0.25, 0.25]],
    [[0.125, -0.125, -0.125]],
    [[0.5, 0.0, 0.0], [0.5, 0.0, 0.0]],
    [[-0.5, 0.0, 0.0], [-0.25, 0.25, 0.25], [-0.125, 0.125, 0.125]],
    [[0.5, 0.0, 0.0], [0.25, -0.25, 0.25], [-0.125, 0.125, -0.125]],
    [[0.25, -0.25, 0.0], [0.25, -0.25, 0.0]],
    [[0.5, 0.0, 0.0], [-0.25, -0.25, 0.25], [-0.125, -0.125, 0.125]],
    [[-0.25, 0.0, 0.25], [-0.25, 0.0, 0.25]],
    [[0.125, 0.125, 0.125], [-0.125, 0.125, 0.125]],
    [[-0.125, 0.125, 0.125]],
    [[0.5, 0.0, -0.0], [0.25, 0.25, 0.25], [0.125, 0.125, 0.125]],
    [[0.125, -0.125, 0.125], [-0.125, -0.125, 0.125]],
    [[-0.25, -0.0, -0.25], [0.25, 0.0, 0.25]],
    [[0.125, -0.125, 0.125]],
    [[-0.25, -0.25, 0.0], [0.25, 0.25, -0.0]],
    [[-0.125, -0.125, 0.125]],
    [[0.125, 0.125, 0.125]],
    [[0, 0, 0]]]
# pylint: enable=line-too-long


def create_table_neighbour_code_to_surface_area(spacing_mm):
    """Returns an array mapping neighbourhood code to the surface elements area.
    Note that the normals encode the initial surface area. This function computes
    the area corresponding to the given `spacing_mm`.
    Args:
      spacing_mm: 3-element list-like structure. Voxel spacing in x0, x1 and x2
        direction.
    """
    # compute the area for all 256 possible surface elements
    # (given a 2x2x2 neighbourhood) according to the spacing_mm
    neighbour_code_to_surface_area = np.zeros([256])
    for code in range(256):
        normals = np.array(_NEIGHBOUR_CODE_TO_NORMALS[code])
        sum_area = 0
        for normal_idx in range(normals.shape[0]):
            # normal vector
            n = np.zeros([3])
            n[0] = normals[normal_idx, 0] * spacing_mm[1] * spacing_mm[2]
            n[1] = normals[normal_idx, 1] * spacing_mm[0] * spacing_mm[2]
            n[2] = normals[normal_idx, 2] * spacing_mm[0] * spacing_mm[1]
            area = np.linalg.norm(n)
            sum_area += area
        neighbour_code_to_surface_area[code] = sum_area

    return neighbour_code_to_surface_area


# In the neighbourhood, points are ordered: top left, top right, bottom left,
# bottom right.
ENCODE_NEIGHBOURHOOD_2D_KERNEL = np.array([[8, 4], [2, 1]])


def create_table_neighbour_code_to_contour_length(spacing_mm):
    """Returns an array mapping neighbourhood code to the contour length.
    For the list of possible cases and their figures, see page 38 from:
    https://nccastaff.bournemouth.ac.uk/jmacey/MastersProjects/MSc14/06/thesis.pdf
    In 2D, each point has 4 neighbors. Thus, are 16 configurations. A
    configuration is encoded with '1' meaning "inside the object" and '0' "outside
    the object". The points are ordered: top left, top right, bottom left, bottom
    right.
    The x0 axis is assumed vertical downward, and the x1 axis is horizontal to the
    right:
     (0, 0) --> (0, 1)
       |
     (1, 0)
    Args:
      spacing_mm: 2-element list-like structure. Voxel spacing in x0 and x1
        directions.
    """
    neighbour_code_to_contour_length = np.zeros([16])

    vertical = spacing_mm[0]
    horizontal = spacing_mm[1]
    diag = 0.5 * math.sqrt(spacing_mm[0]**2 + spacing_mm[1]**2)
    # pyformat: disable
    neighbour_code_to_contour_length[int("00"
                                         "01", 2)] = diag

    neighbour_code_to_contour_length[int("00"
                                         "10", 2)] = diag

    neighbour_code_to_contour_length[int("00"
                                         "11", 2)] = horizontal

    neighbour_code_to_contour_length[int("01"
                                         "00", 2)] = diag

    neighbour_code_to_contour_length[int("01"
                                         "01", 2)] = vertical

    neighbour_code_to_contour_length[int("01"
                                         "10", 2)] = 2*diag

    neighbour_code_to_contour_length[int("01"
                                         "11", 2)] = diag

    neighbour_code_to_contour_length[int("10"
                                         "00", 2)] = diag

    neighbour_code_to_contour_length[int("10"
                                         "01", 2)] = 2*diag

    neighbour_code_to_contour_length[int("10"
                                         "10", 2)] = vertical

    neighbour_code_to_contour_length[int("10"
                                         "11", 2)] = diag

    neighbour_code_to_contour_length[int("11"
                                         "00", 2)] = horizontal

    neighbour_code_to_contour_length[int("11"
                                         "01", 2)] = diag

    neighbour_code_to_contour_length[int("11"
                                         "10", 2)] = diag
    # pyformat: enable

    return neighbour_code_to_contour_length