package

imea.measure_3d

3-dimensional shape measurements.

module

imea.measure_3d.macro

3-dimensional macrodescriptors.

Functions
  • feret_and_max_dimensions_3d(convex_hull, spatial_resolution, dalpha) (tuple) — Calculates 3D feret diameter (min, max) and max dimensions (x_max, y_max, z_max) [1].
  • min_3d_bounding_box(img_3d_equalspace, spatial_resolution) (tuple) — Calculate minimal 3-dimensional bounding box from a 3D grayscale image.
  • surfacearea_convexhull(convex_hull, spatial_resolution) (float) — Calculate surface area of convex hull.
  • surfacearea_equivalent_diameter(surface_area) (float) — Calculate surfacearea-equivalent diameter.
  • volume(img_3d_equalspace, spatial_resolution) (float) — Calculate volume.
  • volume_convexhull(convex_hull, spatial_resolution) (float) — Calculate volume of convex hull.
  • volume_equivalent_diameter(volume) (float) — Calculate volume equivalent diameter.
function

imea.measure_3d.macro.volume(img_3d_equalspace, spatial_resolution)

Calculate volume.

Parameters
  • img_3d_equalspace (numpy.ndarray, type float) — 2-dimensional grayscale heightmap of single object with equal spacing, i.e. dx = dy = dz. Pixels not showing the pixel should be 0.
  • spatial_resolution (float) — Spatial resolution of img_3d_equalspace in [mm/Voxel]. The following must be true: spatial_resolution == dx == dy == dz.
Returns (float)
  • volume (float): Volume in [mm^3].
function

imea.measure_3d.macro.volume_convexhull(convex_hull, spatial_resolution)

Calculate volume of convex hull.

Parameters
  • convex_hull (scipy.spatial.ConvexHull) — Convex Hull.
  • spatial_resolution (float) — Spatial resolution of convex_hull in [mm/Voxel].
Returns (float)
  • volume_convexhull (float): Volume of convex hull in [mm^3].
function

imea.measure_3d.macro.volume_equivalent_diameter(volume)

Calculate volume equivalent diameter.

Parameters
  • volume (float) — Volume.
Returns (float)
  • volume_equivalent_diameter (float): Volume-equivalent diameter.
function

imea.measure_3d.macro.surfacearea_convexhull(convex_hull, spatial_resolution)

Calculate surface area of convex hull.

Parameters
  • convex_hull (scipy.spatial.ConvexHull) — Convex Hull.
  • spatial_resolution (float) — Spatial resolution of convex_hull in [mm/Voxel].
Returns (float)
  • surface_area (float): Surface area of convex hull in [mm^2].
function

imea.measure_3d.macro.surfacearea_equivalent_diameter(surface_area)

Calculate surfacearea-equivalent diameter.

Parameters
  • surface_area (float) — Surface area.
Returns (float)
  • surfacearea_equivalent_diameter (float): Surface area-equivalent diameter.
function

imea.measure_3d.macro.min_3d_bounding_box(img_3d_equalspace, spatial_resolution)

Calculate minimal 3-dimensional bounding box from a 3D grayscale image.

Parameters
  • img_3d_equalspace (numpy.ndarray, type float) — 2-dimensional grayscale heightmap of single object with equal spacing, i.e. dx = dy = dz. Pixels not showing the pixel should be 0.
  • spatial_resolution (float) — Spatial resolution of img_3d_equalspace in [mm/Voxel]. The following must be true: spatial_resolution == dx == dy == dz.
Returns (tuple)
  • length (float): Length of minimal 3-dimensional bounding box.
  • width (float): Width of minimal 3-dimensional bounding box.
  • height (float): Height of minimal 3-dimensional bounding box.

Notes

length and width are identical to the 2d bounding box. height is the maximum height in z-direction.

function

imea.measure_3d.macro.feret_and_max_dimensions_3d(convex_hull, spatial_resolution, dalpha=9)

Calculates 3D feret diameter (min, max) and max dimensions (x_max, y_max, z_max) [1].

Parameters
  • convex_hull (scipy.spatial.ConvexHull) — 3D convex hull.
  • spatial_resolution (float) — Spatial resolution of convex_hull in [mm].
  • dalpha (int, optional) — Angle in degrees by which convex_hull at each iteration, by default 9.
Returns (tuple)
  • feret_3d_max (float): Max feret diameter.
  • feret_3d_min (float): Min feret diameter.
  • x_max_3d (float): x_max (equal to max_feret) [1].
  • y_max_3d (float): y_max (orthogonal to x_max) [1].
  • z_max_3d (float): z_max (orthogonal to x_max and y_max) [1].
References

[1] M. Steuer (2010). "Serial classification". In: AT Mineral Processing 51(1).

module

imea.measure_3d.utils

Helping functions for 3-dimensional shape measurements.

Functions
  • compute_convexhull(img_3d_equalspace) (scipy.spatial.ConvexHull) — Calculate convex hull from 3d image.
function

imea.measure_3d.utils.compute_convexhull(img_3d_equalspace)

Calculate convex hull from 3d image.

Parameters
  • img_3d_equalspace (numpy.ndarray, type float) — 2-dimensional grayscale heightmap of single object with equal spacing, i.e. dx = dy = dz. Pixels not showing the pixel should be 0.
Returns (scipy.spatial.ConvexHull)
  • convex_hull (scipy.spatial.ConvexHull): Convex hull.