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Morphometrics Quantifications Documentation

Index

  • Type: Integer
  • Description:
    An identifier for each triangle in the mesh. Serves as the primary key for a given surface and is used to cross-reference data (e.g., in the [label]_neighbor_index column). The index is set when pycurv is run; any filtering afterward (such as patch extraction or edge filtering) does not reindex.

Area

  • Type: Float
  • Description:
    The surface area of the individual triangle. Important for quantitative analysis, as it allows for area-weighted statistical calculations (e.g., histograms). By weighting metrics by triangle area, larger membrane regions contribute proportionally more to overall statistics, providing a more accurate representation of the surface's properties.

min_curvature

  • Type: Float
  • Description:
    The minimum absolute curvature value at each point on the surface.

max_curvature

  • Type: Float
  • Description:
    The maximum absolute curvature value at each point on the surface.

Gauss_curvature

  • Type: Float
  • Description:
    The Gaussian curvature measured at each point on the surface, prior to vector voting. Calculated as the product of the two principal curvatures at that point. Note: Use gauss_curvature_vv instead for analysis, as it provides more robust measurements.

mean_curvature

  • Type: Float
  • Description:
    The mean curvature value computed at each point on the surface, before any vector voting or smoothing operations. Mean curvature is calculated as the average of the curvatures in all directions at a point. Note: Use mean_curvature_vv instead for analysis, as it provides more robust measurements.

kappa_1

  • Type: Float
  • Description:
    The first principal curvature value at each point on the surface.

kappa_2

  • Type: Float
  • Description:
    The second principal curvature value at each point on the surface.

gauss_curvature_vv

  • Type: Float
  • Description:
    PREFERRED VERSION - The Gaussian curvature, calculated as the product of the two principal curvatures (kappa_1 * kappa_2) after vector voting. The sign indicates local surface shape:
    • Positive (> 0): Surface is elliptical or "bowl-shaped"
    • Negative (< 0): Surface is hyperbolic or "saddle-shaped"
    • Zero (= 0): Surface is flat in at least one direction

mean_curvature_vv

  • Type: Float
  • Description:
    PREFERRED VERSION - The mean curvature, calculated as the average of the two principal curvatures: (kappa_1 + kappa_2) / 2 after vector voting. Describes the average bending of the surface at a specific point:
    • Positive (> 0): The surface is, on average, curving inwards (concave)
    • Negative (< 0): The surface is, on average, curving outwards (convex)
    • Zero (= 0): The surface is a minimal surface

Orientation_class

  • Description:
    A classification for each triangle describing the consistency of normal vectors within its local geodesic neighborhood. Controlled by the epsilon and eta parameters in pycurv functions, which set thresholds for the classes.
  • Classes:
    • Class 1 (Preferred Orientation): Neighboring triangle normals are highly consistent and point in a similar direction, indicating a smooth, well-defined surface patch. Most triangles on a quality mesh belong to this class.
    • Class 2 (Crease Junction): Neighboring normals are aligned along a line or "crease," indicating a sharp edge or fold.
    • Class 3 (No Preferred Orientation): Neighboring normals are inconsistent and point in random directions, indicating high, complex curvature, noise, or mesh artifact.

shape_index_VV

  • Description:
    PREFERRED VERSION - A continuous value ranging from -1 to +1 that describes the local shape of the surface at each triangle, derived from principal curvatures (kappa_1 and kappa_2) after vector voting.
  • Values:
    • -0.75: Trough
    • -0.5: Rut (concave cylinder)
    • -0.25: Saddle Rut
    • 0.0: Saddle (a perfect saddle shape, where kappa_1 = -kappa_2)
    • +0.25: Saddle Ridge
    • +0.5: Ridge (convex cylinder)
    • +0.75: Dome
    • +1.0: Spherical Cap (a perfectly convex bump)

curvedness_vv

  • Type: Float
  • Description:
    PREFERRED VERSION - A measure of the overall magnitude of curvature at a given point on the surface, calculated as sqrt((kappa_1^2 + kappa_2^2) / 2) after vector voting. Always non-negative.

shape_index_cat

  • Description:
    A numerical property that categorizes the continuous shape_index_VV value into one of nine shape classes, storing a single representative float value for each class. Based on the preferred vector-voted shape index.
  • Values:
    • -0.75: Trough
    • -0.5: Rut (concave cylinder)
    • -0.25: Saddle Rut
    • 0.0: Saddle (a perfect saddle shape, where kappa_1 = -kappa_2)
    • +0.25: Saddle Ridge
    • +0.5: Ridge (convex cylinder)
    • +0.75: Dome
    • +1.0: Spherical Cap (a perfectly convex bump)

Verticality

  • Description:
    The angle of the triangle's surface plane relative to the XY plane of the tomogram, ranging from 0° (perfectly horizontal, parallel to XY) to 90° (perfectly vertical, perpendicular to XY). Calculated using the vector-voted normal (n_v).

self_dist_min

  • Description:
    The shortest distance from the center of a triangle to another part of the same surface, measured along the triangle's normal vector. For each triangle, two rays are cast from its center along the normal vector (n_v), one in each direction. The first intersection point with the mesh is found in each direction; self_dist_min is the shorter of these distances. If no intersection is found, the value is NaN.

self_id_min

  • Description:
    The index of the triangle on the same surface that was intersected at the distance reported in self_dist_min.

self_dist_far

  • Description:
    The longest distance from the center of a triangle to another part of the same surface, measured along the triangle's normal vector. This value is calculated in the same process as self_dist_min.

self_id_far

  • Description:
    The index of the triangle on the same surface that was intersected at the distance reported in self_dist_far.

average_width

  • Description:
    The width of the overall connected component. This is not an average for individual triangles, but a measurement representing the connected region as a whole.

CLASS_dist

  • Description:
    The shortest Euclidean distance from a given triangle to the closest triangle that belongs to a different class or category. [CLASS] is a placeholder for the name of the other surface being measured against.

CLASS_neighbor_index

  • Description:
    The index of the nearest triangle on the target surface specified by [CLASS].

CLASS_orientation

  • Description:
    The relative angle between the normal vector (n_v) of a triangle on the current surface and the normal vector of its neighbor on the target surface specified by [CLASS]. The angle is calculated as the acute angle, always between 0 and 90 degrees.

Subcompartment

  • Description:
    A label assigned to a group of triangles on a larger surface to define a region of biological interest.

xyz_x, xyz_y, xyz_z

  • Description:
    The coordinates representing the center of each triangle in the mesh.

normal_x, normal_y, normal_z

  • Description:
    The x, y, and z components of the normal vector representing the orientation of the surface at each point, as a unit vector in 3D space.

n_v_x, n_v_y, n_v_z

  • Description:
    The x, y, and z components of the voted normal vector for each triangle.

t_v_x, t_v_y, t_v_z

  • Description:
    The components of a tangent vector assigned to each vertex of the surface mesh.

t_1_x, t_1_y, t_1_z

  • Description:
    The components of the first principal direction (tangent) vector at each vertex, typically aligned with the direction of maximum curvature on the surface at that point.

t_2_x, t_2_y, t_2_z

  • Description:
    The components of the second principal direction (tangent) vector at each vertex, typically perpendicular to the first principal direction.

Average_width

  • Description:
    A value representing the average width of an entire connected component of a surface. This is a per-component metric, not a per-triangle one.

Thickness

  • Description:
    A per-triangle value representing the local thickness of a single membrane sheet. It is calculated by measuring the shortest distance from a triangle's center along its normal vector until the surface is intersected again.