pykarambola 0.3.0

Python implementation of Karambola – Minkowski tensors on 3D triangulated surfaces

pykarambola

pykarambola computes Minkowski tensors for 3D objects represented as triangulated meshes — a family of shape descriptors rooted in integral geometry that rigorously quantify size, shape, and orientation. Given a mesh, it returns scalar, vector, and tensor quantities including volume, surface area, integrated mean curvature, and Euler characteristic (the Minkowski functionals), as well as higher-rank tensors that capture anisotropy and preferred orientation independently of coordinate frame. pykarambola is a Python implementation of karambola, the reference C++ package for Minkowski tensor computation on 3D triangulated surfaces. Minkowski tensors are widely applicable to analyzing 3D structures in biomedical imaging, computational physics, and materials science.

New in pykarambola

Compared to the original C++ karambola, this Python port adds:

• OBJ and GLB parsers — read Wavefront OBJ and binary glTF (.glb) meshes directly, in addition to the original .poly and .off formats.
• High-level API — minkowski_tensors() accepts NumPy arrays and returns a plain dict, making it easy to integrate into pipelines without dealing with the lower-level triangulation types.
• labels='auto' — pass labels='auto' to detect connected mesh components automatically and compute tensors for each body separately, without supplying a face-label array.
• return_count=True — append the number of connected objects to the return value as a (results, n_objects) tuple.
• Derived scalar quantities — each rank-2 tensor (e.g. w020) additionally yields {name}_beta (anisotropy index: ratio of smallest to largest eigenvalue magnitude), {name}_trace (matrix trace), and {name}_trace_ratio (trace divided by the corresponding Minkowski scalar, e.g. w020_trace_ratio = Tr(w020) / w000). These are pykarambola-specific extensions not present in C++ karambola; they are included in the compute='all' preset.
• Label-image API — minkowski_tensors_from_label_image() extracts surfaces from a 3D integer label image via marching cubes and computes tensors for every label in one call.

Requirements

• Python ≥ 3.9
• NumPy
• SciPy

Optional:

• Cython ≥ 3.0 — compiled C acceleration (pip install "pykarambola[accel]")
• scikit-image — label-image API (pip install "pykarambola[dev]")
• trimesh — GLB/glTF file support (pip install "pykarambola[glb]")

Installation

pip install pykarambola

For optional Cython acceleration:

pip install "pykarambola[accel]"

For development (includes pytest and scikit-image):

pip install "pykarambola[dev]"

GLB/glTF support requires trimesh:

pip install "pykarambola[glb]"

High-level API

From NumPy arrays

minkowski_tensors() is the main entry point. Pass vertices and faces as NumPy arrays and get back a plain dict:

import pykarambola as pk

result = pk.minkowski_tensors(
    verts,   # (V, 3) float64 array of vertex positions
    faces,   # (F, 3) int64 array of vertex indices
)

print(result["w000"])   # volume
print(result["w100"])   # surface area
print(result["w200"])   # integrated mean curvature
print(result["w300"])   # Euler characteristic
print(result["w020"])   # 3×3 Minkowski tensor
print(result["w020_eigvals"])   # eigenvalues of w020
print(result["w020_eigvecs"])   # eigenvectors of w020 (columns)

Control which quantities are computed with the compute argument:

# default: 14 standard tensors + eigensystems for rank-2 tensors
result = pk.minkowski_tensors(verts, faces, compute="standard")

# include higher-order tensors (w103, w104) and spherical Minkowski metrics
result = pk.minkowski_tensors(verts, faces, compute="all")

# compute only specific quantities
result = pk.minkowski_tensors(verts, faces, compute=["w000", "w100", "w020"])

If the mesh has boundary edges (open surface), w000 and w020 are set to NaN and a UserWarning is emitted. Non-manifold meshes also emit a UserWarning but are otherwise computed.

From a 3D label image

minkowski_tensors_from_label_image() takes a 3D integer array, runs marching cubes on each label, and returns a dict of results keyed by label value. Requires scikit-image.

import numpy as np
import pykarambola as pk

label_image = np.zeros((64, 64, 64), dtype=int)
label_image[10:40, 10:40, 10:40] = 1
label_image[40:60, 40:60, 40:60] = 2

result = pk.minkowski_tensors_from_label_image(
    label_image,
    spacing=(0.5, 0.5, 0.5),   # voxel size in physical units
    center="centroid_mesh",     # shift tensors to per-label centroid
)

print(result[1]["w000"])   # volume of label 1
print(result[2]["w100"])   # surface area of label 2

By default a 1-voxel zero border is added before running marching cubes (pad=True), so objects touching the array boundary produce closed surfaces. Pass pad=False to skip this.

The center argument controls the reference point for position-dependent tensors:

Value	Behaviour
None (default for mesh API)	Use the array origin (0, 0, 0)
'centroid_mesh' (default for label-image API)	Shift each object to its volume-weighted centre of mass
'centroid_voxel'	Use the mean voxel coordinate (label-image API only)
'reference_centroid'	Reproduce the C++ karambola --reference_centroid flag
(3,) array	Apply an explicit fixed shift

Multi-label meshes

Pass per-face integer labels to compute tensors for multiple bodies in a single mesh:

result = pk.minkowski_tensors(verts, faces, labels=face_labels)
# result is dict[int, dict]
print(result[1]["w000"])
print(result[2]["w000"])

Or let pykarambola detect connected components automatically:

result = pk.minkowski_tensors(verts, faces, labels="auto")
# bodies are numbered 1, 2, … by connected component
print(result[1]["w000"])

File I/O

pykarambola can read four mesh formats. The parsers return a Triangulation object that can be passed directly to minkowski_tensors().

surface = pk.parse_poly_file("my_surface.poly")   # karambola native
surface = pk.parse_off_file("my_surface.off")     # Object File Format
surface = pk.parse_obj_file("my_surface.obj")     # Wavefront OBJ  (new)
surface = pk.parse_glb_file("my_surface.glb")     # binary glTF    (new, requires trimesh)

result = pk.minkowski_tensors(surface)

Extension	Description
.poly	karambola native format
.off	Object File Format
.obj	Wavefront OBJ
.glb	GL Transmission Format (binary glTF) — requires trimesh

Command-line interface

python -m pykarambola [options] <surface_file>

Supported input formats: .poly, .off, .obj, .glb. Run python -m pykarambola --help for the full list of options.

Computed quantities

All quantities below are returned by compute='standard' unless noted (compute='all').

Name	Type	Description
w000	scalar	Volume
w100	scalar	Surface area
w200	scalar	Integrated mean curvature
w300	scalar	Euler characteristic
w010	vector	Minkowski vector (volume)
w110	vector	Minkowski vector (surface)
w210	vector	Minkowski vector (curvature)
w310	vector	Minkowski vector (topology)
w020	rank-2 tensor	Minkowski tensor (volume)
w120	rank-2 tensor	Minkowski tensor (surface)
w220	rank-2 tensor	Minkowski tensor (curvature)
w320	rank-2 tensor	Minkowski tensor (topology)
w102	rank-2 tensor	Minkowski tensor (surface, normal-normal)
w202	rank-2 tensor	Minkowski tensor (curvature, normal-normal)
w103	rank-3 tensor	Higher-order tensor (compute='all')
w104	rank-4 tensor	Higher-order tensor (compute='all')
msm_ql, msm_wl	arrays	Minkowski structure metrics (spherical, compute='all')
{name}_beta	scalar	Anisotropy index: min|λ| / max|λ| for each rank-2 tensor (compute='all')
{name}_trace	scalar	Trace of each rank-2 tensor matrix (compute='all')
{name}_trace_ratio	scalar	Trace divided by corresponding Minkowski scalar, e.g. Tr(w020)/w000 (wX20 family only; compute='all')

Rank-2 tensors additionally yield {name}_eigvals and {name}_eigvecs entries.

Citation

If you use pykarambola in published work, please cite both pykarambola and the original karambola package.

Ishihara, K., & Khurana, Y. pykarambola: Minkowski tensor morphometry of 3D structures (v0.3.0). https://doi.org/10.5281/zenodo.XXXXXXX

Schaller, F. M., Kapfer, S. C., & Schröder-Turk, G. E. karambola — 3D Minkowski Tensor Package (v2.0). https://github.com/morphometry/karambola

Note: Version, DOI, and release year will be updated after v1.0.0 is released (see CITATION.cff for machine-readable metadata).

Contributing

See CONTRIBUTING.md for development setup, Git workflow, versioning, and release instructions. See CHANGELOG.md for a history of changes between versions.

License

See LICENSE.