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bkgco — Python wrapper for the BK and GCO optimization libraries

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The bkgco Python package wraps two related C++ libraries:

  • maxflow: the Boykov-Kolmogorov (BK) algorithm for graph-cuts, and
  • gco: graph-cut optimization (GCO) algorithms for minimizing multi-label energies.

Three types are provided by bkgco:

  • BKGraph constructs a graph from arc weights and maximizes an s-t maximum flow.
  • BKEnergy constructs a graph from binary energy terms and minimizes the energy.
  • GCO iteratively minimizes a multi-label energy, using a graph-cut at each iteration.

Cost terms, neighbour indices, and weights are all passed as NumPy arrays for efficiency. See the

BKGraph example

from bkgco import BKGraph

with BKGraph() as g:

    # Arc weights (from source, to sink) for each node
    g.add_tweights([[5, 0],
                    [2, 0],
                    [0, 9]])

    # Arc weights between nodes
    g.add_edges([[0, 1], [1, 2]],  # Node index pairs (i,j)
                [[1, 0], [4, 0]])  # Weights for each (i->j) and (j->i)

    # Maximum flow is 3 with only node 0 disconnected from the sink.
    flow = g.maxflow()       # 3
    segs = g.get_segments()  # array([0, 1, 1], dtype=uint8)

The above code builds the s-t flow graph below and maximizes the flow, cutting off node 0 (leftmost) from the sink (t).

      ┌────────(s)
      │         │
     5│        2│
      │         │
      ▼         ▼   
     (0)──────▶(1)─────▶(2)
           1        4    │
                         │ 9
                         │
               (t)◀──────┘

BKEnergy example

The code below defines a binary energy corresponding exactly to the above s-t flow graph.

from bkgco import BKEnergy

with BKEnergy() as e:

	# Add unary terms for E(x,y,z) = 5x + 2y + 9(1-z) + (1-x)y + 4(1-y)z
	e.add_term1([[0, 5],           # 5x
	             [0, 2],           # 2y
	             [9, 0]])          # 9(1-z)

	# Add pairwise terms
	e.add_term2([[0, 1], [1, 2]],  # Indices of (x,y) and (y,z) respectively.
	            [[0, 1, 0, 0],     # (1-x)y
	             [0, 4, 0, 0]])    # 4(1-y)z

	# Minimum is 3 with x=0, y=1, z=1
	e_min = e.minimize()      # 3
	e_sol = e.get_solution()  # array([0, 1, 1], dtype=uint8)

GCO example

from bkgco import GCO

D = [[0, 3, 5],  # Data cost (4 sites x 3 labels)
     [9, 9, 0],
     [2, 0, 3],
     [0, 3, 5]]

V = [[0, 1, 2],  # Smooth cost (3 labels x 3 labels)
     [1, 0, 1],
     [2, 1, 0]]

N = [[0, 1],     # Neighbours (i,j) at which to apply cost V
     [1, 2],
     [2, 3]]

W = [3, 1, 3]    # Weight of cost V for each neighbour in N

with GCO(num_sites=4, num_labels=3) as g:
    # Set costs and neighbours
    g.set_data_cost(D)
    g.set_smooth_cost(V)
    g.set_neighbors(N, W)

    # Minimum is 9 with labeling (2,2,0,0)
    e = g.expansion()         # 9
    l = g.get_labeling()      # array([2, 2, 0, 0], dtype=int32)

Docs

See the API docs.

Dependencies

  • Python >= 3.10
  • Numpy >= 1.21

Building

Build in-place for testing:

python setup.py build_ext --inplace     # builds bkgco/_bkgco*.so
python -m unittest discover -s tests

Build and install locally, so that import bkgco works from anywhere:

pip install -e .

Note for macOS. If a non-Apple clang++ is first on PATH, e.g. Homebrew LLVM, then prefix build commands with CC=/usr/bin/clang CXX=/usr/bin/clang++ or first run export SDKROOT=$(xcrun --show-sdk-path).

Notes

Features:

  • Label costs. Label costs and label subset costs are supported on GCO.
  • Data types. Arc weights and energy term costs can be NumPy arrays of dtype=int32/int64/float64.
  • No dynamic cuts. The reuse_trees feature of maxflow is not yet exposed by this wrapper.
  • Ctrl-C. Calls to expansion/swap are safely keyboard-interruptible, for interactive development in notebooks.
  • Typed. All methods carry inline type hints for improved type checking and success rates by coding agents.

Usage:

  • Specifying a dtype. With dtype=None (the default) the dtype is determined by the first cost array passed in.
  • Recommended dtype. Map costs to the smallest int32 range that suffices for your application. With float64, expansion/swap can rarely report a small energy increase from rounding inside max-flow, and Inf/NaN terms are undefined behavior.

Technical:

  • Array sharing. GCO's data and smooth cost arrays are passed to C++ by reference (no copy). Changes to the D and V arrays are seen immediately, but call set_data_cost(D) and set_smooth_cost(V) again (cheap) to invalidate cached energy values.
  • Threads. The GIL is released so that independent GCO objects run in parallel; calls on one object are serialized by a per-object mutex. The module declares Py_MOD_GIL_NOT_USED, so it works on free-threaded CPython without re-enabling the GIL.
  • Errors. Invalid arguments raise ValueError/TypeError; the C++ library's own checks (overflow, non-metric smooth costs, unsorted sparse costs, ...) raise RuntimeError.

Citation / license

Usage of this wrapper is governed by the terms in cpp/gco/GCO_README.TXT.

Acknowledgements

This wrapper was generated mostly by Claude Code under the guidance of a human with expertise on the underlying software. All credit for the maxflow and GCO libraries goes to their original developers.

Metadata

Release files for bkgco 0.1.0

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Source distribution (sdist)

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Table of built distributions (wheels) for bkgco 0.1.0
File
bkgco-0.1.0-cp314-cp314t-win_amd64.whl CPython 3.14 CPython 3.14 free-threading Windows x86-64 Details
bkgco-0.1.0-cp314-cp314t-musllinux_1_2_x86_64.whl CPython 3.14 CPython 3.14 free-threading Linux musl 1.2+ x86-64 Details
bkgco-0.1.0-cp314-cp314t-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64 Details
bkgco-0.1.0-cp314-cp314t-macosx_11_0_arm64.whl CPython 3.14 CPython 3.14 free-threading macOS 11.0+ ARM64 Details
bkgco-0.1.0-cp314-cp314t-macosx_10_15_x86_64.whl CPython 3.14 CPython 3.14 free-threading macOS 10.15+ x86-64 Details
bkgco-0.1.0-cp313-cp313-win_amd64.whl CPython 3.13 CPython 3.13 Windows x86-64 Details
bkgco-0.1.0-cp313-cp313-musllinux_1_2_x86_64.whl CPython 3.13 CPython 3.13 Linux musl 1.2+ x86-64 Details
bkgco-0.1.0-cp313-cp313-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl CPython 3.13 CPython 3.13 Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64 Details
bkgco-0.1.0-cp313-cp313-macosx_11_0_arm64.whl CPython 3.13 CPython 3.13 macOS 11.0+ ARM64 Details
bkgco-0.1.0-cp313-cp313-macosx_10_13_x86_64.whl CPython 3.13 CPython 3.13 macOS 10.13+ x86-64 Details
bkgco-0.1.0-cp312-cp312-win_amd64.whl CPython 3.12 CPython 3.12 Windows x86-64 Details
bkgco-0.1.0-cp312-cp312-musllinux_1_2_x86_64.whl CPython 3.12 CPython 3.12 Linux musl 1.2+ x86-64 Details
bkgco-0.1.0-cp312-cp312-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl CPython 3.12 CPython 3.12 Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64 Details
bkgco-0.1.0-cp312-cp312-macosx_11_0_arm64.whl CPython 3.12 CPython 3.12 macOS 11.0+ ARM64 Details
bkgco-0.1.0-cp312-cp312-macosx_10_13_x86_64.whl CPython 3.12 CPython 3.12 macOS 10.13+ x86-64 Details
bkgco-0.1.0-cp311-cp311-win_amd64.whl CPython 3.11 CPython 3.11 Windows x86-64 Details
bkgco-0.1.0-cp311-cp311-musllinux_1_2_x86_64.whl CPython 3.11 CPython 3.11 Linux musl 1.2+ x86-64 Details
bkgco-0.1.0-cp311-cp311-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl CPython 3.11 CPython 3.11 Linux glibc 2.24+ x86-64, Linux glibc 2.28+ x86-64 Details
bkgco-0.1.0-cp311-cp311-macosx_11_0_arm64.whl CPython 3.11 CPython 3.11 macOS 11.0+ ARM64 Details
bkgco-0.1.0-cp311-cp311-macosx_10_9_x86_64.whl CPython 3.11 CPython 3.11 macOS 10.9+ x86-64 Details
bkgco-0.1.0-cp310-cp310-win_amd64.whl CPython 3.10 CPython 3.10 Windows x86-64 Details
bkgco-0.1.0-cp310-cp310-musllinux_1_2_x86_64.whl CPython 3.10 CPython 3.10 Linux musl 1.2+ x86-64 Details
bkgco-0.1.0-cp310-cp310-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl CPython 3.10 CPython 3.10 Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64 Details
bkgco-0.1.0-cp310-cp310-macosx_11_0_arm64.whl CPython 3.10 CPython 3.10 macOS 11.0+ ARM64 Details
bkgco-0.1.0-cp310-cp310-macosx_10_9_x86_64.whl CPython 3.10 CPython 3.10 macOS 10.9+ x86-64 Details

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