An extension module implementing the fast marching method

fast, marching, method, Eikonal, equation, interface, boundary, boundaries, differential-equations, numpy-arrays, python, python-extension, scikit-fmm, surface-modeling, surface-reconstruction
pip install scikit-fmm==2022.8.15


Linux build Windows build PyPI versionDocumentation StatusDownloads

scikit-fmm: the fast marching method for Python

scikit-fmm is a Python extension module which implements the fast marching method. The fast marching method is used to model the evolution of boundaries and interfaces in a variety of application areas. More specifically, the fast marching method is a numerical technique for finding approximate solutions to boundary value problems of the Eikonal equation:

F(x) | grad T(x) | = 1

Typically, such a problem describes the evolution of a closed curve as a function of time T with speed F(x)>0 in the normal direction at a point x on the curve. The speed function is specified, and the time at which the contour crosses a point x is obtained by solving the equation.

scikit-fmm is a simple module which provides functions to calculate the signed distance and travel time to an interface described by the zero contour of the input array phi.

import skfmm
import numpy as np
phi = np.ones((3, 3))
phi[1, 1] = -1
 array([[ 1.20710678,  0.5       ,  1.20710678],
        [ 0.5       , -0.35355339,  0.5       ],
        [ 1.20710678,  0.5       ,  1.20710678]])

skfmm.travel_time(phi, speed = 3.0 * np.ones_like(phi))
array([[ 0.40236893,  0.16666667,  0.40236893],
       [ 0.16666667,  0.11785113,  0.16666667],
       [ 0.40236893,  0.16666667,  0.40236893]])

The input array can be of 1, 2, 3 or higher dimensions and can be a masked array. A function is provided to compute extension velocities.




  • Numpy >= 1.0.2
  • Building requires a C/C++ compiler (gcc, MinGW, MSVC)

Bugs, questions, patches, feature requests, discussion & cetera


Running Tests

  • python -c "import skfmm; skfmm.test(True)"
  • When running the tests from the source directory use python develop
  • Tests are doctests in skfmm/

Building documentation

  • Requires sphinx and numpydoc
  • make html

Publications using scikit-fmm

  • Akinola, I., J Varley, B. Chen, and P.K. Allen (2018) "Workspace Aware Online Grasp Planning" arXiv:1806.11402v1 [cs.RO] 29 Jun 2018

  • Bortolussi, V., B. Figliuzzi, F. Willot, M. Faessel, M. Jeandin (2018) "Morphological modeling of cold spray coatings" Image Anal Stereol 2018;37:145-158 doi:10.5566/ias.1894

  • Chalmers, S., C.D. Saunter, J.M. Girkin and J.G. McCarron (2016) "Age decreases mitochondrial motility and increases mitochondrial size in vascular smooth muscle." Journal of Physiology, 594.15 pp 4283–4295.

  • Diogo Brandão Amorim (2014) "Efficient path planning of a mobile robot on rough terrain" Master's Thesis, Department of Aerospace Engineering, University of Lisbon.

  • Giometto, A., D.R. Nelson, and A.W. Murray (2018) "Physical interactions reduce the power of natural selection in growing yeast colonies", PNAS November 6, 2018 115 (45) 11448-11453; published ahead of print October 23, 2018

  • Joshua A. Taillon, Christopher Pellegrinelli, Yilin Huang, Eric D. Wachsman, and Lourdes G. Salamanca-Riba (2014) "Three Dimensional Microstructural Characterization of Cathode Degradation in SOFCs Using Focused Ion Beam and SEM" ECS Trans. 2014 61(1): 109-120;

  • Marshak, C., I. Yanovsky, and L. Vese (2017) "Energy Minimization for Cirrus and Cumulus Cloud Separation in Atmospheric Images" IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium DOI: 10.1109/IGARSS.2018.8517940

  • Moon, K. R., V. Delouille, J.J. Li, R. De Visscher, F. Watson and A.O. Hero III (2016) "Image patch analysis of sunspots and active regions." J. Space Weather Space Clim., 6, A3, DOI: 10.1051/swsc/2015043.

  • Tao, M., J. Solomon and A. Butscher (2016) "Near-Isometric Level Set Tracking." in Eurographics Symposium on Geometry Processing 2016 Eds: M. Ovsjanikov and D. Panozzo. Volume 35 (2016), Number 5

  • Thibaut, R., Laloy, E., Hermans, T., 2021. A new framework for experimental design using Bayesian Evidential Learning: The case of wellhead protection area. J. Hydrol. 603, 126903.

  • Vargiu, Antioco, M. Marrocu, L. Massidda (2015) "Implementazione e valutazione su un caso reale del servizio di Cloud Computing per la simulazione di incendi boschivi in Sardegna" (Implementation and evaluation on a real case of Cloud computing service for simulation of Forest fires in Sardinia). Sardinia Department of Energy and Environment. CRS4 PIA 2010 D5.4.

  • Wronkiewicz, M. (2018) "Mapping buildings with help from machine learning" Medium article, June 29th 2018

  • Makki, K., Ben Salem, D., Ben Amor, B. (2021) "Toward the Assessment of Intrinsic Geometry of Implicit Brain MRI Manifolds" IEEE Access, volume 9, pages 131054 - 131071 (September 2021) DOI: 10.1109/ACCESS.2021.3113611

Version History:

  • 0.0.1: February 13 2012
    • Initial release
  • 0.0.2: February 26th 2012
    • Including tests and docs in source distribution. Minor changes to documentation.
  • 0.0.3: August 4th 2012
    • Extension velocities.
    • Fixes for 64 bit platforms.
    • Optional keyword argument for point update order.
    • Bug reports and patches from three contributors.
  • 0.0.4: October 15th 2012
    • Contributions from Daniel Wheeler:
      • Bug fixes in extension velocity.
      • Many additional tests and migration to doctest format.
      • Additional optional input to extension_velocities() for FiPy compatibly.
  • 0.0.5: May 12th 2014
    • Fix for building with MSVC (Jan Margeta).
    • Corrected second-order point update.
  • 0.0.6: February 20th 2015
    • Documentation clarification (Geordie McBain).
    • Python 3 port (Eugene Prilepin).
    • Python wrapper for binary min-heap.
    • Freeze equidistant narrow-band points simultaneously.
  • 0.0.7: October 21st 2015
    • Bug fix to upwind finite difference approximation for negative phi from Lester Hedges.
  • 0.0.8: March 9th 2016
    • Narrow band capability: an optional "narrow" keyword argument limits the extent of the marching algorithm (Adrian Butscher).
  • 0.0.9: August 5th 2016
    • Periodic boundaries: an optional "periodic" keyword argument enables periodic boundaries in one or more directions (Wolfram Moebius).
  • 2019.1.30 January 30th 2019
    • Abrupt change to version numbering scheme.
    • Bugfix in to allow installing via pip with numpy (ManifoldFR).
    • Handle C++ exceptions during fast marching (Jens Glaser).
    • Accept a zero discriminant in travel time point update.
  • 2021.1.20 January 20th 2021
    • Fix divide by zero bugs in travel_time and extension_velocities
    • Contributions from Murray Cutforth, f-fanni, and okonrad
  • 2021.1.21 January 21st 2021
    • Minor C++ change (removed the auto keyword) to fix the compile on TravisCI.
  • 2021.2.2 February 2nd 2021
    • Add a pyproject.toml file to specify numpy as a build requirement, this is needed to build with new version of pip (David Parsson).
  • 2021.7.8 July 8th 2021
    • Add a pyproject.toml file to the file to fix the numpy build dependency (David Parsson). Fix numpy deprecation warnings and improve source code formatting (Robin Thibaut).
  • 2021.9.23 September 23rd 2021
    • Make the pyproject.toml file specify the oldest supported numpy as a build requirement, to allow using wheels with any numpy version. (David Parsson).
  • 2021.10.29 October 29th 2021
    • Fix for point update discriminant exactly equal to zero
    • Fall back calculation for point update when discriminant becomes negative
    • (Joshua Gehre)
  • 2022.02.02 February 2nd 2022
    • Fixes for Python 3.10 compatibility
    • (Amin Sadeghi, Xylar Asay-Davis, David Parsson)
  • 2022.03.26 March 26th 2022
    • Following the breaking changes in setuptools v61.0.0 it is suggested to set py_modules to disable auto-discovery behavior.
    • (Daniel Ammar)
  • 2022.08.15 August 15th 2022
    • Following the breaking changes in setuptools v65 pin setuptools to v64
    • (DorSSS)
  • 2022.04.02 April 2nd 2023
    • Build fixes for Python 3.11 (update pheap cython wrapper)
    • No solver changes

Copyright 2023 The scikit-fmm team.

BSD-style license. See LICENSE.txt in the source directory.