Seeded ND medical image segmentation by cellular automaton on GPU

Original Article



We present a GPU-based framework to perform organ segmentation in N-dimensional (ND) medical image datasets by computation of weighted distances using the Ford–Bellman algorithm (FBA). Our GPU implementation of FBA gives an alternative and optimized solution to other graph-based segmentation techniques.


Given a number of K labelled-seeds, the segmentation algorithm evolves and segments the ND image in K objects. Each region is guaranteed to be connected to seeds with the same label. The method uses a Cellular Automata (CA) to compute multiple shortest-path-trees based on the FBA. The segmentation result is obtained by K-cuts of the graph in order to separate it in K sets. A quantitative evaluation of the method was performed by measuring renal volumes of 20 patients based on magnetic resonance angiography (MRA) acquisitions. Inter-observer reproducibility, accuracy and validity were calculated and associated computing times were recorded. In a second step, the computational performances were evaluated with different graphics hardware and compared to a CPU implementation of the method using Dijkstra’s algorithm.


The ICC for inter-observer reproducibility of renal volume measurements was 0.998 (0.997–0.999) for two radiologists and the absolute mean difference between the two readers was lower than 1.2% of averaged renal volumes. The validity analysis shows an excellent agreement of our method with the results provided by a supervised segmentation method, used as reference.


The formulation of the FBA in the form of a CA is simple, efficient and straightforward, and can be implemented in low cost vendor-independent graphics hardware. The method can efficiently be applied to perform organ segmentation and quantitative evaluation in clinical routine.


Cellular automaton GPU Medical image segmentation Ford–Bellman shortest path 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Vezhnevets V, Konouchine V, Moscow R (2005) “GrowCut”-interactive multi-label NDImage segmentation by cellular automata. In: Proceedings of Graphicon, Novosibirsk Akademgorodok, Russia, pp 150–156Google Scholar
  2. 2.
    Bai X, Sapiro G (2007) A geodesic framework for fast interactive image and video segmentation and matting. In: IEEE 11th international conference on computer vision, pp 1–8Google Scholar
  3. 3.
    Qu Y, Wong TT, Heng PA (2006) Manga colorization. Proc ACM SIGGRAPH 25: 1214–1220CrossRefGoogle Scholar
  4. 4.
    Konushin V, Vezhnevets V, Moscow R (2006) Interactive image colorization and recoloring based on coupled map lattices. In: Conference proceedings of Graphicon’2006 Novosibirsk Akademgorodok, Russia, pp 231–234Google Scholar
  5. 5.
    Yin L, Jian S, Chi-Keung T, Heung-Yeung S (2004) Lazy snapping. In: ACM SIGGRAPH 2004 papers. ACM, Los AngelesGoogle Scholar
  6. 6.
    Rother C, Kolmogorov V, Blake A (2004) GrabCut: interactive foreground extraction using iterated graph cuts. ACM Trans Graph (TOG) 23: 309–314CrossRefGoogle Scholar
  7. 7.
    Mortensen EN, Barrett WA (1998) Interactive segmentation with intelligent scissors. Graph Models Image Process 60: 349–384CrossRefGoogle Scholar
  8. 8.
    Boykov Y, Jolly MP (2000) Interactive organ segmentation using graph cuts. In: Proceedings of the medical image computing and computer-assisted intervention, pp 276–286Google Scholar
  9. 9.
    Xu N, Ahuja N, Bansal R (2007) Object segmentation using graph cuts based active contours. Comput Vis Image Underst 107: 210–224CrossRefGoogle Scholar
  10. 10.
    Protiere A, Sapiro G (2007) Interactive image segmentation via adaptive weighted distances. IEEE Trans Image Process 16: 1046CrossRefPubMedGoogle Scholar
  11. 11.
    Chefd’hotel C, Sebbane A (2007) Random walk and front propagation on watershed adjacency graphs for multilabel image segmentation. In: IEEE 11th international conference on computer vision, pp 1–7Google Scholar
  12. 12.
    Falcão AX, Stolfi J, de Alencar Lotufo R (2004) The image foresting transform: theory, algorithms, and applications. IEEE Trans Pattern Anal Mach Intell 26: 19–29CrossRefPubMedGoogle Scholar
  13. 13.
    Sinop AK, Grady L (2007) A seeded image segmentation framework unifying graph cuts and random walker which yields a new algorithm. In: IEEE 11th international conference on computer vision, pp 1–8Google Scholar
  14. 14.
    Boykov Y, Funka-Lea G (2006) Graph cuts and efficient NDImage segmentation. Int J Comput Vis 70: 109–131CrossRefGoogle Scholar
  15. 15.
    Grady L, Funka-Lea G (2004) Multi-label image segmentation for medical applications based on graph-theoretic electrical potentials. In: ECCV2004 workshop, pp 230–245Google Scholar
  16. 16.
    Raspe M, Muller S (2007) Using a GPU-based framework for interactive tone mapping of medical volume data. In: SIGRAD, vol 28Google Scholar
  17. 17.
    Owens JD, Luebke D, Govindaraju N, Harris M, Kruger J, Lefohn AE, Purcell TJ (2007) A survey of general-purpose computation on graphics hardware. In: Computer graphics forum, pp 80–113Google Scholar
  18. 18.
    Vineet V, Narayanan PJ (2008) CUDA cuts: fast graph cuts on the GPU. In: IEEE CVPR workshops, pp 1–8Google Scholar
  19. 19.
    Dixit N, Keriven R, Paragios N (2005) GPU-Cuts: combinatorial optimisation, graphic processing units and adaptive object extraction. CERTIS, ENPC, Marne la Vallee, FranceGoogle Scholar
  20. 20.
    Volkov V, Demmel J (2007) Using GPUs to accelerate the bisection algorithm for finding eigenvalues of symmetric tridiagonal matrices. Electrical Engineering and Computer Sciences, University of California, BerkeleyGoogle Scholar
  21. 21.
    Aharon S, Grady L, Schiwietz T (2005) GPU accelerated isoperimetric algorithm for image segmentation, digital photo and video editing. In: Google PatentsGoogle Scholar
  22. 22.
    Von Neumann J, Burks AW (1966) Theory of self-reproducing automata. University of Illinois Press, UrbanaGoogle Scholar
  23. 23.
    Wolfram S (2002) A new kind of science. Wolfram Media, ChampaignGoogle Scholar
  24. 24.
    Ganguly N, Sikdar BK, Deutsch A, Canright G, Chaudhuri PP (2003) A survey on cellular automata. Dresden University of Technology, Technical Report Centre for High Performance ComputingGoogle Scholar
  25. 25.
    Gardner M (1970) Mathematical games: the fantastic combinations of John Conway’s New Solitaire Game ‘Life’. Sci Am 223: 120–123CrossRefGoogle Scholar
  26. 26.
    Zhao Y (2008) Lattice Boltzmann based PDE solver on the GPU. Vis Comput 24: 323–333CrossRefGoogle Scholar
  27. 27.
    Gobron S, Devillard F, Heit B (2007) Retina simulation using cellular automata and GPU programming. Mach Vis Appl 18: 331–342CrossRefGoogle Scholar
  28. 28.
    Alonso Atienza F, Requena Carrión J, García Alberola A, Rojo Álvarez JL, SÁnchez Muñoz JJ, Martínez SÁnchez J, Valdés Chávarri M (2005) A probabilistic model of cardiac electrical activity based on a cellular automata system. Revista Española de Cardiología (Internet) 58: 41–47CrossRefGoogle Scholar
  29. 29.
    Bellman R, Rand Corp Santa Monica Calif (1958) On a rooting problem. Q Appl Math 16:87–90Google Scholar
  30. 30.
    Ford LR, Fulkerson DR (1956) Maximal flow through a network. Can J Math 8: 399–404Google Scholar
  31. 31.
    Nepomniaschaya AS (2001) An associative version of the Bellman–Ford algorithm for finding the shortest paths in directed graphs. In: Parallel computing technologies, vol 2127. Springer, Berlin, pp 285–292Google Scholar
  32. 32.
    Kauffmann C, Piche N (2008) Cellular automaton for ultra-fast watershed transform on GPU. In: ICPR 2008. Tampa bay, FL, USA, pp 1–4Google Scholar
  33. 33.
    Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1: 269–271CrossRefGoogle Scholar
  34. 34.
    Yatziv L, Bartesaghi A, Sapiro G (2006) O (N) implementation of the fast marching algorithm. J Comput Phys 212: 393–399CrossRefGoogle Scholar
  35. 35.
    Even S (1979) Graph algorithms, vol 249. Computer Science Press, RockvilleGoogle Scholar
  36. 36.
    Fung J, Mann S (2008) Using graphics devices in reverse: GPU-based image processing and computer vision. In: IEEE international conference on multimedia and expo, pp 9–12Google Scholar
  37. 37.
    Gernot Z, Christian T, Ivo I, Marcus M, Art T, Hans-Peter S (2007) GPU-based light wavefront simulation for real-time refractive object rendering. In: ACM SIGGRAPH 2007 sketches. ACM, San DiegoGoogle Scholar
  38. 38.
    Koutis I (2008) Faster algebraic algorithms for path and packing problems. In: Proceedings of the 35th international colloquium on automata, languages and programming, Part I. Springer, ReykjavikGoogle Scholar
  39. 39.
    Bolz J, Farmer I, Grinspun E, Schröoder P (2003) Sparse matrix solvers on the GPU: conjugate gradients and multigrid. In: International conference on computer graphics and interactive techniques, pp 917–924Google Scholar
  40. 40.
    Owens JD, Houston M, Luebke D, Green S, Stone JE, Phillips JC (2008) GPU computing. In: Proceedings of the IEEE, vol 96(5), May 2008Google Scholar

Copyright information

© CARS 2009

Authors and Affiliations

  1. 1.Department of Medical ImagingNotre-Dame Hospital, CHUMMontrealCanada
  2. 2.Object Research System Inc. (ORS)MontrealCanada

Personalised recommendations