Advertisement

Fracture Detection Using Max-Flow Min-Cut

  • Ananda S. ChowdhuryEmail author
  • Suchendra M. Bhandarkar
Chapter
  • 701 Downloads
Part of the Advances in Computer Vision and Pattern Recognition book series (ACVPR)

Abstract

In this chapter, we propose an alternative technique for detection and localization of mandibular fractures using the concepts underlying network flow. As mentioned previously, the fractures mandibular could be either (a) hairline or minor, denoting situations where the broken bone fragments are not visibly out of alignment or have incurred very little relative displacement, or (b) major, denoting situations where the broken fragments are clearly displaced relative to each other. In the previous chapter, we modeled a minor or hairline fracture as a stochastic degradation of a hypothetical intact mandible. Here, we model a fracture as a discontinuity or cut in the flow of intensities between two designated points, termed as the source and sink in a directed graph or flow network. A fracture is detected by determining a minimum cut in the flow network using the well-known Maximum-Flow Minimum-Cut (Max-Flow Min-Cut) algorithm by Ford and Fulkerson. This approach for identification and localization of fractures is shown to yield more promising results in the case of minor fractures while requiring very little preprocessing of the input image data. We first model a sequence of 2D CT image slices as a collection of independent 2D directed graphs and execute the max-flow min-cut algorithm on each such directed graph. Later, we model the sequence of 2D CT image slices containing a fractured mandible as one complete 3D directed graph and run the same max-flow min-cut algorithm on it. The max-flow min-cut algorithm is shown to be successful for both 2D flow network and 3D flow network representations. The flow network is constructed based on the knowledge of the geometry of the human mandible and the fracture pattern. Although, simple capacity functions are designed as edge weights in the flow network representation, the network flow-based scheme is shown to be effective in the detection of minor fractures.

References

  1. 2.
    Ogundare BO, Bonnick A, Bayley N (2003) Pattern of mandibular fractures in an urban major trauma center. J Oral Maxillofac Surg 61(6):713–718 CrossRefGoogle Scholar
  2. 35.
    Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms. MIT Press, Cambridge zbMATHGoogle Scholar
  3. 36.
    Ford LR Jr, Fulkerson DR (1962) Flows in networks. Princeton University Press, Princeton zbMATHGoogle Scholar
  4. 146.
    Giannoudis PV, Dinopoulos H (2005) Current concepts of the inflammatory response after major trauma: an update. Injury 36(1):229–230 CrossRefGoogle Scholar
  5. 149.
    Boykov Y, Veksler O, Zabih R (2001) Fast approximate energy minimization via graph cuts. IEEE Trans Pattern Anal Mach Intell 23(11):1222–1239 CrossRefGoogle Scholar
  6. 150.
    Boykov Y, Jolly MP (2001) Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images. In: Proc IEEE int conf on computer vision (ICCV), Vancouver, Canada, pp 105–112 Google Scholar
  7. 151.
    Xu N, Bansal R, Ahuja N (2003) Object segmentation using graph cuts based active contours. In: Proc IEEE int conf on computer vision pattern recognition (CVPR), Madison, WI, USA, pp 46–53 Google Scholar
  8. 152.
    Freedman D, Zhang T (2005) Interactive graph cut based segmentation with shape priors. In: Proc IEEE int conf on computer vision pattern recognition (CVPR), San Diego, CA, USA, pp 755–762 Google Scholar
  9. 153.
    Funka-Lea G, Boykov Y, Florin C, Jolly MP, Moreau-Gobard R, Ramaraj R, Rinck D (2006) Automatic heart isolation for CT coronary visualization using graph-cuts. In: Proc IEEE int symp on biomedical imaging, Arlington, VA, USA, pp 614–617 Google Scholar
  10. 154.
    Song Z, Tustison N, Avants B, Gee J (2006) Adaptive graph cuts with tissue priors for brain MRI segmentation. In: Proc IEEE int symp on biomedical imaging (ISBI), Arlington, VA, USA, pp 762–765 Google Scholar
  11. 155.
    Boykov Y, Jolly MP (2006) Graph cuts and efficient N-D image segmentation. Int J Comput Vis 70(2):109–131 CrossRefGoogle Scholar
  12. 156.
    Boykov Y, Kolmogorov V (2004) Fast approximate energy minimization via graph cuts. IEEE Trans Pattern Anal Mach Intell 26(9):1124–1137 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Ananda S. Chowdhury
    • 1
    Email author
  • Suchendra M. Bhandarkar
    • 2
  1. 1.Department of Electronics & Telecommunication EngineeringJadavpur UniversityKolkataIndia
  2. 2.Department of Computer ScienceThe University of GeorgiaAthensUSA

Personalised recommendations