Topological Characterization of Signal in Brain Images Using Min-Max Diagrams

  • Moo K. Chung
  • Vikas Singh
  • Peter T. Kim
  • Kim M. Dalton
  • Richard J. Davidson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5762)


We present a novel computational framework for characterizing signal in brain images via nonlinear pairing of critical values of the signal. Among the astronomically large number of different pairings possible, we show that representations derived from specific pairing schemes provide concise representations of the image. This procedure yields a “min-max diagram” of the image data. The representation turns out to be especially powerful in discriminating image scans obtained from different clinical populations, and directly opens the door to applications in a variety of learning and inference problems in biomedical imaging. It is noticed that this strategy significantly departs from the standard image analysis paradigm – where the ‘mean’ signal is used to characterize an ensemble of images. This offers robustness to noise in subsequent statistical analyses, for example; however, the attenuation of the signal content due to averaging makes it rather difficult to identify subtle variations. The proposed topologically oriented method seeks to address these limitations by characterizing and encoding topological features or attributes of the image. As an application, we have used this method to characterize cortical thickness measures along brain surfaces in classifying autistic subjects. Our promising experimental results provide evidence of the power of this representation.


Cortical Thickness Heat Kernel Cortical Surface Morse Function Autistic Subject 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Cachia, A., Mangin, J.-F., Riviere, D., et al.: A primal sketch of the cortex mean curvature: a morphogenesis based approach to study the variability of the folding patterns. IEEE Transactions on Medical Imaging 22, 754–765 (2003)CrossRefGoogle Scholar
  2. 2.
    Chung, M.K., Bubenik, P., Kim, P.T.: Persistence diagrams of cortical surface data. In: Proc. of Information Processing in Medical Imaging, IPMI (2009)Google Scholar
  3. 3.
    Chung, M.K., Dalton, K.M., Shen, L., Evans, A.C., Davidson, R.J.: Weighted fourier representation and its application to quantifying the amount of gray matter. IEEE Transactions on Medical Imaging 26, 566–581 (2007)CrossRefGoogle Scholar
  4. 4.
    De Berg, M., Cheong, O., van Kreveld, M.: Computational Geometry: Algorithms and Applications. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  5. 5.
    Deza, E., Deza, M.M.: Dictionary of Distances. Elsevier Science, Amsterdam (2006)Google Scholar
  6. 6.
    Edelsbrunner, H., Harer, J.: Persistent homology - a survey. A survey on Discrete and Computational Geometry: Twenty Years Later, 257–282 (2006)Google Scholar
  7. 7.
    MacDonald, J.D., Kabani, N., Avis, D., Evans, A.C.: Automated 3-D extraction of inner and outer surfaces of cerebral cortex from MRI. NeuroImage 12, 340–356 (2000)CrossRefGoogle Scholar
  8. 8.
    Singh, V., Mukherjee, L., Chung, M.K.: Cortical surface thickness as a classifier: Boosting for autism classification. In: Proc. of Medical Image Computing and Computer Assisted Intervention (2008)Google Scholar
  9. 9.
    Worsley, K.J., Marrett, S., Neelin, P., Vandal, A.C., Friston, K.J., Evans, A.C.: A unified statistical approach for determining significant signals in images of cerebral activation. Human Brain Mapping 4, 58–73 (1996)CrossRefGoogle Scholar
  10. 10.
    Zomorodian, A.J., Carlsson, G.: Computing persistent homology. Discrete and Computational Geometry 33, 249–274 (2005)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Moo K. Chung
    • 1
    • 2
  • Vikas Singh
    • 1
  • Peter T. Kim
    • 4
  • Kim M. Dalton
    • 2
  • Richard J. Davidson
    • 2
    • 3
  1. 1.Department of Biostatistics and Medical Informatics 
  2. 2.Waisman Laboratory for Brain Imaging and Behavior 
  3. 3.Department of Psychology and PsychiatryUniversity of WisconsinMadisonUSA
  4. 4.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada

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