Image Scale-Space from the Heat Kernel

  • Fan Zhang
  • Edwin R. Hancock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3773)


In this paper, we show how the heat-kernel can be used to construct a scale-space for image smoothing and edge detection. We commence from an affinity weight matrix computed by exponentiating the difference in pixel grey-scale and distance. From the weight matrix, we compute the graph Laplacian. Information flow across this weighted graph-structure with time is captured by the heat-equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigen-system with time. Our scale-space is constructed by varying the time parameter of the heat-kernel. The larger the time the greater the the amount of information flow across the graph. The method has the effect of smoothing within regions, but does not blur region boundaries. Moreover, the boundaries do not move with time and this overcomes one of the problems with Gaussian scale-space. We illustrate the effectiveness of the method for image smoothing and edge detection.


Heat Kernel Coarse Scale Laplacian Matrix Discrete Image Degree Matrix 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Fan Zhang
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkYorkUK

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