Image scale-space from the heat kernel

Authors:
Fan Zhang;Edwin R. Hancock
Affiliations:
Department of Computer Science, University of York, York, UK;Department of Computer Science, University of York, York, UK
Venue:
CIARP'05 Proceedings of the 10th Iberoamerican Congress conference on Progress in Pattern Recognition, Image Analysis and Applications
Year:
2005

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Abstract

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.