Diffusion-Based Similarity for Image Analysis

  • Jan GauraEmail author
  • Eduard Sojka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9493)


Measuring the distances is a key problem in many image-analysis algorithms. This is especially true for image segmentation. It provides a basis for the decision whether two image points belong to a single or to two different image segments. Many algorithms use the Euclidean distance, which may not be the right choice. The geodesic distance or the k shortest paths measure the distance along the surface that is defined by the image function. The diffusion distance seems to provide better properties since all the paths are taken into account. In this paper, we show that the diffusion distance has the properties that make it difficult to use in some image processing algorithms, mainly in image segmentation, which extends the recent observations of some other authors. We propose a new measure called normalised diffusion cosine similarity that overcomes some problems of diffusion distance. Lastly, we present the necessary theory and the experimental results.


Distance measurement Euclidean distance Geodesic distance Diffusion distance Normalised diffusion similarity 



This work was partially supported by the grant of SGS No. SP2015/141, VŠB - Technical University of Ostrava, Czech Republic.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering and Computer ScienceVŠB - Technical University of OstravaOstrava-PorubaCzech Republic

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