Hot Spots Conjecture and Its Application to Modeling Tubular Structures

  • Moo K. Chung
  • Seongho Seo
  • Nagesh Adluru
  • Houri K. Vorperian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7009)


The second eigenfunction of the Laplace-Beltrami operator follows the pattern of the overall shape of an object. This geometric property is well known and used for various applications including mesh processing, feature extraction, manifold learning, data embedding and the minimum linear arrangement problem. Surprisingly, this geometric property has not been mathematically formulated yet. This problem is directly related to the somewhat obscure hot spots conjecture in differential geometry. The aim of the paper is to raise the awareness of this nontrivial issue and formulate the problem more concretely. As an application, we show how the second eigenfunction alone can be used for complex shape modeling of tubular structures such as the human mandible.


Heat Kernel Tubular Structure Cold Spot Sign Graph Geodesic Path 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Moo K. Chung
    • 1
    • 2
    • 3
    • 4
  • Seongho Seo
    • 4
  • Nagesh Adluru
    • 2
  • Houri K. Vorperian
    • 3
  1. 1.Department of Biostatistics and Medical InformaticsUniversity of WisconsinMadisonUSA
  2. 2.Waisman Laboratory for Brain Imaging and BehaviorUniversity of WisconsinMadisonUSA
  3. 3.Vocal Tract Development Laboratory, Waisman CenterUniversity of WisconsinMadisonUSA
  4. 4.Department of Brain and Cognitive SciencesSeoul National UniversityKorea

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