title: Hot Spots Conjecture and Its Application to Modeling Tubular Structures.
abstract: 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 obscurehot spots conjecturein 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.
authors: Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, WI 53706, USA; Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin, Madison, WI 53706, USA; Vocal Tract Development Laboratory, Waisman Center, University of Wisconsin, Madison, WI 53706, USA; Department of Brain and Cognitive Sciences, Seoul National University, Korea.
authors: Moo K
authors: MK
authors: Chung
authors: Department of Brain and Cognitive Sciences, Seoul National University, Korea.
authors: Seongho
authors: S
authors: Seo
authors: Waisman Laboratory for Brain Imaging and Behavior, University of Wisconsin, Madison, WI 53706, USA.
authors: Nagesh
authors: N
authors: Adluru
authors: Vocal Tract Development Laboratory, Waisman Center, University of Wisconsin, Madison, WI 53706, USA.
authors: Houri K
authors: HK
authors: Vorperian