Talk:Heat kernel signature

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Note that besides Ovjanikov et.al, Heat Kernel Signature was invented indenpendantly (under the name "auto diffusion function") and published as the same conference (SGP) by Gebal et.al, see the following reference: http://dl.acm.org/citation.cfm?id=1735623

12.96.84.3 (talk) 01:04, 24 March 2012 (UTC) Bruno LevyReply

Problematic sentence

In the section Technical details, this sentence appears:

"For a concise feature descriptor, HKS restricts the heat kernel only to the temporal ___domain

${\displaystyle h_{t}(x,x)=\sum _{i=0}^{\infty }\exp(-\lambda _{i}t)\phi _{i}^{2}(x).}$ "

But ${\displaystyle h_{t}(x,x)=\sum _{i=0}^{\infty }\exp(-\lambda _{i}t)\phi _{i}^{2}(x)}$  is not any kind of "___domain"; it is a function.

I hope someone knowledgeable about this subject can fix this problem.

Necessary information is omitted

The article Heat kernel defines what a heat kernel is, and implies that there is a distinct heat kernel for each initial value-boundary value problem of a certain kind.

But this article addresses several aspects of the heat kernel without ever stating which heat kernel it is referring to.

I hope that someone knowledgeable about this subject will fix this very serious omission.

Related: The symbol "${\displaystyle h_{t}(x,y)}$ " is used in this article without its ever being defined. Is this the "heat kernel" that this article is referring to??? If so, this needs to be stated explicitly.

Also: The following sentence is fascinating, but it neglects to fully say what it is talking about:

"'The heat kernel fully characterizes a surface up to an isometry: For any surjective map ${\displaystyle T:M\rightarrow N}$  between two Riemannian manifolds ${\displaystyle M}$  and ${\displaystyle N}$ , if ${\displaystyle h_{t}(x,y)=h_{t}(T(x),T(y))}$  then ${\displaystyle T}$  is an isometry, and vice versa."

Does this mean for one value of t ??? Or does it mean for all t > 0 ???

I hope someone knowledgeable about this subject can include this omitted information.