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Morse theory in image edge detection

Author: SongFei
Tutor: ZouJianCheng
School: North China University of
Course: Applied Mathematics
Keywords: Morse function Edge Detection Riemann surface Morse theory
CLC: TP391.41
Type: Master's thesis
Year: 2011
Downloads: 26
Quote: 0
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Abstract


Morse theory is a very useful tool in differential topology , it is also one of the hot people in recent years . At the same time Morse theory to help people solve the other branches of a series of mathematical difficulties and difficult problem . Morse theory provides a wide range of analysis tools and convection shape the overall decomposition ideas , people can have a deeper understanding of the nature of the general differentiable manifold geometry and topology . In recent years , Morse theory in the theory of partial differential equations and the theory of Lie groups in a wide range of applications attracted the attention of more people . But, regrettably , Morse theory with another door useful discipline : the theory of functions of a complex variable and not a good combination . This paper attempts to construct a one-dimensional complex manifold typical Morse function and use of Morse theory to the overall structure of differentiable manifold is an important theorem on Riemann surfaces : single-value theorem a new proof . Single value theorem of the theory of functions of a complex variable help is very great, over the nature of the coverage , we can -shaped micro- shunt very good basic model Riemann surface and has a very good structure in mathematics Teichmuller space the theoretical depth analysis . Morse theory can be seen from the complex structure of the Riemann surface . In addition, Morse Lemma promotion. We give a sufficient condition for a relatively easy to verify , and extended to the case of multiple functions at the same time set up initially focused only on a Morse function established local standardized form , and gives the proof . As a result , the Morse lemma Under these conditions, a good promotion . The basic work of this paper include the following aspects : First , the system introduced Morse theory . Second, the use of Morse theory to a single value theorem a relatively simplified proof . Third , given a sufficient condition Under these conditions, the promotion of the Morse lemma . Fourth , the use of Morse lemma line right edges of objects in a digital image is equivalent to a description of the classification , so that it is standardized . The Fifth , an example is briefly described above theoretical .

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CLC: > Industrial Technology > Automation technology,computer technology > Computing technology,computer technology > Computer applications > Information processing (information processing) > Pattern Recognition and devices > Image recognition device
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