Symmetries of differential equations in computer vision applications
نویسندگان
چکیده
منابع مشابه
Reduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
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This special issue commemorated the bicentenary of the birth of Évariste Galois who introduced the notion of a group and made fundamental contributions to the solution of polynomial equations.The formal mathematical concept of symmetry thus came fromGalois theory. Symmetry was inaugurated andutilized in the solution of differential equations by Sophus Lie in the 1870s. The algebraic approach ha...
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Partial differential equations (PDEs) have been successful for solving many problems in computer vision. However, the existing PDEs are all crafted by people with skill, based on some limited and intuitive considerations. As a result, the designed PDEs may not be able to handle complex situations in real applications. Moreover, human intuition may not apply if the vision task is hard to describ...
متن کاملSymmetries of Differential Equations
In this chapter we discuss the foundations and some applications of Lie’s theory of symmetry groups of differential equations. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of some particular differential equations of interest. The reader interested in pursuing these matters in greater depth should consult the texts...
متن کاملLie Symmetries of Differential Equations by Computer Algebra
Secondly combining group theory and singularity analysis we obtained some information about the similarity solutions of the fourth order generalized Boussinesq equation GBE4. It has been shown that this equation possess a three dimensional Lie algebra of the point symmetries and the similarity reductions due to these symmetries have been obtained.
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ژورنال
عنوان ژورنال: Computer Research and Modeling
سال: 2010
ISSN: 2076-7633,2077-6853
DOI: 10.20537/2076-7633-2010-2-4-369-376