Differential and Integral Invariants Under M(o)bius Transformation
One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation.From the perspective of transformation groups,the conformal transformation is a key part of the diffeomorphism.According to the Liouville Theorem,an important part of the conformal transformation is the M¨obius transformation,so we focus on M¨obius transformation and propose two differential expressions that are invariable under 2-D and 3-D M¨obius transformation respectively.Next,we analyze the absoluteness and relativity of invariance on them and their components.After that,we propose integral invariants under M¨obius transformation based on the two differential expressions.Finally,we propose a conjecture about the structure of differential invariants under conformal transformation according to our observation on the composition of above two differential invariants.
Conformal transformation M(o)bius transformation Differential invariant Integral invariant
He Zhang Hanlin Mo You Hao Qi Li Hua Li
Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences,Beijing,China;University of Chinese Academy of Sciences,Beijing,China
国际会议
广州
英文
280-291
2018-11-23（万方平台首次上网日期，不代表论文的发表时间）