2018/08/30 by He Zhang, Hanlin Mo, Zhang, He +7
Business, Management and Accounting · Computer Science · Engineering · Mathematics · #Computer Vision and Pattern Recognition (cs.CV) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #Optical measurement and interference techniques #Optics and Image Analysis #Robotic Mechanisms and Dynamics #cs.CV #cs.GR #math.DG
paper · pdf · doi:10.48550/arxiv.1808.10083
arxiv created 2018/08/30 · openalex publication_date 2018/08/30 · arxiv updated 2018/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Mobius transformation, so we focus on Mobius transformation and propose two differential expressions that are invariable under 2-D and 3-D Mobius transformation respectively. Next, we analyze the absoluteness and relativity of invariance on them and their components. After that, we propose integral invariants under Mobius 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 the above two differential invariants.