Möbius Registration. (8th August 2018)

• Record Type: Journal Article
• Authors: Baden, Alex; Crane, Keenan; Kazhdan, Misha
• Is Part Of: Computer graphics forum. Volume 37:Number 5(2018)
• Page Start: 211
• Page End: 220
• Publication Date: 2018-08-08
• Subjects: Categories and Subject Descriptors (according to ACM CCS): -- 1.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.13503
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract: Conformal parameterizations over the sphere provide high‐quality maps between genus zero surfaces, and are essential for applications such as data transfer and comparative shape analysis. However, such maps are not unique: to define correspondence between two surfaces, one must find the Möbius transformation that best aligns two parameterizations—akin to picking a translation and rotation in rigid registration problems. We describe a simple procedure that canonically centers and rotationally aligns two spherical maps. Centering is implemented via elementary operations on triangle meshes in ℝ 3, and minimizes area distortion. Alignment is achieved using the FFT over the group of rotations. We examine this procedure in the context of spherical conformal parameterization, orbifold maps, non‐rigid symmetry detection, and dense point‐to‐point surface correspondence.