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A Variational Approach to Registration with Local Exponential Coordinates

Paman, Ashish and Rangarajan, Ramsharan (2019) A Variational Approach to Registration with Local Exponential Coordinates. In: COMPUTER GRAPHICS FORUM, 38 (1). pp. 482-506.

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Official URL: http://dx.doi.org/10.1111/cgf.13587

Abstract

We identify a novel parameterization for the group of finite rotations (SO3), consisting of an atlas of exponential maps defined over local tangent planes, for the purpose of computing isometric transformations in registration problems that arise in machine vision applications. Together with a simple representation for translations, the resulting system of coordinates for rigid body motions is proper, free from singularities, is unrestricted in the magnitude of motions that can be represented and poses no difficulties in computer implementations despite their multi-chart nature. Crucially, such a parameterization helps to admit varied types of data sets, to adopt data-dependent error functionals for registration, seamlessly bridges correspondence and pose calculations, and inspires systematic variational procedures for computing optimal solutions. As a representative problem, we consider that of registering point clouds onto implicit surfaces without introducing any discretization of the latter. We derive coordinate-free stationarity conditions, compute consistent linearizations, provide algorithms to compute optimal solutions and examine their performance with detailed examples. The algorithm generalizes naturally to registering curves and surfaces onto implicit manifolds, is directly adaptable to handle the familiar problem of pairwise registration of point clouds and allows for incorporating scale factors during registration.

Item Type: Journal Article
Additional Information: Copyright belongs to Blackwell Publishing Ltd
Keywords: computer vision - tracking; methods and applications; implicit surfaces; modelling; computational geometry
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Depositing User: Id for Latest eprints
Date Deposited: 21 Apr 2019 08:05
Last Modified: 21 Apr 2019 08:05
URI: http://eprints.iisc.ac.in/id/eprint/62296

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