A Variational Approach to Registration with Local Exponential Coordinates

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dc.contributor.authorPaman, Ashishen_US
dc.contributor.authorRangarajan, Ramsharanen_US
dc.contributor.editorChen, Min and Benes, Bedrichen_US
dc.date.accessioned2019-03-17T09:57:01Z
dc.date.available2019-03-17T09:57:01Z
dc.date.issued2019
dc.description.abstractWe identify a novel parameterization for the group of finite rotations (SO), 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.We identify a novel parameterization for the group of finite rotations (SO), 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.en_US
dc.description.number1
dc.description.sectionheadersArticles
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume38
dc.identifier.doi10.1111/cgf.13587
dc.identifier.issn1467-8659
dc.identifier.pages482-506
dc.identifier.urihttps://doi.org/10.1111/cgf.13587
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13587
dc.publisher© 2019 The Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectcomputer vision ‐ tracking
dc.subjectmethods and applications
dc.subjectimplicit surfaces
dc.subjectmodelling
dc.subjectcomputational geometry
dc.subject• Computing methodologies → Computer vision
dc.titleA Variational Approach to Registration with Local Exponential Coordinatesen_US
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