LSMAT Least Squares Medial Axis Transform

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dc.contributor.authorRebain, Danielen_US
dc.contributor.authorAngles, Baptisteen_US
dc.contributor.authorValentin, Julienen_US
dc.contributor.authorVining, Nicholasen_US
dc.contributor.authorPeethambaran, Jijuen_US
dc.contributor.authorIzadi, Shahramen_US
dc.contributor.authorTagliasacchi, Andreaen_US
dc.contributor.editorChen, Min and Benes, Bedrichen_US
dc.date.accessioned2019-09-27T14:11:20Z
dc.date.available2019-09-27T14:11:20Z
dc.date.issued2019
dc.description.abstractThe medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers, perturbations and/or noise along the boundary of objects. To overcome this limitation, we introduce a new formulation of the medial axis transform which is naturally robust in the presence of these artefacts. Unlike previous work which has approached the medial axis from a computational geometry angle, we consider it from a numerical optimization perspective. In this work, we follow the definition of the medial axis transform as ‘the set of maximally inscribed spheres’. We show how this definition can be formulated as a least squares relaxation where the transform is obtained by minimizing a continuous optimization problem. The proposed approach is inherently parallelizable by performing independent optimization of each sphere using Gauss–Newton, and its least‐squares form allows it to be significantly more robust compared to traditional computational geometry approaches. Extensive experiments on 2D and 3D objects demonstrate that our method provides superior results to the state of the art on both synthetic and real‐data.The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers, perturbations and/or noise along the boundary of objects. To overcome this limitation, we introduce a new formulation of the medial axis transform which is naturally robust in the presence of these artefacts. Unlike previous work which has approached the medial axis from a computational geometry angle, we consider it from a numerical optimization perspective. In this work, we follow the definition of the medial axis transform as ‘the set of maximally inscribed spheres’.en_US
dc.description.number6
dc.description.sectionheadersArticles
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume38
dc.identifier.doi10.1111/cgf.13599
dc.identifier.issn1467-8659
dc.identifier.pages5-18
dc.identifier.urihttps://doi.org/10.1111/cgf.13599
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13599
dc.publisher© 2019 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltden_US
dc.subjectmedial axis transform
dc.subjectoptimization
dc.subjectleast squares
dc.subjectComputing methodologies → Point‐based models
dc.subjectVolumetric models
dc.subjectShape analysis
dc.titleLSMAT Least Squares Medial Axis Transformen_US
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