Shape Tracking Using Centroid-Based Methods

Abrantes, Arnaldo J.; Marques, Jorge S.

doi:10.1007/3-540-44745-8_38

Lecture Notes in Computer Science

2001

DOI: 10.1007/3-540-44745-8_38

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Shape Tracking Using Centroid-Based Methods

Arnaldo J. Abrantes

Jorge S. Marques²

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A globally convergent numerical algorithm for computing the centre of mass on compact Lie groups

Manton

ICARCV 2004 8th Control, Automation, Robotics and Vision Conference, 2004.

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Motivated by applications in fuzzy control, robotics and vision, this paper considers the problem of computing the centre of mass (precisely, the Karcher mean) of a set of points defined on a compact Lie group, such as the special orthogonal group consisting of all orthogonal matrices with unit determinant. An iterative algorithm, whose derivation is based on the geometry of the problem, is proposed. It is proved to be globally convergent. Interestingly, the proof starts by showing the algorithm is actually a Riemannian gradient descent algorithm with fixed step size.

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A globally convergent numerical algorithm for computing the centre of mass on compact Lie groups

Manton

ICARCV 2004 8th Control, Automation, Robotics and Vision Conference, 2004.

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show abstract

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Shape Tracking Using Centroid-Based Methods

Cited by 1 publication

References 16 publications

A globally convergent numerical algorithm for computing the centre of mass on compact Lie groups

A globally convergent numerical algorithm for computing the centre of mass on compact Lie groups

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