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Regression on Lie groups and its application to affine motion tracking. (English) Zbl 1376.94006

Minh, Hà Quang (ed.) et al., Algorithmic advances in Riemannian geometry and applications. For machine learning, computer vision, statistics, and optimization. Cham: Springer (ISBN 978-3-319-45025-4/hbk; 978-3-319-45026-1/ebook). Advances in Computer Vision and Pattern Recognition, 173-185 (2016).
Summary: In this chapter, we present how to learn regression models on Lie groups and apply our formulation to visual object tracking tasks. Many transformations used in computer vision, for example orthogonal group and rotations, have matrix Lie group structure. Unlike conventional methods that proceed by directly linearizing these transformations, thus, making an implicit Euclidean space assumption, we formulate a regression model on the corresponding Lie algebra that minimizes a first order approximation to the geodesic error. We demonstrate our method on affine motions, however, it generalizes to any matrix Lie group transformations.
For the entire collection see [Zbl 1357.53004].

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
22E15 General properties and structure of real Lie groups
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68T45 Machine vision and scene understanding

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