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• W2952017517 abstract "Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:mathbb{R}^{d} rtimes S^{d-1} to mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores." @default.
• W2952017517 created "2019-06-27" @default.
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• W2952017517 date "2015-02-27" @default.
• W2952017517 modified "2023-10-17" @default.
• W2952017517 title "Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging" @default.
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• W2952017517 doi "https://doi.org/10.48550/arxiv.1502.08002" @default.
• W2952017517 hasPublicationYear "2015" @default.
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