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PDE-Based Group Equivariant Convolutional Neural Networks

Journal of mathematical imaging and vision, 2023, Vol.65 (1), p.209-239

2023

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Analysis of (sub-)Riemannian PDE-G-CNNs

Journal of mathematical imaging and vision, 2023-12, Vol.65 (6), p.819-843

2023

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Total Variation and Mean Curvature PDEs on the Homogeneous Space of Positions and Orientations

Journal of mathematical imaging and vision, 2021-02, Vol.63 (2), p.237-262

2021

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Geodesic Tracking via New Data-Driven Connections of Cartan Type for Vascular Tree Tracking

Journal of mathematical imaging and vision, 2024-04, Vol.66 (2), p.198-230

2024

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Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to Linear PDEs

Entropy (Basel, Switzerland), 2019-01, Vol.21 (1), p.38

2019

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Evaluating contextual processing in diffusion MRI: application to optic radiation reconstruction for epilepsy surgery

PloS one, 2014-07, Vol.9 (7), p.e101524-e101524

2014

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Left-Invariant Diffusions on the Space of Positions and Orientations and their Application to Crossing-Preserving Smoothing of HARDI images

International journal of computer vision, 2011-05, Vol.92 (3), p.231-264

2011

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Crossing-Preserving Coherence-Enhancing Diffusion on Invertible Orientation Scores

International journal of computer vision, 2009-12, Vol.85 (3), p.253-278

2009

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Left-invariant evolutions of wavelet transforms on the similitude group

Applied and computational harmonic analysis, 2015-07, Vol.39 (1), p.110-137

2015

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LEFT-INVARIANT PARABOLIC EVOLUTIONS ON SE(2) AND CONTOUR ENHANCEMENT VIA INVERTIBLE ORIENTATION SCORES PART I: LINEAR LEFT-INVARIANT DIFFUSION EQUATIONS ON SE(2)

Quarterly of applied mathematics, 2010-06, Vol.68 (2), p.255-292

2010

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A variational approach to cardiac motion estimation based on covariant derivatives and multi-scale Helmholtz decomposition

Quarterly of applied mathematics, 2013-01, Vol.71 (1), p.1-36

2013

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Robust Retinal Vessel Segmentation via Locally Adaptive Derivative Frames in Orientation Scores

IEEE transactions on medical imaging, 2016-12, Vol.35 (12), p.2631-2644

2016

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LEFT-INVARIANT PARABOLIC EVOLUTIONS ON SE(2) AND CONTOUR ENHANCEMENT VIA INVERTIBLE ORIENTATION SCORES PART II: NONLINEAR LEFT-INVARIANT DIFFUSIONS ON INVERTIBLE ORIENTATION SCORES

Quarterly of applied mathematics, 2010-06, Vol.68 (2), p.293-331

2010

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Mathematical Methods for Signal and Image Analysis and Representation

1. Aufl., 2012

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A Multi-Orientation Analysis Approach to Retinal Vessel Tracking

Journal of mathematical imaging and vision, 2014, Vol.49 (3), p.583-610

2014

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Roto-translation equivariant convolutional networks: Application to histopathology image analysis

Medical image analysis, 2021-02, Vol.68, p.101849-101849, Article 101849

2021

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Roto-Translation Covariant Convolutional Networks for Medical Image Analysis

Medical Image Computing and Computer Assisted Intervention – MICCAI 2018, p.440-448

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Lesion Segmentation in Ultrasound Using Semi-Pixel-Wise Cycle Generative Adversarial Nets

IEEE/ACM transactions on computational biology and bioinformatics, 2021-11, Vol.18 (6), p.2555-2565

2021

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Stability metrics for optic radiation tractography: Towards damage prediction after resective surgery

Journal of neuroscience methods, 2017-08, Vol.288, p.34-44

2017

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Optimal Paths for Variants of the 2D and 3D Reeds–Shepp Car with Applications in Image Analysis

Journal of mathematical imaging and vision, 2018, Vol.60 (6), p.816-848

2018

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Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2)

Journal of mathematical imaging and vision, 2014, Vol.49 (2), p.384-417

2014

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Template Matching via Densities on the Roto-Translation Group

IEEE transactions on pattern analysis and machine intelligence, 2018-02, Vol.40 (2), p.452-466

2018

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Curve cuspless reconstruction via sub-Riemannian geometry

ESAIM. Control, optimisation and calculus of variations, 2014-07, Vol.20 (3), p.748-770

2014

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Differential Geometry and Orientation Analysis in Image Processing

Journal of mathematical imaging and vision, 2018-07, Vol.60 (6), p.763-765

2018

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Probability of detection curve for the automatic visual inspection of steel bridges

ce/papers, 2023-09, Vol.6 (3-4), p.814-824

2023

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PDE-Based Group Equivariant Convolutional Neural Networks

Analysis of (sub-)Riemannian PDE-G-CNNs

Total Variation and Mean Curvature PDEs on the Homogeneous Space of Positions and Orientations

Geodesic Tracking via New Data-Driven Connections of Cartan Type for Vascular Tree Tracking

Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to Linear PDEs

Evaluating contextual processing in diffusion MRI: application to optic radiation reconstruction for epilepsy surgery

Left-Invariant Diffusions on the Space of Positions and Orientations and their Application to Crossing-Preserving Smoothing of HARDI images

Crossing-Preserving Coherence-Enhancing Diffusion on Invertible Orientation Scores

Left-invariant evolutions of wavelet transforms on the similitude group

LEFT-INVARIANT PARABOLIC EVOLUTIONS ON SE(2) AND CONTOUR ENHANCEMENT VIA INVERTIBLE ORIENTATION SCORES PART I: LINEAR LEFT-INVARIANT DIFFUSION EQUATIONS ON SE(2)

A variational approach to cardiac motion estimation based on covariant derivatives and multi-scale Helmholtz decomposition

Robust Retinal Vessel Segmentation via Locally Adaptive Derivative Frames in Orientation Scores

LEFT-INVARIANT PARABOLIC EVOLUTIONS ON SE(2) AND CONTOUR ENHANCEMENT VIA INVERTIBLE ORIENTATION SCORES PART II: NONLINEAR LEFT-INVARIANT DIFFUSIONS ON INVERTIBLE ORIENTATION SCORES

Mathematical Methods for Signal and Image Analysis and Representation

A Multi-Orientation Analysis Approach to Retinal Vessel Tracking

Roto-translation equivariant convolutional networks: Application to histopathology image analysis

Roto-Translation Covariant Convolutional Networks for Medical Image Analysis

Lesion Segmentation in Ultrasound Using Semi-Pixel-Wise Cycle Generative Adversarial Nets

Stability metrics for optic radiation tractography: Towards damage prediction after resective surgery

Optimal Paths for Variants of the 2D and 3D Reeds–Shepp Car with Applications in Image Analysis

Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2)

Template Matching via Densities on the Roto-Translation Group

Curve cuspless reconstruction via sub-Riemannian geometry

Differential Geometry and Orientation Analysis in Image Processing

Probability of detection curve for the automatic visual inspection of steel bridges

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