Homepage of Remco Duits
· E r.duits@tue.nl
· T +31-624983108
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· List
of publications: pdf
· Google
Scholar: link
Present Affiliation
Eindhoven
University of Technology
Dep. Mathematics and Computer Science,
MF 5.071B
PO Box 513,
NL-5600 MB Eindhoven,
The Netherlands.
Research
Profile:
I am a Mathematician.
I develop new mathematical theory and algorithms to tackle
image analysis applications.
Main Expertises:
Differential Geometry, Harmonic Analysis, Probability Theory,
Numerical
Analysis, Functional Analysis, Machine Learning &
PDEs on Lie Groups, Mathematical
Image Analysis & Medical Image Analysis.
Complete list
of publications: pdf
Presentations:
IHP-presentations:
Geometry Talk: youtube
Machine Learning Talk : youtube
Slides recent
presentations :
pptx (short & small) pptx (middle size) pptx
(long & large)
General presentations
see:
pptx pptx
Overview invited talks & conferences: pdf
Link to Mathematica package
orientation score processing: html
PhD Thesis R.Duits:
pdf (cum laude, nom. as best
of the dep. for TU/e PhD prize 2005)
Master Thesis R.Duits: pdf (cum laude 2001)
PhDThesis of PhD Projects (under daily supervision R.Duits)
:
J.M. Portegies pdf
E.J. Bekkers pdf (cum laude,
nominated as best of the dep.
for TU/e PhD prize 2017)
E.M. Franken pdf (cum laude,
nominated as best of the dep.
for TU/e PhD prize 2009)
J. Zhang pdf
S.P.L. Meesters pdf
B.J. Janssen pdf
Recent
Master Thesis (under daily
supervision R.Duits) :
B.M.N. Smets pdf
Links to key publications
(ordered over 5 research
areas) :
Orientation Score Theory
PDE Theory, Fourier Theory, Wavelet
Theory, Probability Theory & Geometric
Control & Machine Learning on Lie group SE(d).
- Brownian motion in orientation scores:
pdf (QAM 2010),
pdf (QAM 2010),
pdf
(IJCV 2009)
Example crossing-preserving diffusion 2D image avi
of 3D image: pdf
- Direction process in orientation
scores :
pdf (QAM 2008),
pdf (LNCS 2007),
- Exact solutions Brownian
motion & Direction process on SE(3):
pdf
(DGA 2017)
-
New Fourier Transform on the homogeneous space of positions
and orientations for exact solutions of linear PDEs
pdf (Entropy-2019)
- Introduction to orientation score processing
- Construction of invertible
orientation scores (2D & 3D) :
pdf (IJCV 2007),
pdf (PRIA 2007)
pdf
(SSVM 2015)
pdf (PhD-thesis),
complete review:
pdf
- Review on numerics left-inv PDE’s & comparion to exact solutions:
pdf (NM-TMA 2015)
- Tracking and geometric
control within orientation scores :
pdf (JMIV
2018)
pdf (JMIV 2014)
- Multiple scale orientation scores: pdf / pdf (ACHA 2015)
-
Sub-Riemannian geodesics in Euclidean
motion group:
2D : pdf (JMIV 2014),
pdf (ESAIM-cocv 2014),
PDE & data-driven approach:
pdf (SIIMS 2015),
pdf
(SSVM 2015)
Fast-marching approach :
pdf
(2015)
Maxwell sets pdf
(GSI 2017)
3D : pdf (JDCS 2016) (package)
dD : pdf (bookchapter 2013)
-
Sub-Riemannian geodesics in SO(3):
pdf
(JMIV 2017)
-
Locally adaptive frame theory in SE(d)
pdf (JMIV 2016)
-
Finsler geometry:
pdf (JMIV 2018)
-
Cartan connections
for image processing
pdf (2020)
-
Geometric deep-learning on the Euclidean motion group
pdf (MICCAI 2018)
-
PDE-based
Geometric deep-Learning on
SE(d)
pdf (2020)
pdf (2021)
pdf (2022)
pdf
(2023)
pdf (2023)
Medical Image Analysis
Applications of Orientation Scores:
- Training of templates/inverse problem in orientation scores :
pdf (EMMCVPR LNCS 2014)
- Biomarker curvature
pdf (OMIA 2015)
- Crossing-preserving vesselness: pdf (MICCAI 2014)
- Vessel Segmentation via LAD in SE(2):
pdf (TMI 2016)
- Locally Adaptive Derivatives (LAD) in SE(d): pdf (JMIV 2016)
- Curvature estimation via LAD in
SE(3): pdf (SSVM 2017)
- Perceptual grouping:
pdf (Biological Cyb.
2017)
- Crossing-preserving diffusion
3D datasets:
pdf (JMIV 2018)
- Vessel Detection - Mitosis Detection – Cell Boundary Detection
pdf (MICCAI 2018)
- Lesion segmentation via Machine
Learning by localized cyclic
GANs pdf (IEEE-TCCB 2020)
- Template Matching & Machine Learning in SE(2): pdf (PAMI 2017)
- Vessel and Nuclei Segmentation
via Equivariant Deep Learning pdf
- Cancer Detection in Histopathology Images pdf (MEDIA 2020)
- Vascular Tree
tracking in ophthalmology pdf (SSVM 2023)
Diffusion Weighted MRI
Geometric Control & PDE Theory
on SE(3)
Fiber enhancement and completion in
DW-MRI :
-
theory: pdf (IJCV 2010) pdf (LNCS 2011), pdf (LNCS 2011), pdf (JMIV 2014), pdf (SSVM 2015)
-
applications: pdf (LNCS 2011), pdf (MICCAI), pdf
(JNeuMeth2017)
combination with
CSD & practical validations:
pdf (2015)
-
numerics : pdf
(NM-TMA 2013) (package)
pdf (Eurographics)
-
abstracts to open source DiPY implementations:
pdf
(linear contextual
enhancement, 2016)
pdf
(fiber to bundle coherence measures, 2016)
-
Connectivity Measures pdf (MICCAI 2018)
Morphological scale spaces on
DW-MRI :
-
theory : pdf
(JMIV 2014)
-
applications : pdf
(Dagstuhl 2013), new (PlosOne 2014)
Gabor Transform Processing
PDEs on Heisenberg Group
Theory of left-invariant evolutions on Gabor transforms with applications in cardiac imaging :
pdf (ACHA 2013)
-
Differential Reassignment :
pdf
(Book-ch 8 2012)
-
applications : pdf
(FIMH 2013), pdf (STACOM
2013)
Optic Flow
Connections and Flow Fields
Multi-scale Helmholtz decomposition and covariant derivatives
for cardiac motion analysis:
pdf
(QAM 2013) pdf (LNCS 2012)
Scale Space Theory
Evolution Equations &
Inverse Problems
Reconstruction from scale
space singularities via Gelfand triples :
·
theory pdf (IJCV 2009), pdf (LNCS
2006), pdf
·
implementation pdf (IJCV
2006)
·
applications : pdf (QAM
2013), pdf (LNCS 2012), pdf (NW 2008)
Scale spaces on bounded domain:
pdf (IJCV 2007), pdf (LNCS 2005)
Scale spaces on Lie
groups : pdf
(LNCS 2007), pdf
(JMIV 2012)
Axioms of scale space theory :
pdf (JMIV,2004)
Synopsis Lie Group Analysis research and applications: doc
Awards/Achievements: pdf
Research Grants
Main applicant in research grants :
-
VICI
NWO 2021-2026 (personal grant R.Duits)
Full Title: Geometric Learning for Image Analysis (nr. VI.C.202-031)
-
European Research
Council ERC 2014-2019 (personal grant R.Duits)
Title: Lie Analysis (nr. 335555)
Full title: Lie
Group Analysis for Medical Image Processing
- EU-Marie Curie (FP7-PEOPLE-2013-ITN),
Title: MANET (no. 607643)
Full
Title: Metric Analysis and Emerging Technologies.
-
TU/e PhD-TA. Title: Geometric
Image Processing and Probabilistic Deep Learning (2019-2024)
-
REMODEL EU-Marie Curie
-Staff Exchange (2023-2027) WP Title: Differential Equations for Equivariant
Neural Networks.
and previously co-applicant in:
IST/e High Potential Program TU/e (2010-2015).
EU-Marie Curie FIRST (ag.no. PITN-GA-2009-238702)
Lie Analysis Workshop:
Education
2WA80 (Complex Analysis)
2WA08 (Applied Functional Analysis)
2MMA70 (Differential Geometry
for Image Processing)
2DX00 (Mathematics for Physiology)
2MMA70 (Mathematics for Neural Networks)
2DM00 (Basiswiskunde)
2DM60 (Wiskunde II)
8G116 (Aansluitingsmodule voor
BMT)
8D020 (Mathematical Techniques for Image
Analysis)
2WBB0 (Calculus)
Overview Student project supervision, see doc
New Master Course
Differential Geometry for Image Processing
Course Info:
pdf
Lecture Notes:
Part I: pdf
part II: pdf
part III: pdf
part IV: pdf
Summer School Cortona 2017
Orientation Score Theory and Its
Solutions to Cortical PDE, ODE and Wavelet Models
Schedule pdf Course-material
folder zip Slides zip