Homepage of Remco Duits





·          E    r.duits<AT>tue.nl

·          T  +31-40-247-2859  (TU/e W&I)

·          W   https://www.win.tue.nl/~rduits/

·        Curriculum Vitae

                        (CV)  pdf

o    (summary applications)  pdf

o    (complete list of publications) pdf


Present Affiliation

Eindhoven University of Technology

Department of Mathematics and Computer Science, MF 7.072

PO Box 513,

NL-5600 MB Eindhoven,

The Netherlands.






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, Analysis on Lie Groups, 

Mathematical Image Analysis and Medical Image Analysis.


Complete list of publications: pdf

Recent research presentations:

pptx (short & small)   pptx (middle size)   pptx (long & large)

General presentations see: pptx  pptx

Invited Talks & Conferences: pdf

Link to Mathematica package orientation score processing:  html


PhDThesis: pdf (cum laude, nominated as best of the dep. for TU/e PhD prize 2005)  ) :

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


Links to key publications  (ordered over 5 research areas) :


 Orientation Score Theory 

PDE Theory, Fourier Theory, Wavelet Theory, Probability Theory & Geometric Control on SE(d)


- Brownian motion (Diffusion) in orientation scores:


pdf (QAM 2010), pdf (QAM 2010), pdf (IJCV 2009)

            Example Crossing-Preserving Diffusion (CEDOS) of 2D image avi

            Crossing-Preserving Diffusion of 3D images: pdf (arXiv 2017)


- Direction process (Convection-Diffusion) 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- Spec Issue. in honor of Joseph Fourier’s 250 birthday)


- Introduction to orientation score processing

pdf pdf pdf pdf


- Construction of invertible orientation scores (2D & 3D) :

                        pdf (IJCV 2007),  pdf (PRIA 2007)  pdf (SSVM 2015)

                        pdf (PhD-thesis), pdf (new arXiv 2017)

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)


Projective line bundle & 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 on base manifold of positions and orientations:

 pdf (JMIV 2018)


-         Geometric Deep-Learning on Euclidean Motion group

pdf (MICCAI 2018)


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 application: 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 diffusions of 3D datasets: pdf (JMIV 2018) 


-         Vessel Detection - Mitosis DetectionCell Boundary Detection pdf (MICCAI 2018)


- Template Matching & Machine Learning in SE(2): pdf (PAMI 2017)




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

Currently involved as main applicant in the approved research grants :

-         European Research Council 2013-2018  ERC-Stg (personal grant)  Title: Lie Analysis, ( no. 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.

Currently involved as co-applicant in:

IST/e High Potential Program TU/e, image science and technology

EU-Marie Curie FIRST (ag.no. PITN-GA-2009-238702)

Lie Analysis Workshop:







2WA08 (Applied Functional Analysis)

2DX00 (Mathematics for Physiology)

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

CourseInfo: pdf


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










Download links:           jpg1, jpg2, jpg3 jpg4, jpg5, jpg6


Download links:           pdf  pdf  pdf