Luc Florack | Eindhoven University of Technology (original) (raw)

Papers by Luc Florack

Research paper thumbnail of P13.03.B Predicting Functional Connectivity from Structural Connectivity in Glioma Patients

Neuro-Oncology

BACKGROUND The mechanism by which activity in the brain relates to its anatomical structure is a ... more BACKGROUND The mechanism by which activity in the brain relates to its anatomical structure is a central topic of research in neuroscience. In recent years, this relation has been studied in the context of network science, where anatomical white-matter connections are captured in Structural Connectivity (SC) and statistical dependence between grey-matter activity in Functional Connectivity (FC). The relation between SC and FC is poorly understood at an individual level, especially in glioma patients. Developing methods to predict FC from SC in these patients could improve our understanding of how gliomas affect brain function, and consequently cognition. Furthermore, a model accurate at individual patient level could aid in clinical decision-making by identifying eloquent areas and connections in individuals. MATERIAL AND METHODS Building on earlier work predicting FC from SC in healthy subjects, we trained a deep learning model on tractography and resting-state fMRI data of 288 gli...

Research paper thumbnail of L.: Finsler geometry on higher order tensor fields and applications to high angular resolution diffusion imaging

© The Author(s) 2010. This article is published with open access at Springerlink.com Abstract We ... more © The Author(s) 2010. This article is published with open access at Springerlink.com Abstract We study 3D-multidirectional images, using Finsler geometry. The application considered here is in med-ical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med. 48(6):1358–1372, 2004) of the brain. The goal is to reveal the architecture of the neural fibers in brain white matter. To the variety of existing techniques, we wish to add novel approaches that exploit differential geometry and ten-sor calculus. In Diffusion Tensor Imaging (DTI), the diffusion of wa-ter is modeled by a symmetric positive definite second order tensor, leading naturally to a Riemannian geometric frame-work. A limitation is that it is based on the assumption that there exists a single dominant direction of fibers restrict-ing the thermal motion of water molecules. Using HARDI data and higher order tensor models, we can extract mul-tiple relevant direction...

Research paper thumbnail of On the duality of scalar and density flows

Lecture Notes in Computer Science, 1997

Research paper thumbnail of BRST-quantization of gauge eld theories

Research paper thumbnail of Gaussian Scale-Space Theory: Proc. PhD School on Scale-Space Theory

Research paper thumbnail of P01.05.A Working memory performance is associated with functional connectivity between the right dlPFC and DMN in glioma patients

Neuro-Oncology

Background Patients with primary brain tumors frequently suffer from cognitive impairments in mul... more Background Patients with primary brain tumors frequently suffer from cognitive impairments in multiple domains, leading to serious consequences for socio-professional functioning and quality of life. The functional-anatomical basis of these impairments is still poorly understood. The study of correlated BOLD activity in the brain (i.e. functional connectivity) has greatly contributed to our understanding of how brain activity supports cognitive function. In particular, activity observed during the execution of specific tasks can be related to various distributed functional networks, stressing the importance of interactions between remote brain regions. Among these networks, the Default Mode Network (DMN) and the Fronto-Parietal Network (FPN) have consistently been associated with working memory performance. Recently, using task-fMRI in glioma patients, poor performance in a working memory task was associated with less deactivation of the DMN during this task and to a lack of task-ev...

Research paper thumbnail of Modeling of intracerebral interictal epileptic discharges: Evidence for network interactions

Clinical neurophysiology : official journal of the International Federation of Clinical Neurophysiology, 2018

The interictal epileptic discharges (IEDs) occurring in stereotactic EEG (SEEG) recordings are in... more The interictal epileptic discharges (IEDs) occurring in stereotactic EEG (SEEG) recordings are in general abundant compared to ictal discharges, but difficult to interpret due to complex underlying network interactions. A framework is developed to model these network interactions. To identify the synchronized neuronal activity underlying the IEDs, the variation in correlation over time of the SEEG signals is related to the occurrence of IEDs using the general linear model. The interdependency is assessed of the brain areas that reflect highly synchronized neural activity by applying independent component analysis, followed by cluster analysis of the spatial distributions of the independent components. The spatiotemporal interactions of the spike clusters reveal the leading or lagging of brain areas. The analysis framework was evaluated for five successfully operated patients, showing that the spike cluster that was related to the MRI-visible brain lesions coincided with the seizure ...

Research paper thumbnail of Feature Vector Similarity Based on Local Structure

Lecture Notes in Computer Science, 2007

Research paper thumbnail of Coarse‐to‐fine partitioning of signals

PAMM, 2007

An empirically acquired signal can be analyzed in a multi‐scale framework. Its multi‐scale struct... more An empirically acquired signal can be analyzed in a multi‐scale framework. Its multi‐scale structure induces a hierarchical partitioning of the signal domain into topologically meaningful segments. A method is proposed to operationalize this using elementary results from singularity theory for certain generic solutions of the one‐dimensional heat equation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Research paper thumbnail of A Geometric Model for Cortical Magnification

Lecture Notes in Computer Science, 2000

Research paper thumbnail of Data, models, and images

Proceedings of 3rd IEEE International Conference on Image Processing

ABSTRACT

Research paper thumbnail of Image Structure

Computational Imaging and Vision, 1997

notation: A = {F, </>}. In sloppy form: A = J dx f (x) </>( x). Samples are always fi... more notation: A = {F, </>}. In sloppy form: A = J dx f (x) </>( x). Samples are always finite, as opposed to point values of the underlying source field. Apart from this they may be positive, zero, or negative. A positive sample does not imply positivity of the underlying source field; a source is positive if all samples obtained by positive definite detectors tum out positive. If we want to compare different samples, we have to gauge our detectors by a conventional normalisation. For the moment we will require neither positivity nor normalisation. Since Definition 3.1 claims to define a local sample, we have to be able to tell what its base point is. In order to do so we need an explicit definition of a projection map 7r : ~ -+ M which associates each detector element </> E ~ with its corresponding base point x = 7r[</>]. This in tum assumes that we can perceive of ~ as a "bundle" of local device spaces ~x, comprising one "fibre" for each base point: ~ = UxEM~x' The inverse image 7r1(x) of a base point x is, by definition, the entire local device space ~x at that point. A local state space ~x is then established as the physical degrees of freedom probed by a local device space ~x, i.e. "what we are looking at" with a localised detector. We will return to a precise definition of 7r in Section 3.9. For the moment it suffices to think of the base point as a the "centre of gravity" for the filter </>. The base point we would like to attribute to a sample is of course the one corresponding to the detector, but note that there is no way of telling from the value of a local sample "where it's at"; the geometric notion of a base point is established as an extrinsic detector property (a label). Obviously, local samples are obtained at finite resolution. Again, being a spatiotemporal property, resolution cannot be inferred from a sample's value, only 3.1 Local Samples 41 from its underlying aperture. A precise definition of the resolution of a local detector requires us to define a notion of extent or inner scale for that detector. A definition of inner scale will also be postponed until Section 3.9; think of it for the moment as the width of a central region, containing the filter's base point, where most of the filter's weight is concentrated (it is clearly not very useful to relate inner scale to detector support, since by construction this may be all of spacetime). See also Problem 3.2. We can consider the transformation (push forward) of a detector under an arbitrary spacetime automorphism, i.e. a "warping", or a smooth transformation of spacetime with smooth inverse. Definition 3.2 (Push Forward) Let () : M -t M : x 1-+ ()(x) be a smooth spacetime automorphism. The push forward of a filter is then defined as the mapping with Jacobian determinant J'X. == I det Vx I· This induces a natural, so-called pull back (also called "reciprocal image") of the source. Definition 3.3 (Pull Back) With the automorphism () and its push forward ()* as defined in Definition 3.2, the pull back of the source is defined as the mapping ()* : Eo(x) -t Ex : F 1-+ ()* F defined by ()* F[¢] ~f F[()*¢]. In sloppy form this states that ()* f == f 0 (), which physicists tend to refer to as "scalar field transformation" (Problem 3.3). Note that if ¢ lives at base point x, then its push forward ()*¢ is associated with the mapped point ()(x), which explains its name. Naturally, pull back works the other way around. Push forward and pull back are instances of a so-called" carry along" principle. If we have two communicating objects-i.c. sources plus detectors producing a response-then a change of either will in general be reflected in the output. Reversely, a given change in output can be explained as being caused by a change in either object. For example, shifting a patient underneath a scanner will have the same effect as moving the scanner in opposite sense over a stationary patient. This principle generalises to arbitrary deformations beyond rigid transformations (at least conceptually: one of the options is not necessarily in the interest of the patient). The idea is that at least one of these dual views is practicable and legitimate (e.g. processing scanner output). It would be formally more correct to attach base points to sources and detectors matching the labels of E and tl in Definitions 3.2 and 3.3, but that would yield rather cumbersome notations. There ought to be no confusion if we simply 42 Local Samples and Images keep in mind the following commutative diagram:

Research paper thumbnail of A Simplified Algorithm for Inverting Higher Order Diffusion Tensors

Research paper thumbnail of Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition

Lecture Notes in Computer Science, 2012

Research paper thumbnail of Regularization, scale-space, and edge detection filters

Lecture Notes in Computer Science, 1996

Research paper thumbnail of Higher-Order Tensors in Diffusion Imaging

Mathematics and Visualization, 2014

Research paper thumbnail of 6. Sparse Representation of Video Data by Adaptive Tetrahedralizations

… methods for signal and …

... Vision, Mathematical Methods for Signal and Image Analysis and Representation, 2012, DOI: 10.... more ... Vision, Mathematical Methods for Signal and Image Analysis and Representation, 2012, DOI: 10.1007/978-1-4471-2353-8_6,© Springer-Verlag London Limited 2012 6. Sparse Representation of Video Data by Adaptive Tetrahedralizations Laurent Demaret1, Armin Iske2 and ...

Research paper thumbnail of 10. An A Priori Model of Line Propagation

… methods for signal and …

... A numerical method for cyclic spatial boundary condition has been proposed by August Jonas [1... more ... A numerical method for cyclic spatial boundary condition has been proposed by August Jonas [16]. Here, we provide an explicit solution in Fourier space, that we have derived in collaboration with Remco Duits. ... Int. J. Comput. Vis. ...

Research paper thumbnail of 8. Left Invariant Evolution Equations on Gabor Transforms

… methods for signal and …

Luc Florack, Remco Duits, Geurt Jongbloed, Marie-Colette van Lieshout and Laurie Davies (eds.), C... more Luc Florack, Remco Duits, Geurt Jongbloed, Marie-Colette van Lieshout and Laurie Davies (eds.), Computational Imaging and Vision, Mathematical Methods for Signal and Image Analysis and Representation, 2012, DOI: 10.1007/978-1-4471-2353-8_8,© Springer-Verlag ...

Research paper thumbnail of 3. 3D-Coherence-Enhancing Diffusion Filtering for Matrix Fields

… methods for signal and …

Luc Florack, Remco Duits, Geurt Jongbloed, Marie-Colette van Lieshout and Laurie Davies (eds.), C... more Luc Florack, Remco Duits, Geurt Jongbloed, Marie-Colette van Lieshout and Laurie Davies (eds.), Computational Imaging and Vision, Mathematical Methods for Signal and Image Analysis and Representation, 2012, DOI: 10.1007/978-1-4471-2353-8_3,© Springer ... Image Vis. ...

Research paper thumbnail of P13.03.B Predicting Functional Connectivity from Structural Connectivity in Glioma Patients

Neuro-Oncology

BACKGROUND The mechanism by which activity in the brain relates to its anatomical structure is a ... more BACKGROUND The mechanism by which activity in the brain relates to its anatomical structure is a central topic of research in neuroscience. In recent years, this relation has been studied in the context of network science, where anatomical white-matter connections are captured in Structural Connectivity (SC) and statistical dependence between grey-matter activity in Functional Connectivity (FC). The relation between SC and FC is poorly understood at an individual level, especially in glioma patients. Developing methods to predict FC from SC in these patients could improve our understanding of how gliomas affect brain function, and consequently cognition. Furthermore, a model accurate at individual patient level could aid in clinical decision-making by identifying eloquent areas and connections in individuals. MATERIAL AND METHODS Building on earlier work predicting FC from SC in healthy subjects, we trained a deep learning model on tractography and resting-state fMRI data of 288 gli...

Research paper thumbnail of L.: Finsler geometry on higher order tensor fields and applications to high angular resolution diffusion imaging

© The Author(s) 2010. This article is published with open access at Springerlink.com Abstract We ... more © The Author(s) 2010. This article is published with open access at Springerlink.com Abstract We study 3D-multidirectional images, using Finsler geometry. The application considered here is in med-ical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med. 48(6):1358–1372, 2004) of the brain. The goal is to reveal the architecture of the neural fibers in brain white matter. To the variety of existing techniques, we wish to add novel approaches that exploit differential geometry and ten-sor calculus. In Diffusion Tensor Imaging (DTI), the diffusion of wa-ter is modeled by a symmetric positive definite second order tensor, leading naturally to a Riemannian geometric frame-work. A limitation is that it is based on the assumption that there exists a single dominant direction of fibers restrict-ing the thermal motion of water molecules. Using HARDI data and higher order tensor models, we can extract mul-tiple relevant direction...

Research paper thumbnail of On the duality of scalar and density flows

Lecture Notes in Computer Science, 1997

Research paper thumbnail of BRST-quantization of gauge eld theories

Research paper thumbnail of Gaussian Scale-Space Theory: Proc. PhD School on Scale-Space Theory

Research paper thumbnail of P01.05.A Working memory performance is associated with functional connectivity between the right dlPFC and DMN in glioma patients

Neuro-Oncology

Background Patients with primary brain tumors frequently suffer from cognitive impairments in mul... more Background Patients with primary brain tumors frequently suffer from cognitive impairments in multiple domains, leading to serious consequences for socio-professional functioning and quality of life. The functional-anatomical basis of these impairments is still poorly understood. The study of correlated BOLD activity in the brain (i.e. functional connectivity) has greatly contributed to our understanding of how brain activity supports cognitive function. In particular, activity observed during the execution of specific tasks can be related to various distributed functional networks, stressing the importance of interactions between remote brain regions. Among these networks, the Default Mode Network (DMN) and the Fronto-Parietal Network (FPN) have consistently been associated with working memory performance. Recently, using task-fMRI in glioma patients, poor performance in a working memory task was associated with less deactivation of the DMN during this task and to a lack of task-ev...

Research paper thumbnail of Modeling of intracerebral interictal epileptic discharges: Evidence for network interactions

Clinical neurophysiology : official journal of the International Federation of Clinical Neurophysiology, 2018

The interictal epileptic discharges (IEDs) occurring in stereotactic EEG (SEEG) recordings are in... more The interictal epileptic discharges (IEDs) occurring in stereotactic EEG (SEEG) recordings are in general abundant compared to ictal discharges, but difficult to interpret due to complex underlying network interactions. A framework is developed to model these network interactions. To identify the synchronized neuronal activity underlying the IEDs, the variation in correlation over time of the SEEG signals is related to the occurrence of IEDs using the general linear model. The interdependency is assessed of the brain areas that reflect highly synchronized neural activity by applying independent component analysis, followed by cluster analysis of the spatial distributions of the independent components. The spatiotemporal interactions of the spike clusters reveal the leading or lagging of brain areas. The analysis framework was evaluated for five successfully operated patients, showing that the spike cluster that was related to the MRI-visible brain lesions coincided with the seizure ...

Research paper thumbnail of Feature Vector Similarity Based on Local Structure

Lecture Notes in Computer Science, 2007

Research paper thumbnail of Coarse‐to‐fine partitioning of signals

PAMM, 2007

An empirically acquired signal can be analyzed in a multi‐scale framework. Its multi‐scale struct... more An empirically acquired signal can be analyzed in a multi‐scale framework. Its multi‐scale structure induces a hierarchical partitioning of the signal domain into topologically meaningful segments. A method is proposed to operationalize this using elementary results from singularity theory for certain generic solutions of the one‐dimensional heat equation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Research paper thumbnail of A Geometric Model for Cortical Magnification

Lecture Notes in Computer Science, 2000

Research paper thumbnail of Data, models, and images

Proceedings of 3rd IEEE International Conference on Image Processing

ABSTRACT

Research paper thumbnail of Image Structure

Computational Imaging and Vision, 1997

notation: A = {F, </>}. In sloppy form: A = J dx f (x) </>( x). Samples are always fi... more notation: A = {F, </>}. In sloppy form: A = J dx f (x) </>( x). Samples are always finite, as opposed to point values of the underlying source field. Apart from this they may be positive, zero, or negative. A positive sample does not imply positivity of the underlying source field; a source is positive if all samples obtained by positive definite detectors tum out positive. If we want to compare different samples, we have to gauge our detectors by a conventional normalisation. For the moment we will require neither positivity nor normalisation. Since Definition 3.1 claims to define a local sample, we have to be able to tell what its base point is. In order to do so we need an explicit definition of a projection map 7r : ~ -+ M which associates each detector element </> E ~ with its corresponding base point x = 7r[</>]. This in tum assumes that we can perceive of ~ as a "bundle" of local device spaces ~x, comprising one "fibre" for each base point: ~ = UxEM~x' The inverse image 7r1(x) of a base point x is, by definition, the entire local device space ~x at that point. A local state space ~x is then established as the physical degrees of freedom probed by a local device space ~x, i.e. "what we are looking at" with a localised detector. We will return to a precise definition of 7r in Section 3.9. For the moment it suffices to think of the base point as a the "centre of gravity" for the filter </>. The base point we would like to attribute to a sample is of course the one corresponding to the detector, but note that there is no way of telling from the value of a local sample "where it's at"; the geometric notion of a base point is established as an extrinsic detector property (a label). Obviously, local samples are obtained at finite resolution. Again, being a spatiotemporal property, resolution cannot be inferred from a sample's value, only 3.1 Local Samples 41 from its underlying aperture. A precise definition of the resolution of a local detector requires us to define a notion of extent or inner scale for that detector. A definition of inner scale will also be postponed until Section 3.9; think of it for the moment as the width of a central region, containing the filter's base point, where most of the filter's weight is concentrated (it is clearly not very useful to relate inner scale to detector support, since by construction this may be all of spacetime). See also Problem 3.2. We can consider the transformation (push forward) of a detector under an arbitrary spacetime automorphism, i.e. a "warping", or a smooth transformation of spacetime with smooth inverse. Definition 3.2 (Push Forward) Let () : M -t M : x 1-+ ()(x) be a smooth spacetime automorphism. The push forward of a filter is then defined as the mapping with Jacobian determinant J'X. == I det Vx I· This induces a natural, so-called pull back (also called "reciprocal image") of the source. Definition 3.3 (Pull Back) With the automorphism () and its push forward ()* as defined in Definition 3.2, the pull back of the source is defined as the mapping ()* : Eo(x) -t Ex : F 1-+ ()* F defined by ()* F[¢] ~f F[()*¢]. In sloppy form this states that ()* f == f 0 (), which physicists tend to refer to as "scalar field transformation" (Problem 3.3). Note that if ¢ lives at base point x, then its push forward ()*¢ is associated with the mapped point ()(x), which explains its name. Naturally, pull back works the other way around. Push forward and pull back are instances of a so-called" carry along" principle. If we have two communicating objects-i.c. sources plus detectors producing a response-then a change of either will in general be reflected in the output. Reversely, a given change in output can be explained as being caused by a change in either object. For example, shifting a patient underneath a scanner will have the same effect as moving the scanner in opposite sense over a stationary patient. This principle generalises to arbitrary deformations beyond rigid transformations (at least conceptually: one of the options is not necessarily in the interest of the patient). The idea is that at least one of these dual views is practicable and legitimate (e.g. processing scanner output). It would be formally more correct to attach base points to sources and detectors matching the labels of E and tl in Definitions 3.2 and 3.3, but that would yield rather cumbersome notations. There ought to be no confusion if we simply 42 Local Samples and Images keep in mind the following commutative diagram:

Research paper thumbnail of A Simplified Algorithm for Inverting Higher Order Diffusion Tensors

Research paper thumbnail of Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition

Lecture Notes in Computer Science, 2012

Research paper thumbnail of Regularization, scale-space, and edge detection filters

Lecture Notes in Computer Science, 1996

Research paper thumbnail of Higher-Order Tensors in Diffusion Imaging

Mathematics and Visualization, 2014

Research paper thumbnail of 6. Sparse Representation of Video Data by Adaptive Tetrahedralizations

… methods for signal and …

... Vision, Mathematical Methods for Signal and Image Analysis and Representation, 2012, DOI: 10.... more ... Vision, Mathematical Methods for Signal and Image Analysis and Representation, 2012, DOI: 10.1007/978-1-4471-2353-8_6,© Springer-Verlag London Limited 2012 6. Sparse Representation of Video Data by Adaptive Tetrahedralizations Laurent Demaret1, Armin Iske2 and ...

Research paper thumbnail of 10. An A Priori Model of Line Propagation

… methods for signal and …

... A numerical method for cyclic spatial boundary condition has been proposed by August Jonas [1... more ... A numerical method for cyclic spatial boundary condition has been proposed by August Jonas [16]. Here, we provide an explicit solution in Fourier space, that we have derived in collaboration with Remco Duits. ... Int. J. Comput. Vis. ...

Research paper thumbnail of 8. Left Invariant Evolution Equations on Gabor Transforms

… methods for signal and …

Luc Florack, Remco Duits, Geurt Jongbloed, Marie-Colette van Lieshout and Laurie Davies (eds.), C... more Luc Florack, Remco Duits, Geurt Jongbloed, Marie-Colette van Lieshout and Laurie Davies (eds.), Computational Imaging and Vision, Mathematical Methods for Signal and Image Analysis and Representation, 2012, DOI: 10.1007/978-1-4471-2353-8_8,© Springer-Verlag ...

Research paper thumbnail of 3. 3D-Coherence-Enhancing Diffusion Filtering for Matrix Fields

… methods for signal and …

Luc Florack, Remco Duits, Geurt Jongbloed, Marie-Colette van Lieshout and Laurie Davies (eds.), C... more Luc Florack, Remco Duits, Geurt Jongbloed, Marie-Colette van Lieshout and Laurie Davies (eds.), Computational Imaging and Vision, Mathematical Methods for Signal and Image Analysis and Representation, 2012, DOI: 10.1007/978-1-4471-2353-8_3,© Springer ... Image Vis. ...