A New Methodology for Multiscale Myocardial Deformation and Strain Analysis Based on Tagging MRI

Myocardial deformation and strain can be investigated using suitably encoded cine MRI that admits disambiguation of material motion. Practical limitations currently restrict the analysis to in-plane motion in cross-sections of the heart (2D + time), but the proposed method readily generalizes to 3D + time. We propose a new, promising methodology, which departs from a multiscale algorithm that exploits local scale selection so as to obtain a robust estimate for the velocity gradient tensor field. Time evolution of the deformation tensor is governed by a first-order ordinary differential equation, which is completely determined by this velocity gradient tensor field. We solve this matrix-ODE analytically and present results obtained from healthy volunteers as well as from patient data. The proposed method requires only off-the-shelf algorithms and is readily applicable to planar or volumetric tagging MRI sampled on arbitrary coordinate grids

A generic approach to diffusion filtering of matrix-fields

Diffusion tensor magnetic resonance imaging (DT-MRI), is a image acquisition method, that provides matrix-valued data, so-called matrix fields. Hence image processing tools for the filtering and analysis of these data types are in demand. In this artricle we propose a generic framework that allows us to find the matrix-valued counterparts of the Perona-Malik PDEs with various diffusivity functions. To this end we extend the notion of derivatives and associated differential operators to matrix fields of symmetric matrices by adopting an operator-algebraic point of view. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our novel matrix-valued Perona-Malik diffusion filters

A generic approach to the filtering of matrix fields with singular PDEs

There is an increasing demand to develop image processing tools for the filtering and analysis of matrix-valued data, so-called matrix fields. In the case of scalar-valued images parabolic partial differential equations (PDEs) are widely used to perform filtering and denoising processes. Especially interesting from a theoretical as well as from a practical point of view are PDEs with singular diffusivities describing processes like total variation (TV-) diffusion, mean curvature motion and its generalisation, the so-called self-snakes. In this contribution we propose a generic framework that allows us to find the matrix-valued counterparts of the equations mentioned above. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our matrix-valued, singular diffusion filters

The Intrinsic Structure of the Optic Flow Field

n this paper, a generating equation for optic flow is proposed that generalises Horn and Schunck's Optic Flow Constraint Equation (OFCE). Whereas the OFCE has an interpretation as a pointwise conservation law, requiring grey-values associated with fixed-scale volume elements to be constant when co-moving with the flow, the new one can be regarded as a similar conservation requirement in which the flow elements have variable scale consistent with the field's divergence. Thus the equation gives rise to a definition of optic flow which is compatible with the scale-space paradigm. We emphasise the gauge invariant nature of optic flow due to the inherent ambiguity of its components, i.e. the well-known aperture problem. Since gauge invariance is intrinsic to any definition of optic flow based solely on the data, it is argued that the gauge should be fixed on the basis of extrinsic knowledge of the image formation process and of the physics of the scene. The optic flow field is replaced by an approximating field so as to allow for an order-by-order operational definition preserving gauge invariance, i.e.\ the approximation does not add spurious degrees of freedom to the field. One thus obtains a defining system of linear equations in the optic flow components up to arbitrary order, which remains decoupled from any physical considerations of gauge fixing. Such considerations are needed to derive a complementary system of gauge conditions that allows for a unique, physically sensible solution of the optic flow equations. The theory is illustrated by means of several examples

Feature vector similarity based on local structure

Local feature matching is an essential component of many image retrieval algorithms. Euclidean and Mahalanobis distances are mostly used in order to compare two feature vectors. The first distance does not give satisfactory results in many cases and is inappropriate in the typical case where the components of the feature vector are incommensurable, whereas the second one requires training data. In this paper a stability based similarity measure (SBSM) is introduced for feature vectors that are composed of arbitrary algebraic combinations of image derivatives. Feature matching based on SBSM is shown to outperform algorithms based on Euclidean and Mahalanobis distances, and does not require any training

A simplified algorithm for inverting higher order diffusion tensors

In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann-Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI). An important application of DWI is in the inference of the local architecture of the tissue, typically consisting of thin elongated structures, such as axons or muscle fibers, by measuring the constrained diffusion of water within the tissue. From high angular resolution diffusion imaging (HARDI) data, one can estimate the diffusion orientation distribution function (dODF), which indicates the relative diffusivity in all directions and can be represented by a spherical polynomial. We express this dODF as an equivalent spherical monomial (higher order tensor) to directly generalize the (second order) diffusion tensor approach. To enable efficient computation of Riemann-Finslerian quantities on diffusion weighted (DW)-images, such as the metric/norm tensor, we present a simple and efficient algorithm to invert even order spherical monomials, which extends the familiar inversion of diffusion tensors, i.e., symmetric matrices.</p

Working memory performance is associated with functional connectivity between the right dlPFC and DMN in glioma patients

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-evoked changes in the DMN-FPN structure. In this study, we investigated whether these effects are reflected in the resting-state (RS) functional connectivity of the same patient group, i.e. when no task was performed during fMRI. We additionally zoomed in on the part of the FPN located in the dorsolateral Prefrontal Cortex (dlPFC), since this region is believed to be mainly responsible for DMN deactivation.Resting-state functional MRI data were acquired pre-operatively from 45 brain tumor patients (20 low- and 25 high-grade glioma patients). Results of a pre-operative in-scanner N-back working memory fMRI task were used to assess working memory performance.Patient brains were parcellated into ROIs using both the Gordon and Yeo atlas, which have the FPN and DMN network identities readily available. The dlPFC was defined based on masks retrieved from NeuroSynth.To measure DMN-FPN functional connectivity the average Pearson correlation between the activation time series in the regions belonging to the FPN and the DMN was calculated. Functional connectivity between the DMN and the dlPFC was calculated in a similar way.The average correlation between the resting-state fMRI activity in the right dlPFC and in the DMN was negatively associated with working memory performance for both the Gordon atlas (p \\< 0.003) and Yeo atlas (p \\< 0.007). No association was found for the correlation between activity in the left dlPFC and the DMN, nor for the correlation between the activity in the whole FPN and the DMN.Our findings show that working memory performance of glioma patients is related to interactions between networks that can be measured with resting-state fMRI. Furthermore, the results provide further evidence that not only specific brain regions are important for cognitive performance, but that also the interactions between large-scale networks should be considered

Front-End Vision: A Multiscale Geometry Engine

Abstract. The paper is a short tutorial on the multiscale differential geometric possibilities of the front-end visual receptive fields, modeled by Gaussian derivative kernels. The paper is written in, and interactive through the use of Mathematica 4, so each statement can be run and modified by the reader on images of choice. The notion of multiscale invariant feature detection is presented in detail, with examples of second, third and fourth order of differentiation