Jiri Jan

Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering

This paper presents a new approach to inverting (fitting) models of coupled dynamical systems based on state-of-the-art (cubature) Kalman filtering. Crucially, this inversion furnishes posterior estimates of both the hidden states and parameters of a system, including any unknown exogenous input. Because the underlying generative model is formulated in continuous time (with a discrete observation process) it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations. These are an important class of models that are particularly appropriate for biological time-series, where the underlying system is specified in terms of kinetics or dynamics (i.e., dynamic causal models). We provide comparative evaluations with generalized Bayesian filtering (dynamic expectation maximization) and demonstrate marked improvements in accuracy and computational efficiency. We compare the schemes using a series of difficult (nonlinear) toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fMRI. Our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems, even in the absence of known exogenous (experimental) input; e.g., resting state fMRI studies and spontaneous fluctuations in electrophysiological studies. Importantly, unlike current Bayesian filters (e.g. DEM), our scheme provides estimates of time-varying parameters, which we will exploit in future work on the adaptation and enabling of connections in the brain.

Retinal vessel segmentation by improved matched filtering: evaluation on a new high-resolution fundus image database

Automatic assessment of retinal vessels plays an important role in the diagnosis of various eye, as well as systemic diseases. A public screening is highly desirable for prompt and effective treatment, since such diseases need to be diagnosed at an early stage. Automated and accurate segmentation of the retinal blood vessel tree is one of the challenging tasks in the computer-aided analysis of fundus images today. We improve the concept of matched filtering, and propose a novel and accurate method for segmenting retinal vessels. Our goal is to be able to segment blood vessels with varying vessel diameters in high-resolution colour fundus images. All recent authors compare their vessel segmentation results to each other using only low-resolution retinal image databases. Consequently, we provide a new publicly available high-resolution fundus image database of healthy and pathological retinas. Our performance evaluation shows that the proposed blood vessel segmentation approach is at least comparable with recent state-of-the-art methods. It outperforms most of them with an accuracy of 95% evaluated on the new database.

Dynamic Granger causality based on Kalman filter for evaluation of functional network connectivity in fMRI data

Increasing interest in understanding dynamic interactions of brain neural networks leads to formulation of sophisticated connectivity analysis methods. Recent studies have applied Granger causality based on standard multivariate autoregressive (MAR) modeling to assess the brain connectivity. Nevertheless, one important flaw of this commonly proposed method is that it requires the analyzed time series to be stationary, whereas such assumption is mostly violated due to the weakly nonstationary nature of functional magnetic resonance imaging (fMRI) time series. Therefore, we propose an approach to dynamic Granger causality in the frequency domain for evaluating functional network connectivity in fMRI data. The effectiveness and robustness of the dynamic approach was significantly improved by combining a forward and backward Kalman filter that improved estimates compared to the standard time-invariant MAR modeling. In our method, the functional networks were first detected by independent component analysis (ICA), a computational method for separating a multivariate signal into maximally independent components. Then the measure of Granger causality was evaluated using generalized partial directed coherence that is suitable for bivariate as well as multivariate data. Moreover, this metric provides identification of causal relation in frequency domain, which allows one to distinguish the frequency components related to the experimental paradigm. The procedure of evaluating Granger causality via dynamic MAR was demonstrated on simulated time series as well as on two sets of group fMRI data collected during an auditory sensorimotor (SM) or auditory oddball discrimination (AOD) tasks. Finally, a comparison with the results obtained from a standard time-invariant MAR model was provided.

Registration of bimodal retinal images - improving modifications

The proper optical disc segmentation in images provided by confocal laser scanning ophthalmoscope and by color fundus-camera is a necessary step in early glaucoma or arteriosclerosis detection. Fusing information from both modalities into a vector-valued image is expected to improve the segmentation reliability. The paper describes a registration of these images using optimization based on mutual information criterion function extended with gradient-image mutual information. The controlled random search (CRS) has been found to be a more robust optimization routine than the simulated annealing (SA) while tested on a set of 174 image pairs. Finally, the multi-resolution algorithm for bimodal retinal image registration achieving the success-rate of 94% is proposed.

Retinal image analysis aimed at blood vessel tree segmentation and early detection of neural-layer deterioration

An automatic method of segmenting the retinal vessel tree and estimating status of retinal neural fibre layer (NFL) from high resolution fundus camera images is presented. First, reliable blood vessel segmentation, using 2D directional matched filtering, enables to remove areas occluded by blood vessels thus leaving remaining retinal area available to the following NFL detection. The local existence of rather faint and hardly visible NFL is detected by combining several newly designed local textural features, sensitive to subtle NFL characteristics, into feature vectors submitted to a trained neural-network classifier. Obtained binary retinal maps of NFL distribution show a good agreement with both medical expert evaluations and quantitative results obtained by optical coherence tomography.

Improvement of Vessel Segmentation by Matched Filtering in Colour Retinal Images

A method for segmentation of vessel structure in colour retinal fundus images is presented, based on 2D matched filtering correlating the local image areas with 2D masks obtained via averaging of brightness profiles of vessels for several different vessel widths.Each of the basic masks is rotated in twelve different directions; this way, 60 masks for 5 different widths, each with 12 orientations are produced and used as 2D convolution kernels of the matched filters. The maximum response of all the filter responses for a concrete local area thus carries - if there is a vessel present - the information both on the width and orientation of the vessel segment. Compared to the previously published results [6], the segmentation has been improved primarily in two directions: the width resolution has been increased from 3 to 5 classes with a better approximation of the brightness profiles, and the orientation information is now utilized to provide vessel direction maps that are further used in the following phase of complementing the missing vessel segments. The parametric maps representing the maximum responses of the filters are then combined and finally tresholded thus obtaining binary vessel maps to be morphologically cleaned in order to remove the artefacts due to noise and also to complement the obviously missing parts of vessels. The method was designed and tested using the high-resolution fundus camera images provided by a cooperating ophthalmological clinic, and also statistically tested based on the standard public image database DRIVE.

Retrospective illumination correction of retinal images

A method for correction of nonhomogenous illumination based on optimization of parameters of B-spline shading model with respect to Shannons entropy is presented. The evaluation of Shannons entropy is based on Parzen windowing method (Mangin, 2000) with the spline-based shading model. This allows us to express the derivatives of the entropy criterion analytically, which enables efficient use of gradient-based optimization algorithms. Seven different gradient- and nongradient-based optimization algorithms were initially tested on a set of 40 simulated retinal images, generated by a model of the respective image acquisition system. Among the tested optimizers, the gradient-based optimizer with varying step has shown to have the fastest convergence while providing the best precision. The final algorithm proved to be able of suppressing approximately 70% of the artificially introduced non-homogenous illumination. To assess the practical utility of the method, it was qualitatively tested on a set of 336 real retinal images; it proved the ability of eliminating the illumination inhomogeneity substantially in most of cases. The application field of this method is especially in preprocessing of retinal images, as preparation for reliable segmentation or registration.

Registration and Fusion of the Autofluorescent and Infrared Retinal Images

This article deals with registration and fusion of multimodal opththalmologic images obtained by means of a laser scanning device (Heidelberg retina angiograph). The registration framework has been designed and tested for combination of autofluorescent and infrared images. This process is a necessary step for consecutive pixel level fusion and analysis utilizing information from both modalities. Two fusion methods are presented and compared.

Registration of multimodal images of retina

Registration of retinal images provided by different modalities is required to facilitate diagnosis of the optic nerve head and retina. For reliable automatic segmentation of the optic disk, it seems essential to join the image data produced by the Heidelberg Retina Tomograph (HRT) and the standard colour photograph. The proposed method is based on registering both (very different) images using mutual information as the coincidence measure.

Towards automated diagnostic evaluation of retina images

In this paper we describe the automatic segmentation of the optic nerve head (ONH) with the long-term goal of automatically diagnosing early stages of glaucoma. The images are average images obtained from a scanning laser ophthalmoscope (SLO). The segmentation consists of the main s teps of finding a region of interest containing the ONH, constraining the search space for final segmentation, and computing the fine segmentation by an active contour model. The agreement of “true positive pixels,” i.e., pixels attributed to the ONH by both manual and automatic segmentation, is very good. The classification results from three different classifiers using manual or automatic segmentation still show an advantage of manual segmentation. One means to further improve the automatic segmentation is to use information from an SLO as well as from a fundus camera.