Tracking deforming objects involves estimating the global motion of the object and its local deformations as a function of time. Tracking algorithms using Kalman filters or particle filters have been proposed for finite dimensional representations of shape, but these are dependent on the chosen parametrization and cannot handle changes in curve topology. Geometric active contours provide a framework which is parametrization independent and allow for changes in topology. In the present work, we formulate a particle filtering algorithm in the geometric active contour framework that can be used for tracking moving and deforming objects. To the best of our knowledge, this is the first attempt to implement an approximate particle filtering algorithm for tracking on a (theoretically) infinite dimensional state space.
Publications by Year: 2007
Advanced magnetic resonance imaging (MRI) studies often require the transformation of large numbers of images into a common space. Calculating transformations that relate each image to every other and applying them to the images on demand are theoretically possible; however, these can be computationally prohibitive. Therefore, relating each image to only one other image, then linking those transforms together to relate any two images in the database, may be an efficient alternative. Evaluated were the feasibility and validity of image registration to bring intraindividual MR images into mutual correspondence for longitudinal analysis through the concatenation of precomputed transforms. A longitudinal data set of 10 multiple sclerosis patients with nine serial dual-echo spin-echo, 1.5-T MRI scans was used. Intrasubject registrations were performed stepwise between consecutive images and direct from each time point to the baseline. Consecutive transforms were concatenated and evaluated against direct registrations by comparing the resulting transformed images (using Pearson correlation coefficient). Confounding variables such as time between scans, brain atrophy, and change in lesion load were evaluated. We found the images resampled with the direct and the concatenated transforms to be highly correlated, and there was no significant difference between methods. Differences in brain parenchymal fraction (a measure of brain atrophy) showed significant inverse correlation with the correspondence of the resampled images. Results indicate that concatenating multiple transforms that link two images together produces near-identical results to that of direct registration; thus, this method is both useful and valid.
This article discusses and reviews advanced forms of serial morphometry in the context of a disease progression model in multiple sclerosis (MS). This model of disease activity distinguishes between overall disease activity and the proportion thereof that becomes permanent damage. This translates into a progression model that features a repair potential, which, when exhausted, marks the conversion or progression from relapsing to progressive disease. The level of repair capacity at a given time determines the rate of progression. Both clinical and MRI variables appear to be in support of such a model. We examine possible MRI markers for this repair capacity, particularly the short-term behavior of new MRI lesions, quantified by methods of time-series analysis—that is, capturing lesion dynamics in the form of MRI intensity change directly, rather than shape or volume change. Lower rates of individual lesion recovery may represent lower repair and greater proximity to a progressive stage. Individuals with low transient lesion turnover appear to undergo more rapid progression and atrophy. Because disease-modifying therapies aim to alter the pathophysiological chain of inflammation, demyelination, and axonal loss, a therapeutic effect may therefore be more readily apparent as a change in lesion dynamics and recovery rate and level, rather than a change in total lesion burden or enhancing lesion number.
Tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time. Tracking algorithms using Kalman filters or particle filters (PFs) have been proposed for tracking such objects, but these have limitations due to the lack of dynamic shape information. In this paper, we propose a novel method based on employing a locally linear embedding in order to incorporate dynamic shape information into the particle filtering framework for tracking highly deformable objects in the presence of noise and clutter. The PF also models image statistics such as mean and variance of the given data which can be useful in obtaining proper separation of object and background.
Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The L(2) mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods.
In this paper, we present a set of techniques for the evaluation of brain tissue classifiers on a large data set of MR images of the head. Due to the difficulty of establishing a gold standard for this type of data, we focus our attention on methods which do not require a ground truth, but instead rely on a common agreement principle. Three different techniques are presented: the Williams’ index, a measure of common agreement; STAPLE, an Expectation Maximization algorithm which simultaneously estimates performance parameters and constructs an estimated reference standard; and Multidimensional Scaling, a visualization technique to explore similarity data. We apply these different evaluation methodologies to a set of eleven different segmentation algorithms on forty MR images. We then validate our evaluation pipeline by building a ground truth based on human expert tracings. The evaluations with and without a ground truth are compared. Our findings show that comparing classifiers without a gold standard can provide a lot of interesting information. In particular, outliers can be easily detected, strongly consistent or highly variable techniques can be readily discriminated, and the overall similarity between different techniques can be assessed. On the other hand, we also find that some information present in the expert segmentations is not captured by the automatic classifiers, suggesting that common agreement alone may not be sufficient for a precise performance evaluation of brain tissue classifiers.
Mewes AUJ, Zöllei L, Hüppi PS, Als H, McAnulty GB, Inder TE, Wells WM, Warfield SK. Displacement of brain regions in preterm infants with non-synostotic dolichocephaly investigated by MRI. Neuroimage. 2007;36(4):1074–85.
Regional investigations of newborn MRI are important to understand the appearance and consequences of early brain injury. Previously, regionalization in neonates has been achieved with a Talairach parcellation, using internal landmarks of the brain. Non-synostotic dolichocephaly defines a bi-temporal narrowing of the preterm infant’s head caused by pressure on the immature skull. The impact of dolichocephaly on brain shape and regional brain shift, which may compromise the validity of the parcellation scheme, has not yet been investigated. Twenty-four preterm and 20 fullterm infants were scanned at term equivalent. Skull shapes were investigated by cephalometric measurements and population registration. Brain tissue volumes were calculated to rule out brain injury underlying skull shape differences. The position of Talairach landmarks was evaluated. Cortical structures were segmented to determine a positional shift between both groups. The preterm group displayed dolichocephalic head shapes and had similar brain volumes compared to the mesocephalic fullterm group. In preterm infants, Talairach landmarks were consistently positioned relative to each other and to the skull base, but were displaced with regard to the calvarium. The frontal and superior region was enlarged; central and temporal gyri and sulci were shifted comparing preterm and fullterm infants. We found that, in healthy preterm infants, dolichocephaly led to a shift of cortical structures, but did not influence deep brain structures. We concluded that the validity of a Talairach parcellation scheme is compromised and may lead to a miscalculation of regional brain volumes and inconsistent parcel contents when comparing infant populations with divergent head shapes.
We describe a new approach for estimating the posterior probability of tissue labels. Conventional likelihood models are combined with a curve length prior on boundaries, and an approximate posterior distribution on labels is sought via the Mean Field approach. Optimizing the resulting estimator by gradient descent leads to a level set style algorithm where the level set functions are the logarithm-of-odds encoding of the posterior label probabilities in an unconstrained linear vector space. Applications with more than two labels are easily accommodated. The label assignment is accomplished by the Maximum A Posteriori rule, so there are no problems of "overlap" or "vacuum". We test the method on synthetic images with additive noise. In addition, we segment a magnetic resonance scan into the major brain compartments and subcortical structures.
Dauguet J, Peled S, Berezovskii V, Delzescaux T, Warfield SK, Born R, Westin CF. Comparison of fiber tracts derived from in-vivo DTI tractography with 3D histological neural tract tracer reconstruction on a macaque brain. Neuroimage. 2007;37(2):530–8.
Since the introduction of diffusion weighted imaging (DWI) as a method for examining neural connectivity, its accuracy has not been formally evaluated. In this study, we directly compared connections that were visualized using injected neural tract tracers (WGA-HRP) with those obtained using in-vivo diffusion tensor imaging (DTI) tractography. First, we injected the tracer at multiple sites in the brain of a macaque monkey; second, we reconstructed the histological sections of the labeled fiber tracts in 3D; third, we segmented and registered the fibers (somatosensory and motor tracts) with the anatomical in-vivo MRI from the same animal; and last, we conducted fiber tracing along the same pathways on the DTI data using a classical diffusion tracing technique with the injection sites as seeds. To evaluate the performance of DTI fiber tracing, we compared the fibers derived from the DTI tractography with those segmented from the histology. We also studied the influence of the parameters controlling the tractography by comparing Dice superimposition coefficients between histology and DTI segmentations. While there was generally good visual agreement between the two methods, our quantitative comparisons reveal certain limitations of DTI tractography, particularly for regions at remote locations from seeds. We have thus demonstrated the importance of appropriate settings for realistic tractography results.
Nain D, Styner MA, Niethammer M, Levitt JJ, Shenton ME, Gerig G, Bobick A, Tannenbaum A. STATISTICAL SHAPE ANALYSIS OF BRAIN STRUCTURES USING SPHERICAL WAVELETS. Proc IEEE Int Symp Biomed Imaging. 2007;4:209–212.
We present a novel method of statistical surface-based morphometry based on the use of non-parametric permutation tests and a spherical wavelet (SWC) shape representation. As an application, we analyze two brain structures, the caudate nucleus and the hippocampus, and compare the results obtained to shape analysis using a sampled point representation. Our results show that the SWC representation indicates new areas of significance preserved under the FDR correction for both the left caudate nucleus and left hippocampus. Additionally, the spherical wavelet representation provides a natural way to interpret the significance results in terms of scale in addition to knowing the spatial location of the regions.