Simple point detection is an important task for several problems in discrete geometry, such as topology preserving thinning in image processing to compute discrete skeletons. In this paper, the approach to simple point detection is based on techniques from cubical homology, a framework ideally suited for problems in image processing. A (d-dimensional) unitary cube (for a d-dimensional digital image) is associated with every discrete picture element, instead of a point in epsilon(d) (the d-dimensional Euclidean space) as has been done previously. A simple point in this setting then refers to the removal of a unitary cube without changing the topology of the cubical complex induced by the digital image. The main result is a characterization of a simple point p (i.e., simple unitary cube) in terms of the homology groups of the (3d - 1) neighborhood of p for arbitrary, finite dimensions
MR diffusion tensor imaging (DTI) of the brain and spine provides a unique tool for both visualizing directionality and assessing intactness of white matter fiber tracts in vivo. At the spatial resolution of clinical MRI, much of primate white matter is composed of interdigitating fibers. Analyses based on an assumed single diffusion tensor per voxel yield important information about the average diffusion in the voxel but fail to reveal structure in the presence of crossing tracts. Until today, all clinical scans assume only one tensor, causing potential serious errors in tractography. Since high angular resolution imaging remains, so far, untenable for routine clinical use, a method is proposed whereby the single-tensor field is augmented with additional information gleaned from standard clinical DTI. The method effectively resolves two distinct tract directions within voxels, in which only two tracts are assumed to exist. The underlying constrained two-tensor model is fitted in two stages, utilizing the information present in the single-tensor fit. As a result, the necessary MRI time can be drastically reduced when compared with other approaches, enabling widespread clinical use. Upon evaluation in simulations and application to in vivo human brain DTI data, the method appears to be robust and practical and, if correctly applied, could elucidate tract directions at critical points of uncertainty.
OBJECTIVE: Magnetic resonance imaging (MRI) studies of schizophrenia reveal temporal lobe structural brain abnormalities in the superior temporal gyrus and the amygdala-hippocampal complex. However, the middle and inferior temporal gyri have received little investigation, especially in first-episode schizophrenia.
METHOD: High-spatial-resolution MRI was used to measure gray matter volume in the inferior, middle, and superior temporal gyri in 20 patients with first-episode schizophrenia, 20 patients with first-episode affective psychosis, and 23 healthy comparison subjects.
RESULTS: Gray matter volume in the middle temporal gyrus was smaller bilaterally in patients with first-episode schizophrenia than in comparison subjects and in patients with first-episode affective psychosis. Posterior gray matter volume in the inferior temporal gyrus was smaller bilaterally in both patient groups than in comparison subjects. Among the superior, middle, and inferior temporal gyri, the left posterior superior temporal gyrus gray matter in the schizophrenia group had the smallest volume, the greatest percentage difference, and the largest effect size in comparisons with healthy comparison subjects and with affective psychosis patients.
CONCLUSIONS: Smaller gray matter volumes in the left and right middle temporal gyri and left posterior superior temporal gyrus were present in schizophrenia but not in affective psychosis at first hospitalization. In contrast, smaller bilateral posterior inferior temporal gyrus gray matter volume is present in both schizophrenia and affective psychosis at first hospitalization. These findings suggest that smaller gray matter volumes in the dorsal temporal lobe (superior and middle temporal gyri) may be specific to schizophrenia, whereas smaller posterior inferior temporal gyrus gray matter volumes may be related to pathology common to both schizophrenia and affective psychosis.
In Multiple Sclerosis (MS) patients, conventional magnetic resonance imaging (MRI) shows a pattern of white matter (WM) disruption but may also overlook some WM damage. Diffusion tensor MRI (DT-MRI) can provide important in-vivo information about fiber direction that is not provided by conventional MRI. The geometry of diffusion tensors can quantitatively characterize the local structure in tissues. The integration of both conventional MRI and DT-MRI measures together with connectivity-based regional assessment provide a better understanding of the nature and the location of WM abnormalities. Image processing and visualization techniques have been developed and applied to study conventional MRI and DT-MRI of MS patients. These include methods of: Image Segmentation for identifying the different areas of the brain as well as to discriminate normal from abnormal WM, Computerized Atlases, which include structural information obtained from a set of subjects, and Tractographies which can aid in the delineation of WM fiber tracts by tracking connected diffusion tensors. These new techniques hold out the promise of improving our understanding of WM architecture and its disruption in diseases such as MS. In the present study, we review the work that has been done in the development of these techniques and illustrate their applications.
Local conformation is an important determinant of RNA catalysis and binding. The analysis of RNA conformation is particularly difficult due to the large number of degrees of freedom (torsion angles) per residue. Proteins, by comparison, have many fewer degrees of freedom per residue. In this work, we use and extend classical tools from statistics and signal processing to search for clusters in RNA conformational space. Results are reported both for scalar analysis, where each torsion angle is separately studied, and for vectorial analysis, where several angles are simultaneously clustered. Adapting techniques from vector quantization and clustering to the RNA structure, we find torsion angle clusters and RNA conformational motifs. We validate the technique using well-known conformational motifs, showing that the simultaneous study of the total torsion angle space leads to results consistent with known motifs reported in the literature and also to the finding of new ones.
A classical neural tract tracer, WGA-HRP, was injected at multiple sites within the brain of a macaque monkey. Histological sections of the labeled fiber tracts were reconstructed in 3D, and the fibers were segmented and registered with the anatomical post-mortem MRI from the same animal. Fiber tracing along the same pathways was performed on the DTI data using a classical diffusion tracing technique. The fibers derived from the DTI were compared with those segmented from the histology in order to evaluate the performance of DTI fiber tracing. While there was generally good agreement between the two methods, our results reveal certain limitations of DTI tractography, particularly at regions of fiber tract crossing or bifurcation.
Quantitative analysis of computed tomographic (CT) images of the lungs is becoming increasingly useful in the medical and surgical management of subjects with Chronic Obstructive Pulmonary Disease (COPD). Current methods for the assessment of airway wall work well in idealized models of the airway. We propose a new method for airway wall detection based on phase congruency. This method does not rely on either a specific model of the airway or the point spread function of the scanner. Our results show that our method gives a better localization of the airway wall than "full width at a half max" and is less sensitive to different reconstruction kernels and radiation doses.
Current methods for extracting models of white matter architecture from diffusion tensor MRI are generally based on fiber tractography. For some purposes a compelling alternative may be found in analyzing the first and second derivatives of diffusion anisotropy. Anisotropy creases are ridges and valleys of locally extremal anisotropy, where the gradient of anisotropy is orthogonal to one or more eigenvectors of its Hessian. We propose that anisotropy creases provide a basis for extracting a skeleton of white matter pathways, in that ridges of anisotropy coincide with interiors of fiber tracts, and valleys of anisotropy coincide with the interfaces between adjacent but distinctly oriented tracts. We describe a crease extraction algorithm that generates high-quality polygonal models of crease surfaces, then demonstrate the method on a measured diffusion tensor dataset, and visualize the result in combination with tractography to confirm its anatomic relevance.
A reoccurring theme in the diffusion tensor imaging literature is the per-voxel estimation of a symmetric 3 x 3 tensor describing the measured diffusion. In this work we attempt to generalize this approach by calculating 2 or 3 or up to k diffusion tensors for each voxel. We show that our procedure can more accurately describe the diffusion particularly when crossing fibers or fiber-bundles are present in the datasets.
We present a two-step process including white matter atlas generation and automatic segmentation. Our atlas generation method is based on population fiber clustering. We produce an atlas which contains high-dimensional descriptors of fiber bundles as well as anatomical label information. We use the atlas to automatically segment tractography in the white matter of novel subjects and we present quantitative results (FA measurements) in segmented white matter regions from a small population. We demonstrate reproducibility of these measurements across scans. In addition, we introduce the idea of using clustering for automatic matching of anatomical structures across hemispheres.
The concept of the Logarithm of the Odds (LogOdds) is frequently used in areas such as artificial neural networks, economics, and biology. Here, we utilize LogOdds for a shape representation that demonstrates desirable properties for medical imaging. For example, the representation encodes the shape of an anatomical structure as well as the variations within that structure. These variations are embedded in a vector space that relates to a probabilistic model. We apply our representation to a voxel based segmentation algorithm. We do so by embedding the manifold of Signed Distance Maps (SDM) into the linear space of LogOdds. The LogOdds variant is superior to the SDM model in an experiment segmenting 20 subjects into subcortical structures. We also use LogOdds in the non-convex interpolation between space conditioned distributions. We apply this model to a longitudinal schizophrenia study using quadratic splines. The resulting time-continuous simulation of the schizophrenic aging process has a higher accuracy then a model based on convex interpolation.
Recent work shows that diffusion tensor imaging (DTI) can help resolving thalamic nuclei based on the characteristic fiber orientation of the corticothalamic/thalamocortical striations within each nucleus. In this paper we describe a novel segmentation method based on spectral clustering. We use Markovian relaxation to handle spatial information in a natural way, and we explicitly minimize the normalized cut criteria of the spectral clustering for a better optimization. Using this modified spectral clustering algorithm, we can resolve the organization of the thalamic nuclei into groups and subgroups solely based on the voxel affinity matrix, avoiding the need for explicitly defined cluster centers. The identification of nuclear subdivisions can facilitate localization of functional activation and pathology to individual nuclear subgroups.
This paper presents a novel active surface segmentation algorithm using a multiscale shape representation and prior. We define a parametric model of a surface using spherical wavelet functions and learn a prior probability distribution over the wavelet coefficients to model shape variations at different scales and spatial locations in a training set. Based on this representation, we derive a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior in the segmentation framework. Additionally, the optimization method can be applied in a coarse-to-fine manner. We apply our algorithm to the segmentation of brain caudate nucleus, of interest in the study of schizophrenia. Our validation shows our algorithm is computationally efficient and outperforms the Active Shape Model algorithm by capturing finer shape details.
The accuracy and precision of segmentations of medical images has been difficult to quantify in the absence of a "ground truth" or reference standard segmentation for clinical data. Although physical or digital phantoms can help by providing a reference standard, they do not allow the reproduction of the full range of imaging and anatomical characteristics observed in clinical data. An alternative assessment approach is to compare to segmentations generated by domain experts. Segmentations may be generated by raters who are trained experts or by automated image analysis algorithms. Typically these segmentations differ due to intra-rater and inter-rater variability. The most appropriate way to compare such segmentations has been unclear. We present here a new algorithm to enable the estimation of performance characteristics, and a true labeling, from observations of segmentations of imaging data where segmentation labels may be ordered or continuous measures. This approach may be used with, amongst others, surface, distance transform or level set representations of segmentations, and can be used to assess whether or not a rater consistently over-estimates or under-estimates the position of a boundary.
This paper presents a registration framework based on the polynomial expansion transform. The idea of polynomial expansion is that the image is locally approximated by polynomials at each pixel. Starting with observations of how the coefficients of ideal linear and quadratic polynomials change under translation and affine transformation, algorithms are developed to estimate translation and compute affine and deformable registration between a fixed and a moving image, from the polynomial expansion coefficients. All algorithms can be used for signals of any dimensionality. The algorithms are evaluated on medical data.
The segmentation of newborn brain MRI is important for assessing and directing treatment options for premature infants at risk for developmental disorders, abnormalities, or even death. Segmentation of infant brain MRI is particularly challenging when compared with the segmentation of images acquired from older children and adults. We sought to develop a fully automated segmentation strategy and present here a Bayesian approach utilizing an atlas of priors derived from previous segmentations and a new scheme for automatically selecting and iteratively refining classifier training data using the STAPLE algorithm. Results have been validated by comparison to hand-drawn segmentations.
Scarless surgery is a new and very promising technique that can mark a new era in surgical procedures. We have created and validated a navigation system for endoscopic and transgastric access interventions in in vivo pilot studies. The system provides augmented visual feedback and additional contextual information by establishing a correspondence between the real time endoscopic ultrasound image and a preoperative CT volume using rigid registration. The system enhances the operator's ability to interpret the ultrasound image reducing the mental burden used in probe placement. Our analysis shows that rigid registration is accurate enough to help physicians in endoscopic abdominal surgery where, by using preoperative data for context and real-time imaging for targeting, distortions that limit the use of only preoperative data can be overcome.
In this note, we present an approach for developing patient-specific 3D models of portal veins to provide geometric boundary conditions for computational fluid dynamics (CFD) simulations of the blood flow inside portal veins. The study is based on MRI liver images of individual patients to which we apply image registration and segmentation techniques and inlet and outlet velocity profiles acquired using PC-MRI in the same imaging session. The portal vein and its connected veins are then extracted and visualized in 3D as surfaces. Image registration is performed to align shifted images between each breath-hold when the MRI images are acquired. The image segmentation method first labels each voxel in the 3D volume of interest by using a Bayesian probability approach, and then isolates the portal veins via active surfaces initialized inside the vessel. The method was tested with two healthy volunteers. In both cases, the main portal vein and its connected veins were successfully modeled and visualized.
This paper describes a novel user-guided method for grouping fibers from diffusion tensor MRI tractography into bundles. The method finds fibers, that passing through user-defined ROIs, still fit to the underlying data model given by the diffusion tensor. This is achieved by filtering the data and the ROIs with a kernel derived from a geodesic metric between tensors. A standard approach using binary decisions defining tracts passing through ROIs is critically dependent on ROIs that includes all trace lines of interest. The method described in this paper uses a softer decision mechanism through a kernel which enables grouping of bundles driven less exact, or even single point, ROIs. The method analyzes the responses obtained from the convolution with a kernel function along the fiber with the ROI data. Results in real data shows the feasibility of the approach to fiber bundling.