Gregory J. Garvin

Intervertebral disc segmentation in MR images using anisotropic oriented flux

This study proposes an unsupervised intervertebral disc segmentation system based on middle sagittal spine MR scans. The proposed system employs the novel anisotropic oriented flux detection scheme which helps distinguish the discs from the neighboring structures with similar intensity, recognize ambiguous disc boundaries, and handle the shape and intensity variation of the discs. Based on minimal user interaction, the proposed system begins with vertebral body tracking to infer the information regarding the positions and orientations of the target intervertebral discs. The information is employed in a set of image descriptors, which jointly constitute an energy functional describing the desired disc segmentation result. The energy functional is minimized by a level set based active contour model to perform disc segmentation. The proposed segmentation system is evaluated using a database consisting of 455 intervertebral discs extracted from 69 middle sagittal slices. It is demonstrated that the proposed method is capable of delivering accurate results for intervertebral disc segmentation.

Graph cuts with invariant object-interaction priors: application to intervertebral disc segmentation

This study investigates novel object-interaction priors for graph cut image segmentation with application to intervertebral disc delineation in magnetic resonance (MR) lumbar spine images. The algorithm optimizes an original cost function which constrains the solution with learned prior knowledge about the geometric interactions between different objects in the image. Based on a global measure of similarity between distributions, the proposed priors are intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive an original fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed priors relax the need of costly pose estimation (or registration) procedures and large training sets (we used a single subject for training), and can tolerate shape deformations, unlike template-based priors. Our formulation leads to an NP-hard problem which does not afford a form directly amenable to graph cut optimization. We proceeded to a relaxation of the problem via an auxiliary function, thereby obtaining a nearly real-time solution with few graph cuts. Quantitative evaluations over 60 intervertebral discs acquired from 10 subjects demonstrated that the proposed algorithm yields a high correlation with independent manual segmentations by an expert. We further demonstrate experimentally the invariance of the proposed geometric attributes. This supports the fact that a single subject is sufficient for training our algorithm, and confirms the relevance of the proposed priors to disc segmentation.

A parameterization of deformation fields for diffeomorphic image registration and its application to myocardial delineation

This study investigates a new parameterization of deformation fields for image registration. Instead of standard displacements, this parameterization describes a deformation field with its transformation Jacobian and curl of end velocity field. It has two important features which make it appealing to image registration: 1) it relaxes the need of an explicit regularization term and the corresponding ad hoc weight in the cost functional; 2) explicit constraints on transformation Jacobian such as topology preserving and incompressibility constraints are straightforward to impose in a unified framework. In addition, this parameterization naturally describes a deformation field in terms of radial and rotational components, making it especially suited for processing cardiac data. We formulate diffeomorphic image registration as a constrained optimization problem which we solve with a step-then-correct strategy. The effectiveness of the algorithm is demonstrated with several examples and a comprehensive evaluation of myocardial delineation over 120 short-axis cardiac cine MRIs acquired from 20 subjects. It shows competitive performance in comparison to two recent segmentation based approaches.

Spine Image Fusion Via Graph Cuts

This study investigates a novel CT/MR spine image fusion algorithm based on graph cuts. This algorithm allows physicians to visually assess corresponding soft tissue and bony detail on a single image eliminating mental alignment and correlation needed when both CT and MR images are required for diagnosis. We state the problem as a discrete multilabel optimization of an energy functional that balances the contributions of three competing terms: (1) a squared error, which encourages the solution to be similar to the MR input, with a preference to strong MR edges; (2) a squared error, which encourages the solution to be similar to the CT input, with a preference to strong CT edges; and (3) a prior, which favors smooth solutions by encouraging neighboring pixels to have similar fused-image values. We further introduce a transparency-labeling formulation, which significantly reduces the computational load. The proposed graph-cut fusion guarantees nearly global solutions, while avoiding the pix elation artifacts that affect standard wavelet-based methods. We report several quantitative evaluations/comparisons over 40 pairs of CT/MR images acquired from 20 patients, which demonstrate a very competitive performance in comparisons to the existing methods. We further discuss various case studies, and give a representative sample of the results.

Vertebral body segmentation in MRI via convex relaxation and distribution matching

We state vertebral body (VB) segmentation in MRI as a distribution-matching problem, and propose a convex-relaxation solution which is amenable to parallel computations. The proposed algorithm does not require a complex learning from a large manually-built training set, as is the case of the existing methods. From a very simple user input, which amounts to only three points for a whole volume, we compute a multi-dimensional model distribution of features that encode contextual information about the VBs. Then, we optimize a functional containing (1) a feature-based constraint which evaluates a similarity between distributions, and (2) a total-variation constraint which favors smooth surfaces. Our formulation leads to a challenging problem which is not directly amenable to convex-optimization techniques. To obtain a solution efficiently, we split the problem into a sequence of sub-problems, each can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed solution can bring a substantial speed-up of more than 30 times for a typical 3D spine MRI volume. We report quantitative performance evaluations over 15 subjects, and demonstrate that the results correlate well with independent manual segmentations.

Gradient competition anisotropy for centerline extraction and segmentation of spinal cords

Centerline extraction and segmentation of the spinal cord--an intensity varying and elliptical curvilinear structure under strong neighboring disturbance are extremely challenging. This study proposes the gradient competition anisotropy technique to perform spinal cord centerline extraction and segmentation. The contribution of the proposed method is threefold--1) The gradient competition descriptor compares the image gradient obtained at different detection scales to suppress neighboring disturbance. It reliably recognizes the curvilinearity and orientations of elliptical curvilinear objects. 2) The orientation coherence anisotropy analyzes the detection responses offered by the gradient competition descriptor. It enforces structure orientation consistency to sustain strong disturbance introduced by high contrast neighboring objects to perform centerline extraction. 3) The intensity coherence segmentation quantifies the intensity difference between the centerline and the voxels in the vicinity of the centerline. It effectively removes the object intensity variation along the structure to accurately delineate the target structure. They constitute the gradient competition anisotropy method which can robustly and accurately detect the centerline and boundary of the spinal cord. It is validated and compared using 25 clinical datasets. It is demonstrated that the proposed method well suits the applications of spinal cord centerline extraction and segmentation.

TRIC: trust region for invariant compactness and its application to abdominal aorta segmentation.

This study investigates segmentation with a novel invariant compactness constraint. The proposed prior is a high-order fractional term, which is not directly amenable to powerful optimizers. We derive first-order Gateâux derivative approximations of our compactness term and adopt an iterative trust region paradigm by splitting our problem into constrained sub-problems, each solving the approximation globally via a Lagrangian formulation and a graph cut. We apply our algorithm to the challenging task of abdominal aorta segmentation in 3D MRI volumes, and report quantitative evaluations over 30 subjects, which demonstrate that the results correlate well with independent manual segmentations. We further show the use of our method in several other medical applications and demonstrate that, in comparison to a standard level-set optimization, our algorithm is one order of magnitude faster.

Area Prior Constrained Level Set Evolution for Medical Image Segmentation

The level set framework has proven well suited to medical image segmentation1-6 thanks to its ability of balancing the contribution of image data and prior knowledge in a principled, flexible and transparent way. It consists of evolving a curve toward the target object boundaries. The curve evolution equation is sought following the optimization of a cost functional containing two types of terms: data terms, which measure the fidelity of segmentation to image intensities, and prior terms, which traduce learned prior knowledge. Without priors many algorithms are likely to fail due to high noise, low contrast and data incompleteness. Different priors have been investigated such as shape1 and appearance priors.7 In this study, we propose a simple type of priors: the area prior. This prior embeds knowledge of an approximate object area and has two positive effects. First, It speeds up significantly the evolution when the curve is far from the target object boundaries. Second, it slows down the evolution when the curve is close to the target. Consequently, it reinforces curve stability at the desired boundaries when dealing with low contrast intensity edges. The algorithm is validated with several experiments using Magnetic Resonance (MR) images and Computed Tomography (CT) images. A comparison with another level set method illustrates the positive effects of the area prior.

Dilated Divergence Based Scale-Space Representation for Curve Analysis

This study proposes the novel dilated divergence scale-space representation for multidimensional curve-like image structure analysis. In the proposed framework, image structures are modeled as curves with arbitrary thickness. The dilated divergence analyzes the structure boundaries along the curve normal space in a multi-scale fashion. The dilated divergence based detection is formulated so as to 1) sustain the disturbance introduced by neighboring objects, 2) recognize the curve normal and tangent spaces. The latter enables the innovative formulation of structure eccentricity analysis and curve tangent space-based structure motion analysis, which have been scarcely investigated in literature. The proposed method is validated using 2D, 3D and 4D images. The structure principal direction estimation accuracies, structure scale detection accuracies and detection stabilities are quantified and compared against two scale-space approaches, showing a competitive performance of the proposed approach, under the disturbance introduced by image noise and neighboring objects. Moreover, as an application example employing the dilated divergence detection responses, an automated approach is tailored for spinal cord centerline extraction. The proposed method is shown to be versatile to well suit a wide range of applications.

Spine labeling in MRI via regularized distribution matching

PurposeThis study investigates an efficient (nearly real-time) two-stage spine labeling algorithm that removes the need for an external training while being applicable to different types of MRI data and acquisition protocols.MethodsBased solely on the image being labeled (i.e., we do not use training data), the first stage aims at detecting potential vertebra candidates following the optimization of a functional containing two terms: (i) a distribution-matching term that encodes contextual information about the vertebrae via a density model learned from a very simple user input, which amounts to a point (mouse click) on a predefined vertebra; and (ii) a regularization constraint, which penalizes isolated candidates in the solution. The second stage removes false positives and identifies all vertebrae and discs by optimizing a geometric constraint, which embeds generic anatomical information on the interconnections between neighboring structures. Based on generic knowledge, our geometric constraint does not require external training.ResultsWe performed quantitative evaluations of the algorithm over a data set of 90 mid-sagittal MRI images of the lumbar spine acquired from 45 different subjects. To assess the flexibility of the algorithm, we used both T1- and T2-weighted images for each subject. A total of 990 structures were automatically detected/labeled and compared to ground-truth annotations by an expert. On the T2-weighted data, we obtained an accuracy of 91.6% for the vertebrae and 89.2% for the discs. On the T1-weighted data, we obtained an accuracy of 90.7% for the vertebrae and 88.1% for the discs.ConclusionOur algorithm removes the need for external training while being applicable to different types of MRI data and acquisition protocols. Based on the current testing data, a subject-specific model density and generic anatomical information, our method can achieve competitive performances when applied to T1- and T2-weighted MRI images.