KEYWORDS: Fourier transforms, Information technology, Magnetic resonance imaging, Fermium, Frequency modulation, Image registration, Statistical analysis, Medical imaging, Image processing, Current controlled current source
In perfusion MRI (p-MRI) exams, short-axis (SA) image sequences are captured at multiple slice levels along the long-axis of the heart during the transit of a vascular contrast agent (Gd-DTPA) through the cardiac chambers and muscle. Compensating cardio-thoracic motions is a requirement for enabling computer-aided quantitative assessment of myocardial ischaemia from contrast-enhanced p-MRI sequences. The classical paradigm consists of registering each sequence frame on a reference image using some intensity-based matching criterion. In this paper, we introduce a novel unsupervised method for the
spatio-temporal groupwise registration of cardiac p-MRI exams based on normalized mutual information (NMI) between high-dimensional feature distributions. Here, local contrast enhancement curves are used as a dense set of spatio-temporal features, and statistically matched through variational optimization to a target feature distribution derived from a registered reference template. The hard issue of probability density estimation in high-dimensional state spaces is bypassed by using consistent geometric entropy estimators, allowing NMI to be computed directly from feature samples. Specifically, a computationally efficient kth-nearest neighbor (kNN) estimation framework is retained, leading to closed-form expressions for the gradient flow of NMI over finite- and infinite-dimensional motion spaces. This approach is applied to the groupwise alignment of cardiac p-MRI exams using a free-form Deformation (FFD) model for cardio-thoracic motions. Experiments on simulated and natural datasets suggest its accuracy and robustness for registering p-MRI exams comprising more than 30 frames.
Hybrid variational image segmentation techniques, involving energy functionals which combine contour- and
region-based terms, have been actively investigated due to their ability to jointly integrate shape and texture cues
about scene objects. Minimizing these functionals can be efficiently achieved using curve evolution techniques,
yielding region competition models along the deforming segmentation boundaries. Within this framework, this
paper presents a novel region-based statistical active contour approach to segmentation, refered to as info-snakes.
Here, the segmentation problem is expressed as the maximization of an information-theoretic similarity measure
between the image luminance distribution, and the label distribution of a regional template defining a multi-object
geometric prior model, subject to regularization constraints on region boundaries. The probability densities
associated with luminance distributions within each template region are estimated using a nonparametric Parzen
technique, which avoids resorting to prior assumptions on image statistics or to a training phase. We shall
focus our attention on the Ali-Silvey class of information measures, and derive the corresponding gradient flows
over nonparametric smooth curve spaces. As expected, the evolution equations for the template boundaries
interpret as a statistical region competition model, promoting statistically consistent regions relative to the
chosen information metrics. An efficient implementation using a multiphase level set technique is finally provided.
Experiments on a cardiac perfusion MRI dataset are presented, demonstrating the relevance of info-snakes for
implementing computer-assisted diagnosis tools in cardiology.
Intensity-based Non Rigid Registration (NRR) techniques using statistical similarity measures have been widely used to address mono- and multimodal image alignment problems in a robust and segmentation-free way. In these approaches, registration is achieved by minimizing the discrepancy between luminance distributions. Classical similarity criteria, including mutual information, f-information and correlation ratio, rely on global luminance statistics over the whole image domain and do not incorporate spatial information. This may lead to inaccurate or geometrically inconsistent (though visually satisfying) alignment of homologous image structures, making these criteria unreliable for atlas-based segmentation purposes. This paper addresses these limitations and presents a region-driven approach to statistical NRR based on regional non-parametric estimates of luminance distributions. The latter are derived from a regional segmentation of the target image which is used as a fixed object/scene template and induces regionalized statistical similarity measures. We provide the expressions of these criteria in the case of generalized information measures and correlation ratio, and derive the corresponding gradient flows over parametric and non-parametric transforms spaces. This approach is then applied to the joint non rigid segmentation and registration of short-axis cardiac perfusion MR sequences using a bi-ventricular heart template. In this framework, region-driven NRR allows for compensating for respiratory/cardiac motion artifacts, and fitting a segmental heart model used for quantitatively assessing regional myocardial perfusion. Experiments have been performed on a 15 pathological subjects database, demonstrating the relevance of region-driven NRR over global NRR in terms of computational performance and registration accuracy with respect to an expert reference.
Quantitatively assessing myocardial perfusion is a key issue for the diagnosis, therapeutic planning and patient follow-up of cardio-vascular diseases. To this end, perfusion MRI (p-MRI) has emerged as a valuable clinical investigation tool thanks to its ability of dynamically imaging the first pass of a contrast bolus in the framework of stress/rest exams. However, reliable techniques for automatically computing regional first pass curves from 2D short-axis cardiac p-MRI sequences remain to be elaborated. We address this problem and develop an unsupervised four-step approach comprising: (i) a coarse spatio-temporal segmentation step, allowing to automatically detect a region of interest for the heart over the whole sequence, and to select a reference frame with maximal myocardium contrast; (ii) a model-based variational segmentation step of the reference frame, yielding a bi-ventricular partition of the heart into left ventricle, right ventricle and myocardium components; (iii) a respiratory/cardiac motion artifacts compensation step using a novel region-driven intensity-based non rigid registration technique, allowing to elastically propagate the reference bi-ventricular segmentation over the whole sequence; (iv) a measurement step, delivering first-pass curves over each region of a segmental model of the myocardium. The performance of this approach is assessed over a database of 15 normal and pathological subjects, and compared with perfusion measurements delivered by a MRI manufacturer software package based on manual delineations by a medical expert.
We address the issue of modeling and quantifying myocardial contraction from 4D MR sequences, and present an unsupervised approach for building and using a statistical 3D motion atlas for the normal heart. This approach relies on a state-of-the-art variational
non rigid registration (NRR) technique using generalized information measures, which allows for robust intra-subject motion estimation and inter-subject anatomical alignment. The atlas is built from a collection of jointly acquired tagged and cine MR exams in short- and long-axis views. Subject-specific non parametric motion estimates are first obtained by incremental NRR of tagged images onto the end-diastolic (ED) frame. Individual motion data are then transformed into the coordinate system
of a reference subject using subject-to-reference mappings derived by NRR of cine ED images. Finally, principal component analysis of aligned motion data is performed for each cardiac phase, yielding a mean model and a set of eigenfields encoding kinematic ariability. The latter define an organ-dedicated hierarchical motion basis which enables parametric motion measurement from arbitrary tagged MR exams. To this end, the atlas is transformed into subject coordinates
by reference-to-subject NRR of ED cine frames. Atlas-based motion estimation is then achieved by parametric NRR of tagged images onto the ED frame,
yielding a compact description of myocardial contraction during diastole.
This article presents a methodology for analyzing the Lagrangian structure of fluid flows generated by the evolution of cloud systems in meteorological multispectral image sequences. The correlation between the orientation of cloud texture and the underlying motion field Lagrangian component allows to adopt a static strategy. Following a scale-space approach, we therefore first construct a non-local robust estimator for the locally dominant orientation field in an image. This estimator, which is derived from the image structure tensor, is relevant in both mono- and multisprectral contexts. In a second step, the Lagrangian component of the flow is estimated over some bounded image region by robustly fitting a hierarchical vector parametric model to the dominant orientation field. Here, a recurrent problem deals with adaptating the geometry of the model support to obtain unbiased estimates. To tackle this classic issue, we introduce a novel variational, semi-parametric approach which allows the joint optimization of model parameters and support. This approach is generic and, in particular, can be readily applied to motion estimation yielding robust measurement of the Eulerian structure of the flow. Finally, a structural characterization of the reflecting vector field is derived by means of classic differential geometry techniques. This methodology is applied to the analysis of temperated latitude depressions in Meteosat images.
Following a PDE-based formulation of low-level vision, recent works have attempted to cast classical mathematical morphology into the axiomatrix framework of scale-space theory. This effort has led to derive continuous elementary morphological operators and revealed deep connections with the theory of reactive PDEs. Until now, researchers have focused their attention of Euclidean morphology. This article aims at setting up the foundations of differential geodesic mathematical morphology. Specifically, we define multiscale geodesic erosions and dilations, and derive their generating PDEs for arbitrary n-dimensional structuring sets or functions. Geodesic reconstruction then corresponds to steady-states of these equations for particular initial conditions. Geodesic morphological operators are further embedded into a general class of one-parameter operator semigroups, called geodesic scale-space operators. Within this framework, regularized geodesic operators are defined in a natural fashion by augmenting the basic PDEs with a diffusive, scale-space-admissible component. Finally, efficient numerical implementations based on monotonic conservative schemes are presented in details. These developments provide the theoretical basis for PDE-based formulations of watershed segmentation and geodesic skeleton computation.
In (linear or nonlinear) diffusive scale-space representations, local variations of the luminance field with respect to infinitesimal scale transitions are described via a first-order parabolic partial differential equation modeling a generalized diffusion process. A geometric characterization of the scale-space structure is then classically derived by analyzing the properties of the deformation flow induced by scale transitions along specific geometric structures embedded on the photometric surface. In particular, studying the simultaneous deformation of the dual families of curves consisting of isophotes and stream lines of the luminance field yields a Euclidean-invariant geometric description of generalized diffusion processes. In this paper, the generalized diffusion equation is interpreted within the framework of the relativistic electromagnetic (EM) theory as a Lorentz gauge condition expressing the trace-invariance of an EM quadripotential with covariant scalar and contravariant vector components respectively related to luminance and geometric properties of the image. This gauge condition determines an EM quadrifield and quadricharge which satisfy Maxwell equations. Deriving the general expressions of these quadrivectors as functions of Euclidean characteristics of isophotes and stream lines leads to identifying Lorentz-invariants which synthetize under an extremely compact form intrinsic multiscale image properties. In addition, weak formulations of diffusive scale-spaces are consistently re-expressed in terms of Em energy density. The specific cases of linear scale-spaces, corresponding to purely electric fields, and of classical anisotropic diffusion models are studied in detail, providing a significant insight in the understanding of the deep structure of diffusive scale-spaces.
Anisotropic diffusion has been extensively used as an efficient nonlinear filtering technique for simultaneously performing contrast enhancement and noise reduction, and for deriving consistent scale-space image descriptions. In this paper, we present a general study of anisotropic diffusion schemes based on differential group-invariant representations of local image structure. We show that the local geometry (i.e., shape and scale) of the photometric surface is intrinsically specified by two dual families of curves, respectively consisting of isophotes and stream lines, which remain invariant under isometries in the image domain. Within this framework, anisotropic diffusive processes induce a deformation flow on the network of isophotes and stream lines. Deriving the general expression of this flow leads to identifying canonical forms for admissible conduction functions, that yield an optimal and stable preservation of significant image structures. Moreover, relating scale to directional variations of isophote density results in controlling the diffusion dynamics by means of a heterogeneous damping density which allows us to adaptively reduce diffusion speed in the vicinity of high gradient lines while increasing it within stationary intensity domains. Finally, these results are extended to arbitrary image dimensions.
Several works have recently underlined the relevance of morphological-filtering-based techniques for accurately segmenting gray-scale images of corneal endothelial tissue. Nonetheless, applied to low-quality and/or highly pathological images, methods exploiting standard morphological filters fail to provide correct segmentations. Moreover, quantification issues remain essentially an open problem. In this paper, we present a robust and accurate method for automatically segmenting and quantifying corneal endothelial images.
KEYWORDS: Image segmentation, Image processing, 3D modeling, 3D image processing, Data modeling, Mathematical modeling, Medical imaging, Magnetic resonance imaging, Statistical modeling, Matrices
In this paper, we address the problem of adapting the functions controlling the material properties of 2D snakes, and show how introducing oriented smoothness constraints results in a novel class of active contour models for segmentation which extends standard isotropic inhomogeneous membrane/thin-plate stabilizers. These constraints, expressed as adaptive L2 matrix norms, are defined by two 2nd-order symmetric and positive definite tensors which are invariant with respect to rigid motions in the image plane. These tensors, equivalent to directional adaptive stretching and bending densities, are quadratic with respect to 1st- and 2nd-order derivatives of the image intensity, respectively. A representation theorem specifying their canonical form is established and a geometrical interpretation of their effects if developed. Within this framework, it is shown that, by achieving a directional control of regularization, such non-isotropic constraints consistently relate the differential properties (metric and curvature) of the deformable model with those of the underlying intensity surface, yielding a satisfying preservation of image contour characteristics.
KEYWORDS: Mathematical modeling, Kinematics, Medical imaging, 3D modeling, Physics, Interfaces, Motion models, Data modeling, Optimization (mathematics), Visual process modeling
In this paper, we present a general study of the kinematics of deformable non-singular manifolds with codimension 1 evolving according to a first-order dynamics within a d- dimensional space, in terms of their intrinsic geometric properties. We formulate the local equations which describe instantaneous variations of their main differential and integral characteristics. In particular, a physical interpretation of curvature evolution in terms of reaction-diffusion-propagation processes is developed. Delocalizing these equations within the time domain leads to describing local evolution along the stream lines of the deformation field. Within this framework, local ergodicity property of curvature processes is underlined. Integrating further within the space domain leads to global evolution theorems. These results are then applied to the kinematical study of 2D and 3D active models of the inhomogeneous membrane/thin-plate under pressure type (g-snakes) when their optimization is performed via a purely dissipative Lagrangian deformation process. They yield a complete mathematical characterization of the instantaneous behavior of snake-like models.
In physics, a large class of problems, such as crystal growth or flame fronts propagation, are concerned with the motion of a deformable boundary separating time-dependent domains in which the interface itself satisfies an equation of motion. Recently, similar questions have been introduced in image processing through the concept of physically based active contour models or snakes. In snake modeling, a deformable boundary endowed with elastic properties interacts with a constant external field derived from image properties. In the most general case, the interfacial motion is governed by a set of partial differential equations that nonlinearily couple interface intrinsics and external fields. In this paper, we present a general study of the kinematics of deformable regular (d-1)-dimensional interfaces evolving according to a first- order dynamic in a d-dimensional (d >= 2) space, in terms of their intrinsic geometric properties. We formulate local equations of motion and derive evolution theorems. These results are then applied to the kinematical study of a specific 2-dimensional active contour model when its optimization is performed via a first-order deformation process. This provides a significant insight in the instantaneous behavior of snake-like models as well as the nature of their steady-states.
The concept of a deformable (active) marker of an image, defined as a numerical marker whose support is limited by a deformable (active) contour, is introduced. An active marker is specified by defining (1) an interface deformable model as well as the deformation process associated with it, and (2) an interaction process between the marker and the external field. We present a particular active marker model relying on a novel expanding-contracting inhomogeneous membrane/thin-plate model called a g-snake, and an interaction process based on controlled morphological marking techniques. We show that by allowing the external force field to be simplified and taking into account a global source of information, active markers provide a consistent solution to three major problems encountered by active contour models when applied to the segmentation of highly noisy images: (1) sensitivity to initialization, (2) undesirable attractions by non-significant localized or regionalized zones in the image, and (3) no relationship between their state of equilibrium and the real contours to be extracted. The efficiency and robustness of the method are demonstrated on ultrasound medical images.
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