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10
A Bayesian Approach to Dynamic Contours through Stochastic Sampling and Simulated Annealing
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 1994
"... In many applications of image analysis, simply connected objects are to be located in noisy images. During the last 56 years active contour models have become popular for finding the contours of such objects. Connected to these models are iterative algorithms for finding the minimizing energy curve ..."
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Cited by 63 (1 self)
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In many applications of image analysis, simply connected objects are to be located in noisy images. During the last 56 years active contour models have become popular for finding the contours of such objects. Connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations. These approaches do however have several disadvantages. The numerical algorithms that are in use constraint the models that can be used. Furthermore, in many cases only local minima can be achieved.
Automated extraction and variability analysis of sulcal neuroanatomy
 IEEE Trans. Med. Imag
, 1999
"... Abstract — Systematic mapping of the variability in cortical sulcal anatomy is an area of increasing interest which presents numerous methodological challenges. To address these issues, we have implemented sulcal extraction and assisted labeling (SEAL) to automatically extract the twodimensional (2 ..."
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Cited by 52 (5 self)
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Abstract — Systematic mapping of the variability in cortical sulcal anatomy is an area of increasing interest which presents numerous methodological challenges. To address these issues, we have implemented sulcal extraction and assisted labeling (SEAL) to automatically extract the twodimensional (2D) surface ribbons that represent the median axis of cerebral sulci and to neuroanatomically label these entities. To encode the extracted threedimensional (3D) cortical sulcal schematic topography (CSST) we define a relational graph structure composed of two main features: vertices (representing sulci) and arcs (representing the relationships between sulci). Vertices contain a parametric representation of the surface ribbon buried within the sulcus. Points on this surface are expressed in stereotaxic coordinates (i.e., with respect to a standardized brain coordinate system). For each of these vertices, we store
Auxiliary variables and twostep iterative algorithms in computer vision problems
 J. Math. Imag. Vision
, 1995
"... Abstract. We present a new mathematical formulation of some curve and surface reconstmctien algorithms by the introduction of auxiliary variables. For deformable models and templates, the extraction of a shape is obtained through the minimization of an energy composed of an internal regularization t ..."
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Cited by 39 (10 self)
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Abstract. We present a new mathematical formulation of some curve and surface reconstmctien algorithms by the introduction of auxiliary variables. For deformable models and templates, the extraction of a shape is obtained through the minimization of an energy composed of an internal regularization term (not necessary in the case of parametric models) and an external attraction potential. Twostep iterative algorithms have been often used where, at each iteration, the model is first locally deformed according to the potential data attraction and then globally smoothed (or fitted in the parametric case). We show how these approaches can be interpreted as the introduction of auxiliary variables and the minimization of a twovariables energy. The first variable corresponds to the original model we are looking for, while the second variable represents an auxiliary shape close to the first one. This permits to transform an implicit data constraint defined by a non convex potential into an explicit convex reconstruction problem. This approach is much simpler since each iteration is composed of two simple to solve steps. Our formulation permits a more precise setting of parameters in the iterative scheme to ensure convergence to a minimum. We show some mathematical properties and results on this new auxiliary problem, in particular when the potential is a function of the distance to the closest feature point. We then illustrate our approach for some deformable models and templates.
Avoiding Local Minima for Deformable Curves in Image Analysis
 in Curves and Surfaces with Applications in CAGD
, 1997
"... We present an overview of part of our work over the past few years on snakes, balloons, and deformable models, with applications to image analysis. The main drawbacks of the active contour model being its initialization and minimization, we present three approaches that help to avoid being trapped i ..."
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Cited by 18 (12 self)
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We present an overview of part of our work over the past few years on snakes, balloons, and deformable models, with applications to image analysis. The main drawbacks of the active contour model being its initialization and minimization, we present three approaches that help to avoid being trapped in a local minimum of the energy. We introduced the balloon model to extract a contour being less demanding on the initial curve. In a more recent approach, based on minimal paths and geodesics, we find the global minimum of the energy between two points. A third approach is defined by a hybrid regionbased energy taking into account homogeneity of the region inside the contour.
Tamed Snake: A Particle System for Robust SemiAutomatic Segmentation
 Second International conference on Medical Image computing and Computerassisted intervention (MICCAI'99), number 1679 in LNCS
, 1999
"... Semiautomatic segmentation approaches tend to overlook the problems caused by missing or incomplete image information. In such situations, powerful control mechanisms and intuitive modelling metaphors should be provided in order to make the methods practically applicable. Taking this problem into a ..."
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Cited by 13 (2 self)
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Semiautomatic segmentation approaches tend to overlook the problems caused by missing or incomplete image information. In such situations, powerful control mechanisms and intuitive modelling metaphors should be provided in order to make the methods practically applicable. Taking this problem into account, the usage of subdivision curves in combination with the simulation of edge attracted mass points is proposed as a novel way towards a more robust interactive segmentation methodology. Subdivision curves provide a hierarchical and smooth representation of a shape which can be modified on coarse and on fine scales as well. Furthermore, local adaptive subdivision gives the required flexibility when dealing with a discrete curve representation. In order to incorporate image information, the control vertices of a curve are considered mass points, attracted by edges in the local neighbourhood of the image. This socalled Tamed Snake framework is illustrated by means of the segmentation of two medical data sets and the results are compared with those achieved by traditional Snakes.
Frequency Based Nonrigid Motion Analysis: Application to Four Dimensional Medical Images
"... AbstractWe present a method for nonrigid motion analysis in time sequences of volume images (4D data). In this method, nonrigid motion of the deforming object contour is dynamically approximated by a physicallybased deformable surface. In order to reduce the number of parameters describing the def ..."
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Cited by 3 (0 self)
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AbstractWe present a method for nonrigid motion analysis in time sequences of volume images (4D data). In this method, nonrigid motion of the deforming object contour is dynamically approximated by a physicallybased deformable surface. In order to reduce the number of parameters describing the deformation, we make use of a modal analysis which provides a spatial smoothing of the surface. The deformation spectrum, which outlines the main excited modes, can be efficiently used for deformation comparison. Fourier analysis on time signals of the main deformation spectrum components provides a ternporal smoothing of the data. Thus a complex nonrigid deformation is described by only a few parameters: the main excited modes and the main Fourier harmonics. Therefore, 4D data can be analyzed in a very concise manner. The power and robustness of the approach is illustrated by various results on medical data. We believe that our method has important applications in automatic diagnosis of heart diseases and in motion compression. Index TermsMedical image analysis, nonrigid motion, deformable models, modal analysis, Fourier analysis, compression, dynamic data, fourdimensional images, cardiac imagery, automatic diagnosis.
Auxiliary Variables for Deformable Models
 In International Conference on Computer Vision
, 1995
"... We present a new mathematical formulation for curve and surface reconstruction algorithms by introduction of auxiliary variables. For deformable models and templates, twostep iterative algorithms have been often used where, at each iteration, the model is first locally deformed according to the pot ..."
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Cited by 2 (1 self)
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We present a new mathematical formulation for curve and surface reconstruction algorithms by introduction of auxiliary variables. For deformable models and templates, twostep iterative algorithms have been often used where, at each iteration, the model is first locally deformed according to the potential data attraction and then globally smoothed. We show how these approaches can be interpreted as the introduction of auxiliary variables and the minimization of a twovariables energy. This permits to transform an implicit data constraint defined by a non convex potential into an explicit convex reconstruction problem. We show some mathematical properties and results on this new auxiliary problem, in particular when the potential is a function of the distance to the closest feature point. We then illustrate our approach for some deformable models and templates and image restoration.
Volumic Segmentation using Hierarchical Representation and Triangulated Surface
, 1995
"... This research report presents a new algorithm for segmenting threedimensional images. It is based on a dynamic triangulated surface and on a pyramidal representation. The triangulated surface, which follows a physical modelization and which can as well modify its geometry as its topology, segmen ..."
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This research report presents a new algorithm for segmenting threedimensional images. It is based on a dynamic triangulated surface and on a pyramidal representation. The triangulated surface, which follows a physical modelization and which can as well modify its geometry as its topology, segments images into their components by altering its shape according to internal and external constraints. In order to speed up the whole process, an algorithm for pyramid building with any reduction factor allows us to transform the image into a set of images with progressive resolutions. This organization into a hierarchy, combined with a model that can adapt its mesh refinement to the resolution of the workspace, authorizes a fast estimation of the general forms included in the image. After that, the model searches for finer and finer details while relying successively on the different levels of the pyramid. Keywords: threedimensional segmentation, deformable model, threedimensional ...
Display Methods for GreyScale, VoxelBased Data Sets
"... The dramatic increase in the use of 3D image acquisition devices over the past decade has inspired major new developments in the display of volume data sets. In this chapter we present an overview of these diverse display methods and discuss the relative advantages and disadvantages of each of the d ..."
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The dramatic increase in the use of 3D image acquisition devices over the past decade has inspired major new developments in the display of volume data sets. In this chapter we present an overview of these diverse display methods and discuss the relative advantages and disadvantages of each of the different approaches. In addition, we touch upon some of the major issues involved in creating highquality images from volume data, including the problems of surface definition and object segmentation. Due in part to the rapid, almost frantic, pace of recent developments in methods for rendering images from volume data, there has not yet emerged any widely accepted taxonomy for these methods. Because the human visual system is adapted for environments in which images of surfaces predominate, most algorithms emphasize in one way or another the display of surfacelike information, either implicitly or explicitly. For clarity, we will avoid using the terms &quot;surface rendering &quot; and &quot;volume rendering &quot; to describe the various methods, since although prevalent in the literature they have no precise, commonly accepted definitions. Instead, we will differentiate the various rendering methods using the following three characteristics, which are somewhat more precise and, we hope, less misleading: 1) whether the explicit creation of an intermediate surface representation is required (if so,
SurfaceBased Labeling of Cortical Anatomy Using a Deformable Atlas
"... Abstract—We describe a computerized method to automatically find and label the cortical surface in threedimensional (3D) magnetic resonance (MR) brain images. The approach we take is to model a prelabeled brain atlas as a physical object and give it elastic properties, allowing it to warp itself o ..."
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Abstract—We describe a computerized method to automatically find and label the cortical surface in threedimensional (3D) magnetic resonance (MR) brain images. The approach we take is to model a prelabeled brain atlas as a physical object and give it elastic properties, allowing it to warp itself onto regions in a preprocessed image. Preprocessing consists of boundaryfinding and a morphological procedure which automatically extracts the brain and sulci from an MR image and provides a smoothed representation of the brain surface to which the deformable model can rapidly converge. Our deformable models are energyminimizing elastic surfaces that can accurately locate image features. The models are parameterized with 3D bicubic Bspline surfaces. We design the energy function such that cortical fissure (sulci) points on the model are attracted to fissure points on the image and the remaining model points are attracted to the brain surface. A conjugate gradient method minimizes the energy function, allowing the model to automatically converge to the smoothed brain surface. Finally, labels are propagated from the deformed atlas onto the highresolution brain surface. Index Terms—Brain atlas, deformable surface models, feature extraction, matching. I.