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19
Efficient Energies and Algorithms for Parametric Snakes
 IEEE Transactions on Image Processing
, 2004
"... Abstract—Parametric active contour models are one of the preferred approaches for image segmentation because of their computational efficiency and simplicity. However, they have a few drawbacks which limit their performance. In this paper, we identify some of these problems and propose efficient sol ..."
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Cited by 38 (11 self)
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Abstract—Parametric active contour models are one of the preferred approaches for image segmentation because of their computational efficiency and simplicity. However, they have a few drawbacks which limit their performance. In this paper, we identify some of these problems and propose efficient solutions to get around them. The widelyused gradient magnitudebased energy is parameter dependent; its use will negatively affect the parametrization of the curve and, consequently, its stiffness. Hence, we introduce a new edgebased energy that is independent of the parameterization. It is also more robust since it takes into account the gradient direction as well. We express this energy term as a surface integral, thus unifying it naturally with the regionbased schemes. The unified framework enables the user to tune the image energy to the application at hand. We show that parametric snakes can guarantee low curvature curves, but only if they are described in the curvilinear abscissa. Since normal curve evolution do not ensure constant arclength, we propose a new internal energy term that will force this configuration. The curve evolution can sometimes give rise to closed loops in the contour, which will adversely interfere with the optimization algorithm. We propose a curve evolution scheme that prevents this condition. Index Terms—Active contour, curve, segmentation, snake, spline.
Channel smoothing: Efficient robust smoothing of lowlevel signal features
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2006
"... In this paper, we present a new and efficient method to implement robust smoothing of lowlevel signal features: Bspline channel smoothing. This method consists of three steps: encoding of the signal features into channels, averaging of the channels, and decoding of the channels. We show that line ..."
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Cited by 36 (22 self)
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In this paper, we present a new and efficient method to implement robust smoothing of lowlevel signal features: Bspline channel smoothing. This method consists of three steps: encoding of the signal features into channels, averaging of the channels, and decoding of the channels. We show that linear smoothing of channels is equivalent to robust smoothing of the signal features if we make use of quadratic Bsplines to generate the channels. The linear decoding from Bspline channels allows the derivation of a robust error norm, which is very similar to Tukey’s biweight error norm. We compare channel smoothing with three other robust smoothing techniques: nonlinear diffusion, bilateral filtering, and meanshift filtering, both theoretically and on a 2D orientationdata smoothing task. Channel smoothing is found to be superior in four respects: It has a lower computational complexity, it is easy to implement, it chooses the global minimum error instead of the nearest local minimum, and it can also be used on nonlinear spaces, such as orientation space.
Smoothing BSpline Active Contour or Fast and Robust Image and Video Segmentation
 In International Conference on Image Processing
, 2003
"... This paper deals with fast image and video segmentation using active contours. Region based active contours using levelsets are powerful techniques for video segmentation but they suffer from large computational cost. A parametric active contour method based on BSpline interpolation has been propo ..."
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Cited by 18 (10 self)
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This paper deals with fast image and video segmentation using active contours. Region based active contours using levelsets are powerful techniques for video segmentation but they suffer from large computational cost. A parametric active contour method based on BSpline interpolation has been proposed in [1] to highly reduce the computational cost but this method is sensitive to noise. Here, we choose to relax the rigid interpolation constraint in order to robustify our method in the presence of noise: by using smoothing splines, we trade a tunable amount of interpolation error for a smoother spline curve. We show by experiments on natural sequences that this new flexibility yields segmentation results of higher quality at no additional computational cost. Hence real time processing for moving objects segmentation is preserved.
2006, ‘Segmentation of a vector field: Dominant parameter and shape otimization
 Journal of Mathematical Imaging and Vision (In
"... Vector field segmentation methods usually belong to either of three classes: methods which segment regions homogeneous in direction and/or norm, methods which detect discontinuities in the vector field, and region growing or classification methods. The first two classes of method do not allow segmen ..."
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Cited by 9 (5 self)
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Vector field segmentation methods usually belong to either of three classes: methods which segment regions homogeneous in direction and/or norm, methods which detect discontinuities in the vector field, and region growing or classification methods. The first two classes of method do not allow segmentation of complex vector fields and control of the type of fields to be segmented, respectively. The third class does not directly allow a smooth representation of the segmentation boundaries. In the particular case where the vector field actually represents an optical flow, a fourth class of methods acts as a detector of main motion. The proposed method combines a vector field model and a theoretically founded minimization approach. Compared to existing methods following the same philosophy, it relies on an intuitive, geometric way to define the model while preserving a general point of view adapted to the segmentation of potentially complex vector fields with the condition that they can be described by a finite number of parameters. The energy to be minimized is deduced from the choice of a specific class of field lines, e.g. straight lines or circles, described by the general form of their parametric equations. In that sense, the proposed method is a principled approach for segmenting parametric vector fields. The minimization problem was rewritten into a shape optimization and implemented by splinebased active contours. The algorithm was applied to the segmentation of precomputed optical flow fields given by an external, independent algorithm.
Snakes with ellipsereproducing properties
 IEEE Transactions on Image Processing, in press, doi:10.1109/TIP.2011.2169975
, 2011
"... Abstract—We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency. While the resulting snakes are versati ..."
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Cited by 6 (4 self)
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Abstract—We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency. While the resulting snakes are versatile enough to provide a good approximation of any closed curve in the plane, their most important feature is the fact that they admit ellipses within their span. Thus, they can perfectly generate circular and elliptical shapes. These features are appropriate to delineate cross sections of cylindricallike conduits and to outline bloblike objects. We address the implementation details and illustrate the capabilities of our snake with synthetic and real data. Index Terms—Active contour, exponential Bspline, parameterization, parametric snake, segmentation.
3D Reconstruction Of DNA Filaments From Stereo CryoElectron Micrographs
 HOOD Reference Manual. Issue
, 2002
"... We propose an algorithm for the 3D reconstruction of DNA filaments from a pair of stereo cryoelectron micrographs. The underlying principle is to specify a 3D model of a filament  described as a spline curve  and to fit it to the 2D data using a snakelike algorithm. To drive the snake, we con ..."
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Cited by 5 (3 self)
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We propose an algorithm for the 3D reconstruction of DNA filaments from a pair of stereo cryoelectron micrographs. The underlying principle is to specify a 3D model of a filament  described as a spline curve  and to fit it to the 2D data using a snakelike algorithm. To drive the snake, we constructed a ridgeenhancing vector field for each of the images based on the maximum output of a bank of rotating matched filters. The magnitude of the field gives a confidence measure for the presence of a filament and the phase indicates its direction. We also propose a fast algorithm to perform the matched filtering. The snake algorithm starts with an initial curve (input by the user) and evolves it so that its projections on the viewing plane are in maximal agreement with the corresponding vector fields.
THE SNAKUSCULE
"... Abstract—Traditional snakes, or active contours, are planar parametric curves. Their parameters are determined by optimizing the weighted sum of three energy terms: one depending on the data (typically on the integral of its gradient under the curve, or on its integral over the area enclosed by the ..."
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Cited by 4 (2 self)
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Abstract—Traditional snakes, or active contours, are planar parametric curves. Their parameters are determined by optimizing the weighted sum of three energy terms: one depending on the data (typically on the integral of its gradient under the curve, or on its integral over the area enclosed by the curve), one monitoring the shape of the curve (typically promoting its smoothness, or regularizing ambiguous solutions), and one incorporating prior knowledge (typically favoring a given shape). We present in this paper a snake that we designed to be as simple as possible without losing too many of the characteristics of more complicated, fuller versions. It retains an area data term and requires regularization to avoid an illposed optimization problem. It is parameterized by just two points, thus further easing requirements on the optimizer. Despite its extreme simplicity, this active contour can efficiently solve a variety of problems such as cell counting and segmentation of approximately circular features. Index Terms—Image region analysis, Image shape analysis, Object detection, Parameter estimation, Position measurement, Size measurement, Geometric modeling, Curve fitting.
SplineBased Deforming Ellipsoids for Interactive 3D Bioimage Segmentation
"... Abstract — We present a new fast activecontour model (a.k.a. snake) for image segmentation in 3D microscopy. We introduce a parametric design that relies on exponential Bspline bases and allows us to build snakes that are able to reproduce ellipsoids. We design our bases to have the shortestpossi ..."
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Cited by 2 (0 self)
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Abstract — We present a new fast activecontour model (a.k.a. snake) for image segmentation in 3D microscopy. We introduce a parametric design that relies on exponential Bspline bases and allows us to build snakes that are able to reproduce ellipsoids. We design our bases to have the shortestpossible support, subject to some constraints. Thus, computational efficiency is maximized. The proposed 3D snake can approximate bloblike objects with good accuracy and can perfectly reproduce spheres and ellipsoids, irrespective of their position and orientation. The optimization process is remarkably fast due to the use of Gauss ’ theorem within our energy computation scheme. Our technique yields successful segmentation results, even for challenging data where object contours are not well defined. This is due to our parametric approach that allows one to favor prior shapes. In addition, this paper provides a software that gives full control over the snakes via an intuitive manipulation of few control points. Index Terms — Active contour, active surface, parametric snake, exponential Bspline, segmentation, parameterization,
in Biomedical Imaging
"... et de nationalité indienne acceptée sur proposition du jury: Prof. M. Unser, directeur de thèse ..."
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et de nationalité indienne acceptée sur proposition du jury: Prof. M. Unser, directeur de thèse
Disponible en ligne sur www.sciencedirect.com
, 2013
"... IRBM 34 (2013) 235–243 Original article Splinebased framework for interactive segmentation in biomedical imaging � ..."
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IRBM 34 (2013) 235–243 Original article Splinebased framework for interactive segmentation in biomedical imaging �