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95
A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape
 International Journal of Computer Vision
, 2007
"... Abstract. Since their introduction as a means of front propagation and their first application to edgebased segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of reg ..."
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Cited by 164 (4 self)
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Abstract. Since their introduction as a means of front propagation and their first application to edgebased segmentation in the early 90’s, level set methods have become increasingly popular as a general framework for image segmentation. In this paper, we present a survey of a specific class of regionbased level set segmentation methods and clarify how they can all be derived from a common statistical framework. Regionbased segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity, color, texture or motion in each of a set of regions. In contrast to edgebased schemes such as the classical Snakes, regionbased methods tend to be less sensitive to noise. For typical images, the respective cost functionals tend to have less local minima which makes them particularly wellsuited for local optimization methods such as the level set method. We detail a general statistical formulation for level set segmentation. Subsequently, we clarify how the integration of various low level criteria leads to a set of cost functionals and point out relations between the different segmentation schemes. In experimental results, we demonstrate how the level set function is driven to partition the image plane into domains of coherent color, texture, dynamic texture or motion. Moreover, the Bayesian formulation allows to introduce prior shape knowledge into the level set method. We briefly review a number of advances in this domain.
Kernel Density Estimation and Intrinsic Alignment for Knowledgedriven Segmentation: Teaching Level Sets to Walk
 International Journal of Computer Vision
, 2004
"... We address the problem of image segmentation with statistical shape priors in the context of the level set framework. Our paper makes two contributions: Firstly, we propose to generate invariance of the shape prior to certain transformations by intrinsic registration of the evolving level set fun ..."
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Cited by 115 (16 self)
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We address the problem of image segmentation with statistical shape priors in the context of the level set framework. Our paper makes two contributions: Firstly, we propose to generate invariance of the shape prior to certain transformations by intrinsic registration of the evolving level set function. In contrast to existing approaches to invariance in the level set framework, this closedform solution removes the need to iteratively optimize explicit pose parameters. Moreover, we will argue that the resulting shape gradient is more accurate in that it takes into account the e#ect of boundary variation on the object's pose.
Geometric modeling in shape space
 In Proc. SIGGRAPH
, 2007
"... Figure 1: Geodesic interpolation and extrapolation. The blue input poses of the elephant are geodesically interpolated in an asisometricaspossible fashion (shown in green), and the resulting path is geodesically continued (shown in purple) to naturally extend the sequence. No semantic information, ..."
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Cited by 77 (10 self)
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Figure 1: Geodesic interpolation and extrapolation. The blue input poses of the elephant are geodesically interpolated in an asisometricaspossible fashion (shown in green), and the resulting path is geodesically continued (shown in purple) to naturally extend the sequence. No semantic information, segmentation, or knowledge of articulated components is used. We present a novel framework to treat shapes in the setting of Riemannian geometry. Shapes – triangular meshes or more generally straight line graphs in Euclidean space – are treated as points in a shape space. We introduce useful Riemannian metrics in this space to aid the user in design and modeling tasks, especially to explore the space of (approximately) isometric deformations of a given shape. Much of the work relies on an efficient algorithm to compute geodesics in shape spaces; to this end, we present a multiresolution framework to solve the interpolation problem – which amounts to solving a boundary value problem – as well as the extrapolation problem – an initial value problem – in shape space. Based on these two operations, several classical concepts like parallel transport and the exponential map can be used in shape space to solve various geometric modeling and geometry processing tasks. Applications include shape morphing, shape deformation, deformation transfer, and intuitive shape exploration.
Sobolev active contours
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2007
"... All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L 2type inner product to define the notion of gradient. Recent work has shown that this inner product induces a pathological Riemannian metric on the space of smooth curves. Ho ..."
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Cited by 67 (9 self)
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All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L 2type inner product to define the notion of gradient. Recent work has shown that this inner product induces a pathological Riemannian metric on the space of smooth curves. However, there are also undesirable features associated with the gradient flows that this inner product induces. In this paper, we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with Sobolevtype inner products. We call the resulting flows Sobolev active contours. Sobolev metrics induce favorable regularity properties in their gradient flows. In addition, Sobolev active contours favor global translations, but are not restricted to such motions; they are also less susceptible to certain types of local minima in contrast to traditional active contours. These properties are particularly useful in tracking applications. We demonstrate the general methodology by reformulating some standard edgebased and regionbased active contour models as Sobolev active contours and show the substantial improvements gained in segmentation.
A Pseudodistance for Shape Priors in Level Set Segmentation
, 2003
"... We study the question of integrating prior shape knowledge into level set based segmentation methods. In particular, we investigate dissimilarity measures for shapes encoded by the signed distance function. ..."
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Cited by 46 (3 self)
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We study the question of integrating prior shape knowledge into level set based segmentation methods. In particular, we investigate dissimilarity measures for shapes encoded by the signed distance function.
Prior knowledge, level set representations & visual grouping
 Int. J. Comput. Vision
, 2008
"... In this paper, we propose a level set method for shapedriven object extraction. We introduce a voxelwise probabilistic level set formulation to account for prior knowledge. To this end, objects are represented in an implicit form. Constraints on the segmentation process are imposed by seeking a pr ..."
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Cited by 42 (9 self)
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In this paper, we propose a level set method for shapedriven object extraction. We introduce a voxelwise probabilistic level set formulation to account for prior knowledge. To this end, objects are represented in an implicit form. Constraints on the segmentation process are imposed by seeking a projection to the image plane of the prior model modulo a similarity transformation. The optimization of a statistical metric between the evolving contour and the model leads to motion equations that evolve the contour toward the desired image properties while recovering the pose of the object in the new image. Upon convergence, a solution that is similarity invariant with respect to the model and the corresponding transformation are recovered. Promising experimental results demonstrate the potential of such an approach.
Shape priors using Manifold Learning Techniques
 in &quot;11th IEEE International Conference on Computer Vision, Rio de Janeiro
, 2007
"... We introduce a nonlinear shape prior for the deformable model framework that we learn from a set of shape samples using recent manifold learning techniques. We model a category of shapes as a finite dimensional manifold which we approximate using Diffusion maps, that we call the shape prior manifol ..."
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Cited by 39 (2 self)
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We introduce a nonlinear shape prior for the deformable model framework that we learn from a set of shape samples using recent manifold learning techniques. We model a category of shapes as a finite dimensional manifold which we approximate using Diffusion maps, that we call the shape prior manifold. Our method computes a Delaunay triangulation of the reduced space, considered as Euclidean, and uses the resulting space partition to identify the closest neighbors of any given shape based on its Nyström extension. Our contribution lies in three aspects. First, we propose a solution to the preimage problem and define the projection of a shape onto the manifold. Based on closest neighbors for the Diffusion distance, we then describe a variational framework for manifold denoising. Finally, we introduce a shape prior term for the deformable framework through a nonlinear energy term designed to attract a shape towards the manifold at given constant embedding. Results on shapes of cars and ventricule nuclei are presented and demonstrate the potentials of our method.
ElasticString Models for Representation and Analysis of Planar Shapes
 Proceedings of the IEEE Computer Society International Conference on Computer Vision and Pattern Recognition (CVPR
, 2004
"... We develop a new framework for the quantitative analysis of shapes of planar curves. Shapes are modeled on elastic strings that can be bent, stretched or compressed at different rates along the curve. Shapes are treated as elements of a space obtained as the quotient of an infinitedimensional Riema ..."
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Cited by 34 (6 self)
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We develop a new framework for the quantitative analysis of shapes of planar curves. Shapes are modeled on elastic strings that can be bent, stretched or compressed at different rates along the curve. Shapes are treated as elements of a space obtained as the quotient of an infinitedimensional Riemannian manifold of elastic curves by the action of a reparameterization group. The Riemannian metric encodes the elastic properties of the string and has the property that reparameterizations act by isometries. Geodesics in shape space are used to quantify shape dissimilarities, interpolate and extrapolate shapes, and align shapes according to their elastic properties. The shape spaces and metrics constructed offer a novel environment for the study of shape statistics and for the investigation and simulation of shape dynamics. 1.
Multiphase Dynamic Labeling for Variational RecognitionDriven Image Segmentation
 In ECCV 2004, LNCS 3024
, 2004
"... We propose a variational framework for the integration multiple competing shape priors into level set based segmentation schemes. ..."
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Cited by 33 (9 self)
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We propose a variational framework for the integration multiple competing shape priors into level set based segmentation schemes.
A.: Conformal metrics and true “gradient flows” for curves
 In: ICCV. (2005) 913–919
"... We wish to endow the manifold M of smooth curves in lR n with a Riemannian metric that allows us to treat continuous morphs (homotopies) between two curves c0 and c1 as trajectories with computable lengths which are independent of the parameterization or representation of the two curves (and the cur ..."
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Cited by 33 (10 self)
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We wish to endow the manifold M of smooth curves in lR n with a Riemannian metric that allows us to treat continuous morphs (homotopies) between two curves c0 and c1 as trajectories with computable lengths which are independent of the parameterization or representation of the two curves (and the curves making up the morph between them). We may then define the distance between the two curves using the trajectory of minimal length (geodesic) between them, assuming such a minimizing trajectory exists. At first we attempt to utilize the metric structure implied rather unanimously by the past twenty years or so of shape optimization literature in computer vision. This metric arises as the unique metric which validates the common references to a wide variety of contour evolution models in the literature as “gradient flows ” to various formulated energy functionals. Surprisingly, this implied metric yields a pathological and useless notion of distance between curves. In this paper, we show how this metric can be minimally modified using conformal factors the depend upon a curve’s total arclength. A nice property of these new conformal metrics is that all active contour models that have been called “gradient flows” in the past will constitute true gradient flows with respect to these new metrics under specfic time reparameterizations. 1