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40
Fast Texture Segmentation Model based on the Shape Operator and Active Contour
 In IEEE Conference on Computer Vision and Pattern Recognition
, 2008
"... We present an approach for unsupervised segmentation of natural and textural images based on active contour, differential geometry and information theoretical concept. More precisely, we propose a new texture descriptor which intrinsically defines the geometry of textural regions using the shape ope ..."
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We present an approach for unsupervised segmentation of natural and textural images based on active contour, differential geometry and information theoretical concept. More precisely, we propose a new texture descriptor which intrinsically defines the geometry of textural regions using the shape operator borrowed from differential geometry. Then, we use the popular KullbackLeibler distance to define an active contour model which distinguishes the background and textural objects of interest represented by the probability density functions of our new texture descriptor. We prove the existence of a solution to the proposed segmentation model. Finally, a fast and easy to implement texture segmentation algorithm is introduced to extract meaningful objects. We present promising synthetic and realworld results and compare our algorithm to other stateoftheart techniques. 1.
Shapebased mutual segmentation
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2008
"... We present a novel variational approach for simultaneous segmentation of two images of the same object taken from different viewpoints. Due to noise, clutter and occlusions, neither of the images contains sufficient information for correct objectbackground partitioning. The evolving object contour ..."
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Cited by 7 (1 self)
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We present a novel variational approach for simultaneous segmentation of two images of the same object taken from different viewpoints. Due to noise, clutter and occlusions, neither of the images contains sufficient information for correct objectbackground partitioning. The evolving object contour in each image provides a dynamic prior for the segmentation of the other object view. We call this process mutual segmentation. The foundation of the proposed method is a unified levelset framework for region and edge based segmentation, associated with a shape similarity term. The suggested shape term incorporates the semantic knowledge gained in the segmentation process of the image pair, accounting for excess or deficient parts in the estimated object shape. Transformations, including planar projectivities, between the object views are accommodated by a registration process held concurrently with the segmentation. The proposed segmentation algorithm is demonstrated on a variety of image pairs. The Homography between each of the image pairs is estimated and its accuracy is evaluated.
Interactive Image Segmentation Based on Level Sets of Probabilities
"... Abstract—In this paper, we present a robust and accurate algorithm for interactive image segmentation. The level set method is clearly advantageous for image objects with a complex topology and fragmented appearance. Our method integrates discriminative classification models and distance transforms ..."
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Abstract—In this paper, we present a robust and accurate algorithm for interactive image segmentation. The level set method is clearly advantageous for image objects with a complex topology and fragmented appearance. Our method integrates discriminative classification models and distance transforms with the level set method to avoid local minima and better snap to true object boundaries. The level set function approximates a transformed version of pixelwise posterior probabilities of being part of a target object. The evolution of its zero level set is driven by three force terms, region force, edge field force, and curvature force. These forces are based on a probabilistic classifier and an unsigned distance transform of salient edges. We further propose a technique that improves the performance of both the probabilistic classifier and the level set method over multiple passes. It makes the final object segmentation less sensitive to user interactions. Experiments and comparisons demonstrate the effectiveness of our method. Index Terms—Image segmentation, level set method, statistical classification, distance transform, curvature. Ç 1
Sidescan sonar segmentation using texture descriptors and active contours
 IEEE Journal of Oceanic Engineering
, 2007
"... Abstract—This paper is concerned with the application of active contour methods to unsupervised binary segmentation of highresolution sonar images. First, texture features are extracted from a sidescan image containing two distinct regions. A regionbased active contour model of Chan et al. [J. Vi ..."
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Abstract—This paper is concerned with the application of active contour methods to unsupervised binary segmentation of highresolution sonar images. First, texture features are extracted from a sidescan image containing two distinct regions. A regionbased active contour model of Chan et al. [J. Vis. Commun. Image Represent., vol. 11, pp. 130–141, 2000] is then applied to the vectorvalued image extracted from the original data. Our implementation includes a new automatic feature selection step used to readjust the weights attached to each feature in the curve evolution equation that drives the segmentation. Results are shown on simulated and real data. The influence of the algorithm parameters and contour initialization are also analyzed. Index Terms—Image processing, seabed classification, segmentation, sidescan sonar. I.
Fast Texture Segmentation Based on SemiLocal Region Descriptor and Active
 Contour,” Numerical Math.: Theory, Methods and Applications
, 2009
"... Abstract. In this paper, we present an efficient approach for unsupervised segmentation of natural and textural images based on the extraction of image features and a fast active contour segmentation model. We address the problem of textures where neither the graylevel information nor the boundary ..."
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Abstract. In this paper, we present an efficient approach for unsupervised segmentation of natural and textural images based on the extraction of image features and a fast active contour segmentation model. We address the problem of textures where neither the graylevel information nor the boundary information is adequate for object extraction. This is often the case of natural images composed of both homogeneous and textured regions. Because these images cannot be in general directly processed by the graylevel information, we propose a new texture descriptor which intrinsically defines the geometry of textures using semilocal image information and tools from differential geometry. Then, we use the popular KullbackLeibler distance to design an active contour model which distinguishes the background and textures of interest. The existence of a minimizing solution to the proposed segmentation model is proven. Finally, a texture segmentation algorithm based on the SplitBregman method is introduced to extract meaningful objects in a fast way. Promising synthetic and realworld results for grayscale and color images are presented.
Harmonic active contours
 IEEE Transactions on Image Processing
, 2014
"... Abstract — We propose a segmentation method based on the geometric representation of images as 2D manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set function and the objective functional corresp ..."
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Abstract — We propose a segmentation method based on the geometric representation of images as 2D manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set function and the objective functional corresponds to the surface of the image manifold. In this geometric framework, both datafidelity and regularity terms of the segmentation are represented by a single functional that intrinsically aligns the gradients of the level set function with the gradients of the image and results in a segmentation criterion that exploits the directional information of image gradients to overcome image inhomogeneities and fragmented contours. The proposed formulation combines this robust alignment of gradients with attractive properties of previous methods developed in the same geometric framework: 1) the natural coupling of image channels proposed for anisotropic diffusion and 2) the ability of subjective surfaces to detect weak edges and close fragmented boundaries. The potential of such a geometric approach lies in the general definition of Riemannian manifolds, which naturally generalizes existing segmentation methods (the geodesic active contours, the active contours without edges, and the robust edge integrator) to higher dimensional spaces, nonflat images, and feature spaces. Our experiments show that the proposed technique improves the segmentation of multichannel images, images subject to inhomogeneities, and images characterized by geometric structures like ridges or valleys. Index Terms — Image segmentation, edge detection, active contours, Beltrami.
Minimal surfaces, measurebased metric and image segmentation
, 2006
"... One of the primary goals of low level vision is image segmentation: given data g, defined as a function on the ”pixel space ” B, the objective is to deduce an image u which is composed of subdomains, wherein the image is basically homogeneous, separated by a sharp discontinuities (edges). It has be ..."
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Cited by 2 (2 self)
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One of the primary goals of low level vision is image segmentation: given data g, defined as a function on the ”pixel space ” B, the objective is to deduce an image u which is composed of subdomains, wherein the image is basically homogeneous, separated by a sharp discontinuities (edges). It has been shown that a large number of algorithms for image segmentation are closely related to the MumfordShah functional minimization [42]. This functional involves a tradeoff between the image structure, which is a twodimensional surface, and the contours that surround objects or distinct regions in the image, which are onedimensional parametric curves. This functional was first suggested and analyzed in its onedimensional case by Mumford and Shah for gray level images [41]. The above functional was later extensively studied, (see e.g. [40] for an overview). In particular, the Γconvergence framework [46] was invented to overcome the problem of dealing with objects with different dimentionalities in the same functional. The idea is to approximate the functional by a different, parameter dependent functional, that is expected to be more regular. The approximating functional approaches the original one in the limit, while the parameter goes to zero. According to this approach, minimizers of approximating functional approximate the minimizer of original one, while enjoying greater regularity. In this study we propose an alternative functional to MumfordShah’s one. The proposed functional is independent of parameterization; it is a geometric functional which is given in terms of the geometry of surfaces representing the data and image in the feature space. The Γconvergence technique is merged with the minimal surfaces theory in order to yield a global generalization of the MumfordShah segmentation functional.
MINIMALLY OVERLAPPING PATHS SETS FOR CLOSED CONTOUR EXTRACTION
"... Segmentation, boundary extraction, minimal path, active contour, overlap Active contours and minimal paths have been extensively studied theoretical tools for image segmentation. The recent geodesically linked active contour model, which basically consists in a set of vertices connected by paths of ..."
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Segmentation, boundary extraction, minimal path, active contour, overlap Active contours and minimal paths have been extensively studied theoretical tools for image segmentation. The recent geodesically linked active contour model, which basically consists in a set of vertices connected by paths of minimal cost, blend the benefits of both concepts. This makes up a closed piecewisedefined curve, over which an edge or region energy functional can be formulated. As an important shortcoming, the geodesically linked active contour model in its initial formulation does not guarantee to represent a simple curve, consistent with respect to the purpose of segmentation. In this paper, we propose to extract a similarly piecewisedefined curve from a set of possible paths, such that the resulting structure is guaranteed to represent a relevant closed curve. Toward this goal, we introduce a global constraint penalizing excessive overlap between paths.
The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and ScaleSpace Properties
 J. MATH. IMAGING VIS
, 2006
"... The uncertainty principle is a fundamental concept in the context of signal and image processing, just as much as it has been in the framework of physics and more recently in harmonic analysis. Uncertainty principles can be derived by using a group theoretic approach. This approach yields also a fo ..."
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The uncertainty principle is a fundamental concept in the context of signal and image processing, just as much as it has been in the framework of physics and more recently in harmonic analysis. Uncertainty principles can be derived by using a group theoretic approach. This approach yields also a formalism for finding functions which are the minimizers of the uncertainty principles. A general theorem which associates an uncertainty principle with a pair of selfadjoint operators is used in finding the minimizers of the uncertainty related to various groups. This study is concerned with the uncertainty principle in the context of the WeylHeisenberg, the SIM(2), the Affine and the AffineWeylHeisenberg groups. We explore the relationship between the twodimensional affine group and the SIM(2) group in terms of the uncertainty minimizers. The uncertainty principle is also extended to the AffineWeylHeisenberg group in one dimension. Possible minimizers related to these groups are also presented and the scalespace properties of some of the minimizers are explored.
GRADIENT VECTOR FLOW DRIVEN ACTIVE SHAPE FOR IMAGE SEGMENTATION*
"... We describe a gradient vector flow driven active shape method for modelbased image segmentation. Active shape algorithm retain the shape feature of the interested object, and its performance relies heavily on initialization. Because of a lack of global regulation, the control points tends to be tra ..."
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We describe a gradient vector flow driven active shape method for modelbased image segmentation. Active shape algorithm retain the shape feature of the interested object, and its performance relies heavily on initialization. Because of a lack of global regulation, the control points tends to be trapped in a local optimum in searching. Our proposed method uses the gradient vector flow of an image to guide the optimization process. The control points of an active shape are steered by the direction and the magnitude of gradient vectors. Our experiments demonstrated great improvement in finding the global optimum and resulting correct segmentation. 1.