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A multiphase level set framework for image segmentation using the Mumford and Shah model (2002)

by L A Vese, T F Chan
Venue:Int. Journ. Comp. Vis
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Contour Detection and Hierarchical Image Segmentation

by Pablo Arbeláez, Michael Maire, Charless Fowlkes, Jitendra Malik - IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE , 2010
"... This paper investigates two fundamental problems in computer vision: contour detection and image segmentation. We present state-of-the-art algorithms for both of these tasks. Our contour detector combines multiple local cues into a globalization framework based on spectral clustering. Our segmentati ..."
Abstract - Cited by 389 (24 self) - Add to MetaCart
This paper investigates two fundamental problems in computer vision: contour detection and image segmentation. We present state-of-the-art algorithms for both of these tasks. Our contour detector combines multiple local cues into a globalization framework based on spectral clustering. Our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree. In this manner, we reduce the problem of image segmentation to that of contour detection. Extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms. The automatically generated hierarchical segmentations can be interactively refined by userspecified annotations. Computation at multiple image resolutions provides a means of coupling our system to recognition applications.
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... been developed to minimize the energy (4) or its simplified version, where u is piecewise constant in Ω\C. Koepfler et al. [55] proposed a region merging method for this purpose. Chan and Vese [56], =-=[57]-=- follow a different approach, expressing (4) in the level set formalism of Osher and Sethian [58], [59]. Bertelli et al. [30] extend this approach to more general cost functions based on pairwise pixe...

Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation

by Nikos Paragios, Rachid Deriche - INTERNATIONAL JOURNAL OF COMPUTER VISION , 2002
"... This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and region-based segmentation modules under a curve-based optimization objective function. The task of supervised texture segmentation is considered to demonst ..."
Abstract - Cited by 312 (9 self) - Add to MetaCart
This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and region-based segmentation modules under a curve-based optimization objective function. The task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework. The textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters, and analyzing their responses as multi-component conditional probability density functions. The texture segmentation is obtained by unifying region and boundary-based information as an improved Geodesic Active Contour Model. The defined objective function is minimized using a gradient-descent method where a level set approach is used to implement the obtained PDE. According to this PDE, the curve propagation towards the final solution is guided by boundary and region-based segmentation forces, and is constrained by a regularity force. The level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled. The performance of our method is demonstrated on a variety of synthetic and real textured frames.

A review of statistical approaches to level set segmentation: Integrating color, texture, motion and shape

by Daniel Cremers, Mikael Rousson, Rachid Deriche - International Journal of Computer Vision , 2007
"... Abstract. Since their introduction as a means of front propagation and their first application to edge-based 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 ..."
Abstract - Cited by 169 (4 self) - Add to MetaCart
Abstract. Since their introduction as a means of front propagation and their first application to edge-based 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 region-based level set segmentation methods and clarify how they can all be derived from a common statistical framework. Region-based 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 edge-based schemes such as the classical Snakes, region-based 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 well-suited 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.
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...egant formulation which only requires log 2(n) level set functions to model n regions. Each of the n regions is characterized by the various level set functions being either positive or negative. See =-=[93]-=- for details. 3.4. Scalar, Vector and Tensor-valued images 3.4.1. Scalar images Let us consider a scalar image made up of two regions, the intensities of which are drawn from a Gaussian distribution: ...

Fast Global Minimization of the Active Contour/Snake Model

by Xavier Bresson, Pierre Vandergheynst, Stanley Osher, et al.
"... The active contour/snake model is one of the most successful variational models in image segmentation. It consists of evolving a contour in images toward the boundaries of objects. Its success is based on strong mathematical properties and efficient numerical schemes based on the level set method. ..."
Abstract - Cited by 161 (10 self) - Add to MetaCart
The active contour/snake model is one of the most successful variational models in image segmentation. It consists of evolving a contour in images toward the boundaries of objects. Its success is based on strong mathematical properties and efficient numerical schemes based on the level set method. The only drawback of this model is the existence of local minima in the active contour energy, which makes the initial guess critical to get satisfactory results. In this paper, we propose to solve this problem by determining a global minimum of the active contour model. Our approach is based on the unification of image segmentation and image denoising tasks into a global minimization framework. More precisely, we propose to unify three well-known image variational models, namely the snake model, the Rudin-Osher-Fatemi denoising model and the Mumford-Shah segmentation model. We will establish theorems with proofs to determine the existence of a global minimum of the active contour model. From a numerical point of view, we propose a new practical way to solve the active contour propagation problem toward object boundaries through a dual formulation of the minimization problem. The dual formulation, easy to implement, allows us a fast global minimization of the snake energy. It avoids the usual drawback in the level set approach that consists of initializing the active contour in a distance function and re-initializing it periodically during the evolution, which is time-consuming. We apply our segmentation algorithms on synthetic and real-world images, such as texture images and medical images, to emphasize the performances of our model compared with other segmentation models.

Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models

by Tony F. Chan, Selim Esedoglu, Mila Nikolova - SIAM JOURNAL ON APPLIED MATHEMATICS , 2006
"... We show how certain nonconvex optimization problems that arise in image processing and computer vision can be restated as convex minimization problems. This allows, in particular, the finding of global minimizers via standard convex minimization schemes. ..."
Abstract - Cited by 153 (6 self) - Add to MetaCart
We show how certain nonconvex optimization problems that arise in image processing and computer vision can be restated as convex minimization problems. This allows, in particular, the finding of global minimizers via standard convex minimization schemes.

Robust Object Tracking with Online Multiple Instance Learning

by Boris Babenko, Ming-hsuan Yang, Serge Belongie , 2011
"... In this paper, we address the problem of tracking an object in a video given its location in the first frame and no other information. Recently, a class of tracking techniques called “tracking by detection ” has been shown to give promising results at real-time speeds. These methods train a discrim ..."
Abstract - Cited by 140 (7 self) - Add to MetaCart
In this paper, we address the problem of tracking an object in a video given its location in the first frame and no other information. Recently, a class of tracking techniques called “tracking by detection ” has been shown to give promising results at real-time speeds. These methods train a discriminative classifier in an online manner to separate the object from the background. This classifier bootstraps itself by using the current tracker state to extract positive and negative examples from the current frame. Slight inaccuracies in the tracker can therefore lead to incorrectly labeled training examples, which degrade the classifier and can cause drift. In this paper, we show that using Multiple Instance Learning (MIL) instead of traditional supervised learning avoids these problems and can therefore lead to a more robust tracker with fewer parameter tweaks. We propose a novel online MIL algorithm for object tracking that achieves superior results with real-time performance. We present thorough experimental results (both qualitative and quantitative) on a number of challenging video clips.

A nonparametric statistical method for image segmentation using information theory and curve evolution

by Junmo Kim, John W. Fisher, III, Anthony Yezzi, Müjdat Çetin, Alan S. Willsky - IEEE TRANSACTIONS ON IMAGE PROCESSING , 2005
"... In this paper, we present a new information-theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We as ..."
Abstract - Cited by 82 (1 self) - Add to MetaCart
In this paper, we present a new information-theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques. We use level-set methods to implement the resulting evolution. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems. Furthermore, our method, which does not require any training, performs as good as methods based on training.
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...ours without Edges, Chan and Vese, 2001 [10] Curve Evolution Implementation of the Mumford-Shah Functional, Tsai et al., 2001 [67] Image Segmentation Using Mumford and Shah Model, Vese and Chan, 2002 =-=[71]-=- Region-Based Mumford Shah Functional, 1985, 1989 [46, 47] Figure 2.1. Previous work in active contour models Sec. 2.1. Curve Evolution Theory for Image Segmentation 27 an extensive survey, but rather...

A Level Set Approach for Shape-driven Segmentation and Tracking of the Left Ventricle

by Nikos Paragios , 2002
"... Knowledge-based segmentation has been explored significantly in medical imaging. Prior anatomical knowledge can be used to define constraints that can improve performance of segmentation algorithms to physically corrupted and incomplete data. In this paper our objective is to introduce such knowledg ..."
Abstract - Cited by 74 (0 self) - Add to MetaCart
Knowledge-based segmentation has been explored significantly in medical imaging. Prior anatomical knowledge can be used to define constraints that can improve performance of segmentation algorithms to physically corrupted and incomplete data. In this paper our objective is to introduce such knowledgebased constraints while preserving the ability of dealing with local deformations. Towards this end, we propose a variational level set framework that can account for global shape consistency as well as for local deformations. In order to improve performance the problems of segmentation and tracking of the structure of interest are dealt with simultaneously by introducing the notion of time in the process and looking for a solution that satisfies that prior constraints while being consistent along consecutive frames. Promising experimental results in MR and ultrasonic cardiac images demonstrate the potentials of our approach.
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...imension and define a corresponding flow such that its zero level set yields always to the position of the input structure. A step further is to consider the definition of an objective function [16], =-=[14]-=- to address such a task directly on the space of level set representations. Toward this end, one can define the approximations of Dirac and Heaviside [16] distributions a( )= H ( )= 0; j j > 1 1+cos 2...

Minimization of Region-Scalable Fitting Energy for Image Segmentation

by Chunming Li, Chiu-yen Kao, John C. Gore, Zhaohua Ding - IEEE TRANS. ON IMAGE PROCESSING , 2008
"... Intensity inhomogeneities often occur in real-world images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a region-based active contour model that draws upon intensity information in local regions ..."
Abstract - Cited by 67 (3 self) - Add to MetaCart
Intensity inhomogeneities often occur in real-world images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a region-based active contour model that draws upon intensity information in local regions at a controllable scale. A data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level set formulation with a level set regularization term, from which a curve evolution equation is derived for energy minimization. Due to a kernel function in the data fitting term, intensity information in local regions is extracted to guide the motion of the contour, which thereby enables our model to cope with intensity inhomogeneity. In addition, the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function. Experimental results for synthetic and real images show desirable performances of our method.
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...lysis and recognition. Existing active contour models can be categorized into two major classes: edge-based models [3], [10]–[12], [18], [19], [28], [30], and region-based models[4], [23], [25]–[27], =-=[29]-=-. Manuscript received September 4, 2007; revised April 3, 2008. Current version published September 10, 2008. The associate editor coordinating the review of this manuscript and approving it for publi...

Sobolev active contours

by Andrea C. Mennucci, Ganesh Sundaramoorthi, Anthony Yezzi - 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 2-type 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 ..."
Abstract - Cited by 66 (9 self) - Add to MetaCart
All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L 2-type 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 Sobolev-type 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 edge-based and regionbased active contour models as Sobolev active contours and show the substantial improvements gained in segmentation.
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