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Journal ArticleDOI

Distance Regularized Level Set Evolution and Its Application to Image Segmentation

01 Dec 2010-IEEE Transactions on Image Processing (IEEE Trans Image Process)-Vol. 19, Iss: 12, pp 3243-3254
TL;DR: A new variational level set formulation in which the regularity of the level set function is intrinsically maintained during thelevel set evolution called distance regularized level set evolution (DRLSE), which eliminates the need for reinitialization and thereby avoids its induced numerical errors.
Abstract: Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.
Citations
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Journal ArticleDOI
TL;DR: A novel region-based method for image segmentation, which is able to simultaneously segment the image and estimate the bias field, and the estimated bias field can be used for intensity inhomogeneity correction (or bias correction).
Abstract: Intensity inhomogeneity often occurs in real-world images, which presents a considerable challenge in image segmentation. The most widely used image segmentation algorithms are region-based and typically rely on the homogeneity of the image intensities in the regions of interest, which often fail to provide accurate segmentation results due to the intensity inhomogeneity. This paper proposes a novel region-based method for image segmentation, which is able to deal with intensity inhomogeneities in the segmentation. First, based on the model of images with intensity inhomogeneities, we derive a local intensity clustering property of the image intensities, and define a local clustering criterion function for the image intensities in a neighborhood of each point. This local clustering criterion function is then integrated with respect to the neighborhood center to give a global criterion of image segmentation. In a level set formulation, this criterion defines an energy in terms of the level set functions that represent a partition of the image domain and a bias field that accounts for the intensity inhomogeneity of the image. Therefore, by minimizing this energy, our method is able to simultaneously segment the image and estimate the bias field, and the estimated bias field can be used for intensity inhomogeneity correction (or bias correction). Our method has been validated on synthetic images and real images of various modalities, with desirable performance in the presence of intensity inhomogeneities. Experiments show that our method is more robust to initialization, faster and more accurate than the well-known piecewise smooth model. As an application, our method has been used for segmentation and bias correction of magnetic resonance (MR) images with promising results.

1,201 citations


Cites background from "Distance Regularized Level Set Evol..."

  • ...For example, it can be a truncated uniform function, defined as for and for , with being a positive constant such that ....

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  • ...Image segmentation and bias field estimation can be performed by minimizing this energy with respect to the regions , constants , and bias field ....

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  • ...In level set methods, a level set function is a function that take positive and negative signs, which can be used to represent a partition of the domain into two disjoint regions and ....

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Journal ArticleDOI
TL;DR: The experimental results show the significant performance boost by the SDAE-based CADx algorithm over the two conventional methods, suggesting that deep learning techniques can potentially change the design paradigm of the CADx systems without the need of explicit design and selection of problem-oriented features.
Abstract: This paper performs a comprehensive study on the deep-learning-based computer-aided diagnosis (CADx) for the differential diagnosis of benign and malignant nodules/lesions by avoiding the potential errors caused by inaccurate image processing results (e.g., boundary segmentation), as well as the classification bias resulting from a less robust feature set, as involved in most conventional CADx algorithms. Specifically, the stacked denoising auto-encoder (SDAE) is exploited on the two CADx applications for the differentiation of breast ultrasound lesions and lung CT nodules. The SDAE architecture is well equipped with the automatic feature exploration mechanism and noise tolerance advantage, and hence may be suitable to deal with the intrinsically noisy property of medical image data from various imaging modalities. To show the outperformance of SDAE-based CADx over the conventional scheme, two latest conventional CADx algorithms are implemented for comparison. 10 times of 10-fold cross-validations are conducted to illustrate the efficacy of the SDAE-based CADx algorithm. The experimental results show the significant performance boost by the SDAE-based CADx algorithm over the two conventional methods, suggesting that deep learning techniques can potentially change the design paradigm of the CADx systems without the need of explicit design and selection of problem-oriented features.

601 citations

Proceedings ArticleDOI
23 Jun 2014
TL;DR: A framework which utilizes face tracking and Normalized Least Mean Square adaptive filtering methods to counter their influences is proposed and it is demonstrated that this method substantially outperforms all previous methods.
Abstract: Heart rate is an important indicator of people's physiological state Recently, several papers reported methods to measure heart rate remotely from face videos Those methods work well on stationary subjects under well controlled conditions, but their performance significantly degrades if the videos are recorded under more challenging conditions, specifically when subjects' motions and illumination variations are involved We propose a framework which utilizes face tracking and Normalized Least Mean Square adaptive filtering methods to counter their influences We test our framework on a large difficult and public database MAHNOB-HCI and demonstrate that our method substantially outperforms all previous methods We also use our method for long term heart rate monitoring in a game evaluation scenario and achieve promising results

458 citations


Cites methods from "Distance Regularized Level Set Evol..."

  • ...We use the Distance Regularized Level Set Evolution (DRLSE) method [11] to segment the background region of the video, and achieve gbg by computing the background mean green value of each frame....

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  • ...We segment the background region using the Distance Regularized Level Set Evolution (DRLSE) method [11], and use its average green value as a reference to model the illumination variations at the ROI....

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Journal ArticleDOI
TL;DR: A comprehensive summary of the recent state-of-the-art nucleus/cell segmentation approaches on different types of microscopy images including bright-field, phase-contrast, differential interference contrast, fluorescence, and electron microscopies is provided.
Abstract: Digital pathology and microscopy image analysis is widely used for comprehensive studies of cell morphology or tissue structure. Manual assessment is labor intensive and prone to interobserver variations. Computer-aided methods, which can significantly improve the objectivity and reproducibility, have attracted a great deal of interest in recent literature. Among the pipeline of building a computer-aided diagnosis system, nucleus or cell detection and segmentation play a very important role to describe the molecular morphological information. In the past few decades, many efforts have been devoted to automated nucleus/cell detection and segmentation. In this review, we provide a comprehensive summary of the recent state-of-the-art nucleus/cell segmentation approaches on different types of microscopy images including bright-field, phase-contrast, differential interference contrast, fluorescence, and electron microscopies. In addition, we discuss the challenges for the current methods and the potential future work of nucleus/cell detection and segmentation.

430 citations


Cites methods from "Distance Regularized Level Set Evol..."

  • ...shape model is incorporated into the level set framework [236] to segment overlapping nuclei and lymphocytes in prostate and breast cancer histopathological images; in [74], the shape prior constraint [235] is integrated in the distance regularized level set model [237], and thus, the method can efficiently handle severely overlapping cervical cells....

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Journal ArticleDOI
TL;DR: An improved region-based active contour model in a variational level set formulation that has been applied to brain MR image segmentation with desirable results and is presented as a two-phaselevel set formulation and then extended to a multi-phase formulation.

374 citations

References
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Book
01 Jan 1941
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Abstract: Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear first-order PDE Other ways to represent solutions Part II: Theory for linear partial differential equations: Sobolev spaces Second-order elliptic equations Linear evolution equations Part III: Theory for nonlinear partial differential equations: The calculus of variations Nonvariational techniques Hamilton-Jacobi equations Systems of conservation laws Appendices Bibliography Index.

25,734 citations

Journal ArticleDOI
TL;DR: This work uses snakes for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest, and uses scale-space continuation to enlarge the capture region surrounding a feature.
Abstract: A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. Snakes are active contour models: they lock onto nearby edges, localizing them accurately. Scale-space continuation can be used to enlarge the capture region surrounding a feature. Snakes provide a unified account of a number of visual problems, including detection of edges, lines, and subjective contours; motion tracking; and stereo matching. We have used snakes successfully for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest.

18,095 citations


"Distance Regularized Level Set Evol..." refers background in this paper

  • ...[5] in the context of active contour (or snake) models [6] for image segmentation....

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  • ...A desirable advantage of level set methods is that they can represent contours of complex topology and are able to handle topological changes, such as splitting and merging, in a natural and efficient way, which is not allowed in parametric active contour models [6], [8], [9] unless extra indirect procedures are introduced in the implementations....

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Journal ArticleDOI
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.

13,020 citations

Journal ArticleDOI
TL;DR: A new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets is proposed, which can detect objects whose boundaries are not necessarily defined by the gradient.
Abstract: We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.

10,404 citations

Journal ArticleDOI
20 Jun 1995
TL;DR: A novel scheme for the detection of object boundaries based on active contours evolving in time according to intrinsic geometric measures of the image, allowing stable boundary detection when their gradients suffer from large variations, including gaps.
Abstract: A novel scheme for the detection of object boundaries is presented. The technique is based on active contours deforming according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric as defined by the image content. This geodesic approach for object segmentation allows to connect classical "snakes" based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved as showed by a number of examples. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. >

5,566 citations


"Distance Regularized Level Set Evol..." refers background or methods in this paper

  • ...as an energy of an parameterized contour in their proposed geodesic active contour (GAC) model [11]....

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  • ...To show the advantage of the DRLSE formulation, we also applied the well-known GAC model [11] to this image, and compared the behaviors of the level set evolution in the two formulations....

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  • ...[26] proposed an implementation strategy to avoid separate reinitialization procedures in their implementation of the well-known geodesic active contour (GAC) model in [11]....

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