Automated parameterization of active contours: A brief survey
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paper_title: A convex representation for the vectorial Mumford-Shah functional

paper_content:

We propose the first tractable convex formulation of the vectorial Mumford-Shah functional which allows to compute high-quality solutions independent of the initialization. To this end, we generalize recently introduced convex formulations for scalar functionals to the vector-valued scenario in such a way that discontinuities in the different color channels preferably coincide. Furthermore, we propose an efficient solution which makes the overall optimization problem as tractable as in the scalar-valued case. Numerous experimental comparisons with the naive channel-wise approach, with the well-known Ambrosio-Tortorelli approximation, and with the classical total variation confirm the advantages of the proposed relaxation for contrastpreserving and edge-enhancing regularization.
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paper_title: Distance Regularized Level Set Evolution and Its Application to Image Segmentation

paper_content:

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.
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paper_title: MAC: Magnetostatic Active Contour Model

paper_content:

We propose an active contour model using an external force field that is based on magnetostatics and hypothesized magnetic interactions between the active contour and object boundaries. The major contribution of the method is that the interaction of its forces can greatly improve the active contour in capturing complex geometries and dealing with difficult initializations, weak edges, and broken boundaries. The proposed method is shown to achieve significant improvements when compared against six well-known and state-of-the-art shape recovery methods, including the geodesic snake, the generalized version of gradient vector flow (GVF) snake, the combined geodesic and GVF snake, and the charged particle model.
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paper_title: Active Contours without Edges

paper_content:

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.
---
paper_title: A shape-based approach to the segmentation of medical imagery using level sets

paper_content:

We propose a shape-based approach to curve evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras, we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data. The parameters of this representation are then manipulated to minimize an objective function for segmentation. The resulting algorithm is able to handle multidimensional data, can deal with topological changes of the curve, is robust to noise and initial contour placements, and is computationally efficient. At the same time, it avoids the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications; two-dimensional segmentation of cardiac magnetic resonance imaging (MRI) and three-dimensional segmentation of prostate MRI.
---
paper_title: STACS: new active contour scheme for cardiac MR image segmentation

paper_content:

The paper presents a novel stochastic active contour scheme (STACS) for automatic image segmentation designed to overcome some of the unique challenges in cardiac MR images such as problems with low contrast, papillary muscles, and turbulent blood flow. STACS minimizes an energy functional that combines stochastic region-based and edge-based information with shape priors of the heart and local properties of the contour. The minimization algorithm solves, by the level set method, the Euler-Lagrange equation that describes the contour evolution. STACS includes an annealing schedule that balances dynamically the weight of the different terms in the energy functional. Three particularly attractive features of STACS are: 1) ability to segment images with low texture contrast by modeling stochastically the image textures; 2) robustness to initial contour and noise because of the utilization of both edge and region-based information; 3) ability to segment the heart from the chest wall and the undesired papillary muscles due to inclusion of heart shape priors. Application of STACS to a set of 48 real cardiac MR images shows that it can successfully segment the heart from its surroundings such as the chest wall and the heart structures (the left and right ventricles and the epicardium.) We compare STACS' automatically generated contours with manually-traced contours, or the "gold standard," using both area and edge similarity measures. This assessment demonstrates very good and consistent segmentation performance of STACS.
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paper_title: Statistical shape influence in geodesic active contours

paper_content:

A novel method of incorporating shape information into the image segmentation process is presented. We introduce a representation for deformable shapes and define a probability distribution over the variances of a set of training shapes. The segmentation process embeds an initial curve as the zero level set of a higher dimensional surface, and evolves the surface such that the zero level set converges on the boundary of the object to be segmented. At each step of the surface evolution, we estimate the maximum a posteriori (MAP) position and shape of the object in the image, based on the prior shape information and the image information. We then evolve the surface globally; towards the MAP estimate, and locally based on image gradients and curvature. Results are demonstrated on synthetic data and medical imagery in 2D min 3D.
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paper_title: A Lip Contour Extraction Method Using Localized Active Contour Model with Automatic Parameter Selection

paper_content:

Lip contour extraction is crucial to the success of a lipreading system. This paper presents a lip contour extraction algorithm using localized active contour model with the automatic selection of proper parameters. The proposed approach utilizes a minimum-bounding ellipse as the initial evolving curve to split the local neighborhoods into the local interior region and the local exterior region, respectively, and then compute the localized energy for evolving and extracting. This method is robust against the uneven illumination, rotation, deformation, and the effects of teeth and tongue. Experiments show its promising result in comparison with the existing methods.
---
paper_title: STACS: new active contour scheme for cardiac MR image segmentation

paper_content:

The paper presents a novel stochastic active contour scheme (STACS) for automatic image segmentation designed to overcome some of the unique challenges in cardiac MR images such as problems with low contrast, papillary muscles, and turbulent blood flow. STACS minimizes an energy functional that combines stochastic region-based and edge-based information with shape priors of the heart and local properties of the contour. The minimization algorithm solves, by the level set method, the Euler-Lagrange equation that describes the contour evolution. STACS includes an annealing schedule that balances dynamically the weight of the different terms in the energy functional. Three particularly attractive features of STACS are: 1) ability to segment images with low texture contrast by modeling stochastically the image textures; 2) robustness to initial contour and noise because of the utilization of both edge and region-based information; 3) ability to segment the heart from the chest wall and the undesired papillary muscles due to inclusion of heart shape priors. Application of STACS to a set of 48 real cardiac MR images shows that it can successfully segment the heart from its surroundings such as the chest wall and the heart structures (the left and right ventricles and the epicardium.) We compare STACS' automatically generated contours with manually-traced contours, or the "gold standard," using both area and edge similarity measures. This assessment demonstrates very good and consistent segmentation performance of STACS.
---
paper_title: 3D Deformable Surfaces with Locally Self-Adjusting Parameters - A Robust Method to Determine Cell Nucleus Shapes

paper_content:

When using deformable models for the segmentation of biological data, the choice of the best weighting parameters for the internal and external forces is crucial. Especially when dealing with 3D fluorescence microscopic data and cells within dense tissue, object boundaries are sometimes not visible. In these cases, one weighting parameter set for the whole contour is not desirable. We are presenting a method for the dynamic adjustment of the weighting parameters, that is only depending on the underlying data and does not need any prior information. The method is especially apt to handle blurred, noisy, and deficient data, as it is often the case in biological microscopy.
---
paper_title: Automatic segmentation of liver PET images

paper_content:

Abstract Automation of liver positron emission tomography (PET) image segmentation is proposed in this paper. A new active contour model (ACM), called Poisson Gradient Vector Flow (PGVF), with genetic algorithm (GA) constructs a scheme to automatically find the contour of liver in the PET images. PET is widely used for the clinical purpose, but image quality of PET makes the image segmentation be a tough work. Three image data sets are tested for evaluating the new segmentation approach of liver PET images. One image data set is adapted from the study of one person with a normal liver. The other two image data sets are adapted from the studies of two patients with abnormal livers. The results show that the regions of interest (ROI) of liver are automatically segmented from the images of three data sets.
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paper_title: A genetically optimized level set approach to segmentation of thyroid ultrasound images

paper_content:

This paper presents a novel framework for thyroid ultrasound image segmentation that aims to accurately delineate thyroid nodules. This framework, named GA-VBAC incorporates a level set approach named Variable Background Active Contour model (VBAC) that utilizes variable background regions, to reduce the effects of the intensity inhomogeneity in the thyroid ultrasound images. Moreover, a parameter tuning mechanism based on Genetic Algorithms (GA) has been considered to search for the optimal VBAC parameters automatically, without requiring technical skills. Experiments were conducted over a range of ultrasound images displaying thyroid nodules. The results show that the proposed GA-VBAC framework provides an efficient, effective and highly objective system for the delineation of thyroid nodules.
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paper_title: Variable Background Active Contour Model for Computer-Aided Delineation of Nodules in Thyroid Ultrasound Images

paper_content:

This paper presents a computer-aided approach for nodule delineation in thyroid ultrasound (US) images. The developed algorithm is based on a novel active contour model, named variable background active contour (VBAC), and incorporates the advantages of the level set region-based active contour without edges (ACWE) model, offering noise robustness and the ability to delineate multiple nodules. Unlike the classic active contour models that are sensitive in the presence of intensity inhomogeneities, the proposed VBAC model considers information of variable background regions. VBAC has been evaluated on synthetic images, as well as on real thyroid US images. From the quantification of the results, two major impacts have been derived: 1) higher average accuracy in the delineation of hypoechoic thyroid nodules, which exceeds 91%; and 2) faster convergence when compared with the ACWE model.
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paper_title: Self-adjusted active contours using multi-directional texture cues

paper_content:

Parameterization is an open issue in active contour research, associated with the cumbersome and time-consuming process of empirical adjustment. This work introduces a novel framework for self-adjustment of region-based active contours, based on multi-directional texture cues. The latter are mined by applying filtering transforms characterized by multi-resolution, anisotropy, localization and directionality. This process yields to entropy-based image “heatmaps”, used to weight the regularization and data fidelity terms, which guide contour evolution. Experimental evaluation is performed on a large benchmark dataset as well as on textured images. The segmentation results demonstrate that the proposed framework is capable of accelerating contour convergence, maintaining a segmentation quality which is comparable to the one obtained by empirically adjusted active contours.
---
paper_title: An approach for dynamic combination of region and boundary information in segmentation

paper_content:

Image segmentation combining boundary and region information has been the subject of numerous research works in the past. This combination is usually subject to arbitrary weighting parameters (hyper-parameters) that control the contribution of boundary and region features during segmentation. In this work, we investigate a new approach for estimating the hyper-parameters adaptively to segmentation. The approach takes its roots from the physical properties of the energy functional controlling segmentation and a Bayesian formulation of segmentation and hyper-parameters estimation.
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paper_title: The contourlet transform: an efficient directional multiresolution image representation

paper_content:

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. The main challenge in exploring geometry in images comes from the discrete nature of the data. Thus, unlike other approaches, such as curvelets, that first develop a transform in the continuous domain and then discretize for sampled data, our approach starts with a discrete-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically, we construct a discrete-domain multiresolution and multidirection expansion using nonseparable filter banks, in much the same way that wavelets were derived from filter banks. This construction results in a flexible multiresolution, local, and directional image expansion using contour segments, and, thus, it is named the contourlet transform. The discrete contourlet transform has a fast iterated filter bank algorithm that requires an order N operations for N-pixel images. Furthermore, we establish a precise link between the developed filter bank and the associated continuous-domain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications.
---
paper_title: Active Contours without Edges

paper_content:

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.
---
paper_title: A genetically optimized level set approach to segmentation of thyroid ultrasound images

paper_content:

This paper presents a novel framework for thyroid ultrasound image segmentation that aims to accurately delineate thyroid nodules. This framework, named GA-VBAC incorporates a level set approach named Variable Background Active Contour model (VBAC) that utilizes variable background regions, to reduce the effects of the intensity inhomogeneity in the thyroid ultrasound images. Moreover, a parameter tuning mechanism based on Genetic Algorithms (GA) has been considered to search for the optimal VBAC parameters automatically, without requiring technical skills. Experiments were conducted over a range of ultrasound images displaying thyroid nodules. The results show that the proposed GA-VBAC framework provides an efficient, effective and highly objective system for the delineation of thyroid nodules.
---
paper_title: A Lip Contour Extraction Method Using Localized Active Contour Model with Automatic Parameter Selection

paper_content:

Lip contour extraction is crucial to the success of a lipreading system. This paper presents a lip contour extraction algorithm using localized active contour model with the automatic selection of proper parameters. The proposed approach utilizes a minimum-bounding ellipse as the initial evolving curve to split the local neighborhoods into the local interior region and the local exterior region, respectively, and then compute the localized energy for evolving and extracting. This method is robust against the uneven illumination, rotation, deformation, and the effects of teeth and tongue. Experiments show its promising result in comparison with the existing methods.
---
paper_title: A shape-based approach to the segmentation of medical imagery using level sets

paper_content:

We propose a shape-based approach to curve evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras, we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data. The parameters of this representation are then manipulated to minimize an objective function for segmentation. The resulting algorithm is able to handle multidimensional data, can deal with topological changes of the curve, is robust to noise and initial contour placements, and is computationally efficient. At the same time, it avoids the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications; two-dimensional segmentation of cardiac magnetic resonance imaging (MRI) and three-dimensional segmentation of prostate MRI.
---
paper_title: Self-adjusted active contours using multi-directional texture cues

paper_content:

Parameterization is an open issue in active contour research, associated with the cumbersome and time-consuming process of empirical adjustment. This work introduces a novel framework for self-adjustment of region-based active contours, based on multi-directional texture cues. The latter are mined by applying filtering transforms characterized by multi-resolution, anisotropy, localization and directionality. This process yields to entropy-based image “heatmaps”, used to weight the regularization and data fidelity terms, which guide contour evolution. Experimental evaluation is performed on a large benchmark dataset as well as on textured images. The segmentation results demonstrate that the proposed framework is capable of accelerating contour convergence, maintaining a segmentation quality which is comparable to the one obtained by empirically adjusted active contours.
---
paper_title: STACS: new active contour scheme for cardiac MR image segmentation

paper_content:

The paper presents a novel stochastic active contour scheme (STACS) for automatic image segmentation designed to overcome some of the unique challenges in cardiac MR images such as problems with low contrast, papillary muscles, and turbulent blood flow. STACS minimizes an energy functional that combines stochastic region-based and edge-based information with shape priors of the heart and local properties of the contour. The minimization algorithm solves, by the level set method, the Euler-Lagrange equation that describes the contour evolution. STACS includes an annealing schedule that balances dynamically the weight of the different terms in the energy functional. Three particularly attractive features of STACS are: 1) ability to segment images with low texture contrast by modeling stochastically the image textures; 2) robustness to initial contour and noise because of the utilization of both edge and region-based information; 3) ability to segment the heart from the chest wall and the undesired papillary muscles due to inclusion of heart shape priors. Application of STACS to a set of 48 real cardiac MR images shows that it can successfully segment the heart from its surroundings such as the chest wall and the heart structures (the left and right ventricles and the epicardium.) We compare STACS' automatically generated contours with manually-traced contours, or the "gold standard," using both area and edge similarity measures. This assessment demonstrates very good and consistent segmentation performance of STACS.
---
paper_title: Texture Analysis and Segmentation Using Modulation Features, Generative Models, and Weighted Curve Evolution

paper_content:

In this work we approach the analysis and segmentation of natural textured images by combining ideas from image analysis and probabilistic modeling. We rely on AM-FM texture models and specifically on the Dominant Component Analysis (DCA) paradigm for feature extraction. This method provides a low-dimensional, dense and smooth descriptor, capturing essential aspects of texture, namely scale, orientation, and contrast. Our contributions are at three levels of the texture analysis and segmentation problems: First, at the feature extraction stage we propose a regularized demodulation algorithm that provides more robust texture features and explore the merits of modifying the channel selection criterion of DCA. Second, we propose a probabilistic interpretation of DCA and Gabor filtering in general, in terms of Local Generative Models. Extending this point of view to edge detection facilitates the estimation of posterior probabilities for the edge and texture classes. Third, we propose the weighted curve evolution scheme that enhances the Region Competition/ Geodesic Active Regions methods by allowing for the locally adaptive fusion of heterogeneous cues. Our segmentation results are evaluated on the Berkeley Segmentation Benchmark, and compare favorably to current state-of-the-art methods.
---
paper_title: An approach for dynamic combination of region and boundary information in segmentation

paper_content:

Image segmentation combining boundary and region information has been the subject of numerous research works in the past. This combination is usually subject to arbitrary weighting parameters (hyper-parameters) that control the contribution of boundary and region features during segmentation. In this work, we investigate a new approach for estimating the hyper-parameters adaptively to segmentation. The approach takes its roots from the physical properties of the energy functional controlling segmentation and a Bayesian formulation of segmentation and hyper-parameters estimation.
---
paper_title: Automatic segmentation of liver PET images

paper_content:

Abstract Automation of liver positron emission tomography (PET) image segmentation is proposed in this paper. A new active contour model (ACM), called Poisson Gradient Vector Flow (PGVF), with genetic algorithm (GA) constructs a scheme to automatically find the contour of liver in the PET images. PET is widely used for the clinical purpose, but image quality of PET makes the image segmentation be a tough work. Three image data sets are tested for evaluating the new segmentation approach of liver PET images. One image data set is adapted from the study of one person with a normal liver. The other two image data sets are adapted from the studies of two patients with abnormal livers. The results show that the regions of interest (ROI) of liver are automatically segmented from the images of three data sets.
---
paper_title: Is a single energy functional sufficient? adaptive energy functionals and automatic initialization

paper_content:

Energy functional minimization is an increasingly popular technique for image segmentation. However, it is far too commonly applied with hand-tuned parameters and initializations that have only been validated for a few images. Fixing these parameters over a set of images assumes the same parameters are ideal for each image. We highlight the effects of varying the parameters and initialization on segmentation accuracy and propose a framework for attaining improved results using image adaptive parameters and initializations. We provide an analytical definition of optimal weights for functional terms through an examination of segmentation in the context of image manifolds, where nearby images on the manifold require similar parameters and similar initializations. Our results validate that fixed parameters are insufficient in addressing the variability in real clinical data, that similar images require similar parameters, and demonstrate how these parameters correlate with the image manifold. We present significantly improved segmentations for synthetic images and a set of 470 clinical examples.
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paper_title: An unconstrained hybrid active contour model for image segmentation

paper_content:

In this paper, we propose an unconstrained active contour model combining edge and region information for image segmentation. The new method achieves the segmentation by filternating the regularization term and the data-fidelity term. We use a morphological approach to the regularization term which is the most time-consuming in the energy function. The proposed method is robust to noise and avoids re-initialization. The efficiency of our method is validated by testing it on various images.
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paper_title: Mumford-Shah Regularizer with Contextual Feedback

paper_content:

We present a simple and robust feature preserving image regularization by letting local region measures modulate the diffusivity. The purpose of this modulation is to disambiguate low level cues in early vision. We interpret the Ambrosio-Tortorelli approximation of the Mumford-Shah model as a system with modulatory feedback and utilize this interpretation to integrate high level information into the regularization process. The method does not require any prior model or learning; the high level information is extracted from local regions and fed back to the regularization step. An important characteristic of the method is that both negative and positive feedback can be simultaneously used without creating oscillations. Experiments performed with both gray and color natural images demonstrate the potential of the method under difficult noise types, non-uniform contrast, existence of multi-scale patterns and textures.
---
paper_title: 3D Deformable Surfaces with Locally Self-Adjusting Parameters - A Robust Method to Determine Cell Nucleus Shapes

paper_content:

When using deformable models for the segmentation of biological data, the choice of the best weighting parameters for the internal and external forces is crucial. Especially when dealing with 3D fluorescence microscopic data and cells within dense tissue, object boundaries are sometimes not visible. In these cases, one weighting parameter set for the whole contour is not desirable. We are presenting a method for the dynamic adjustment of the weighting parameters, that is only depending on the underlying data and does not need any prior information. The method is especially apt to handle blurred, noisy, and deficient data, as it is often the case in biological microscopy.
---

Title: Automated parameterization of active contours: A brief survey

Section 1: INTRODUCTION
Description 1: Discuss the challenges associated with empirical parameterization of active contours and the necessity for automated parameter adjustment approaches.

Section 2: Time-Dependent Active Contour Parameterization
Description 2: Review methods where parameters are calculated dynamically as the contour evolves over time, highlighting specific models and algorithms used.

Section 3: Active Contour Parameterization using Shape Priors
Description 3: Explore approaches that use shape priors to automate parameter adjustment, focusing on methods that depend on the target region's shape.

Section 4: Hybrid Active Contour Parameterization using both Empirical and Automatically obtained Parameter Settings
Description 4: Discuss hybrid approaches that combine empirical settings with automated techniques for parameter adjustment.

Section 5: Machine Learning and Spatially Varying Models
Description 5: Examine methods that incorporate machine learning algorithms and spatially varying parameters to adjust active contour parameters based on image features.

Section 6: CONCLUSIONS
Description 6: Summarize the reviewed active contour parameterization approaches, comparing their levels of automation, dependency on shape priors, spatial variability, and the use of machine learning.