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Minimal paths are regarded as a powerful and efficient tool for boundary detection and image segmentation due to its global optimality and the well-established numerical solutions such as fast marching method. In this paper, we introduce a flexible interactive image segmentation model based on the Eikonal partial differential equation (PDE) framework in conjunction with region-based homogeneity enhancement. A key ingredient in the introduced model is the construction of local geodesic metrics, which are capable of integrating anisotropic and asymmetric edge features, implicit region-based homogeneity features and/or curvature regularization. The incorporation of the region-based homogeneity features into the metrics considered relies on an implicit representation of these features, which is one of the contributions of this work. Moreover, we also introduce a way to build simple closed contours as the concatenation of two disjoint open curves. Experimental results prove that the proposed model indeed outperforms state-of-the-art minimal paths-based image segmentation approaches. [ABSTRACT FROM AUTHOR]

The Voronoi diagram-based dual-front scheme is known as a powerful and efficient technique for addressing the image segmentation and domain partitioning problems. In the basic formulation of existing dual-front approaches, the evolving contour can be considered as the interfaces of adjacent Voronoi regions. Among these dual-front models, a crucial ingredient is regarded as the geodesic metrics by which the geodesic distances and the corresponding Voronoi diagram can be estimated. In this paper, we introduce a new dual-front model based on asymmetric quadratic metrics. These metrics considered are built by the integration of the image features and a vector field derived from the evolving contour. The use of the asymmetry enhancement can reduce the risk for the segmentation contours being stuck at false positions, especially when the initial curves are far away from the target boundaries or the images have complicated intensity distributions. Moreover, the proposed dual-front model can be applied for image segmentation in conjunction with various region-based homogeneity terms. The numerical experiments on both synthetic and real images show that the proposed dual-front model indeed achieves encouraging results. [ABSTRACT FROM AUTHOR]

The images used in various practices are often disturbed by noise, such as Gaussian noise, speckled noise, and salt and pepper noise. Images with noise are one of the challenges for segmentation, since the noise may cause inaccurate segmented results. To cope with the effect of noise on images during segmentation, a novel active contour model is proposed in this paper. The newly proposed model consists of fitting term, regularization term and penalty term. The fitting term is designed using a Gaussian kernel function and fractional order differentiation with an adaptively defined fractional order, which applies different orders to different pixels. The regularization term is applied to maintain the smoothness of curves. In order to ensure stable evolution of curves, a penalty term is added into the proposed model. Comparison experiments are conducted to show the effectiveness and efficiency of the proposed model. [ABSTRACT FROM AUTHOR]

Hybrid active contour models with the combination of region and edge information have attracted great interests in image segmentation. To the best of our knowledge, however, the theoretical foundation of these hybrid models with level set evolution is insufficient and limited. More specifically, the weighting factors of their energy terms are difficult to select and are often empirically determined without definite theoretical basis. This problem is particularly prominent in the case of multi-object segmentation when more level set functions must be computed simultaneously. To cope with these challenges, this paper proposes a new level set approach for constructing hybrid active contour models with reliable energy weights, where the weights of region and edge terms can be constrained by the optimization condition deduced from the proposed method. It can be regarded as a general approach since many existing region-based models can be easily used to construct new hybrid models using their equivalent two-phase formulations. Some representative as well as state-of-the-art models are taken as examples to demonstrate the generality of our method. The respective comparative studies validate that under the guidance of the optimization condition, segmentation accuracy, robustness, and computational efficiency can be improved compared with the original models which are used to construct the new hybrid ones. [ABSTRACT FROM AUTHOR]

The active contour models with level set evolution have been visited with a vast number of methods for image segmentation. They can be mainly classified into region-based and edge-based models, and it has been validated that the hybrid variants combining both region and edge information can improve the segmentation performance. However, to the best of our knowledge, the theoretical foundation of collaboration mechanism between the region and the edge information is limited. Specifically, most existing hybrid models are just combining all the energy terms together, resulting in great challenges of choosing an appropriate weight coefficient for each term and accommodating different modalities of imaging. To overcome these difficulties, this paper proposes a region and edge synergetic level set framework named RESLS. It provides an approach to construct new hybrid level set models using a normalized intensity indicator function that allows the region information easily embedding into the edge-based model. In this case, the energy weights of region and edge terms can be constrained by the global optimization condition deduced from the framework. Some representative as well as state-of-the-art models are taken as examples to demonstrate the generality of our method. The experiments validate that under the guidance of the optimization condition, the weighting parameter of each term can be reliably chosen. Meanwhile, the segmentation accuracy, robustness, and computational efficiency of RESLS can be improved compared with its component models. [ABSTRACT FROM AUTHOR]

This paper presents a fast and robust level set method for image segmentation. To enhance the robustness against noise, we embed a Markov random field (MRF) energy function to the conventional level set energy function. This MRF energy function builds the correlation of a pixel with its neighbors and encourages them to fall into the same region. To obtain a fast implementation of the MRF embedded level set model, we explore algebraic multigrid (AMG) and sparse field method (SFM) to increase the time step and decrease the computation domain, respectively. Both AMG and SFM can be conducted in a parallel fashion, which facilitates the processing of our method for big image databases. By comparing the proposed fast and robust level set method with the standard level set method and its popular variants on noisy synthetic images, synthetic aperture radar (SAR) images, medical images, and natural images, we comprehensively demonstrate the new method is robust against various kinds of noises. In particular, the new level set method can segment an image of size $500 \times 500$ within 3 s on MATLAB R2010b installed in a computer with 3.30-GHz CPU and 4-GB memory. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel contour-seed pairs learning-based framework for robust and automated cell/nucleus segmentation. Automated granular object segmentation in microscopy images has significant clinical importance for pathology grading of the cell carcinoma and gene expression. The focus of the past literature is dominated by either segmenting a certain type of cells/nuclei or simply splitting the clustered objects without contours inference of them. Our method addresses these issues by formulating the detection and segmentation tasks in terms of a unified regression problem, where a cascade sparse regression chain model is trained and then applied to return object locations and entire boundaries of clustered objects. In particular, we first learn a set of online convolutional features in each layer. Then, in the proposed cascade sparse regression chain, with the input from the learned features, we iteratively update the locations and clustered object boundaries until convergence. In this way, the boundary evidences of each individual object can be easily delineated and be further fed to a complete contour inference procedure optimized by the minimum description length principle. For any probe image, our method enables to analyze free-lying and overlapping cells with complex shapes. Experimental results show that the proposed method is very generic and performs well on contour inferences of various cell/nucleus types. Compared with the current segmentation techniques, our approach achieves state-of-the-art performances on four challenging datasets, i.e., the kidney renal cell carcinoma histopathology dataset, Drosophila Kc167 cellular dataset, differential interference contrast red blood cell dataset, and cervical cytology dataset. [ABSTRACT FROM AUTHOR]

Selective segmentation methods involve incorporating user input to partition an image into a foreground and background. These methods are often sensitive to some aspect of the user input in a counter intuitive manner, making their use in practice difficult. The most robust methods often involve laborious refinement on the part of the user, and sometimes editing/supervision. The proposed method reduces the burden of the user by simplifying the requirements in the input. Specifically, the fitting term does not depend on a distance function, and so no selection parameter is introduced. Instead, we consider how the user input relates to some general intensity fitting term to ensure the approach is less sensitive to the decisions or intuition of the user. We give comparisons to existing approaches to show the advantages of the new selective segmentation model. [ABSTRACT FROM AUTHOR]

Minimization of boundary curvature is a classic regularization technique for image segmentation in the presence of noisy image data. Techniques for minimizing curvature have historically been derived from gradient descent methods which could be trapped by a local minimum and, therefore, required a good initialization. Recently, combinatorial optimization techniques have overcome this barrier by providing solutions that can achieve a global optimum. However, curvature regularization methods can fail when the true object has high curvature. In these circumstances, existing methods depend on a data term to overcome the high curvature of the object. Unfortunately, the data term may be ambiguous in some images, which causes these methods also to fail. To overcome these problems, we propose a contrast driven elastica model (including curvature), which can accommodate high curvature objects and an ambiguous data model. We demonstrate that we can accurately segment extremely challenging synthetic and real images with ambiguous data discrimination, poor boundary contrast, and sharp corners. We provide a quantitative evaluation of our segmentation approach when applied to a standard image segmentation data set. [ABSTRACT FROM AUTHOR]