In this paper, we propose a PDE-based level set method. Traditionally, interfaces are represented by the zero level set of continuous level set functions. Instead, we let the interfaces be ...represented by discontinuities of piecewise constant level set functions. Each level set function can at convergence only take two values, i.e., it can only be 1 or -1; thus, our method is related to phase-field methods. Some of the properties of standard level set methods are preserved in the proposed method, while others are not. Using this new method for interface problems, we need to minimize a smooth convex functional under a quadratic constraint. The level set functions are discontinuous at convergence, but the minimization functional is smooth. We show numerical results using the method for segmentation of digital images.
Deep Convolutional Neural Networks (DCNNs) can well extract the features from natural images. However, the classification functions in the existing network architecture of CNNs are simple and lack ...capabilities to handle important spatial information as have been done by many well-known traditional variational image segmentation models. Priors such as spatial regularization, volume prior and shapes priors cannot be handled by existing DCNNs. We propose a novel Soft Threshold Dynamics (STD) framework which can integrate many spatial priors of the classic variational models into the DCNNs for image segmentation. The novelty of our method is to interpret the softmax activation function as a dual variable in a variational problem, and thus many spatial priors can be imposed in the dual space. From this viewpoint, we can build a STD based framework which can enable the outputs of DCNNs to have many special priors such as spatial regularization, volume preservation and star-shape prior. The proposed method is a general mathematical framework and it can be applied to any image segmentation DCNNs with a softmax classification layer. To show the efficiency of our method, we applied it to the popular DeepLabV3+ image segmentation network, and the experiments results show that our method can work efficiently on data-driven image segmentation DCNNs.
In this paper, we propose an image segmentation model that incorporates convexity shape priori using level set representations. In the past decade, several discrete and continuous methods have been ...developed to solve this problem. Our method comes from the observation that the signed distance function of a convex region must be a convex function. Based on this observation, we transfer the complicated geometrical convexity shape priori into some simple constraints on the signed distance function. We propose a simple algorithm to keep these constraints exactly. The proposed method could be easily applied to level set based segmentation models, such as the well-known Chan-Vese mode and the active contour models. By setting some good initial curves, the proposed method can easily segment convex objects from images with complicated background. We demonstrate the performance of the proposed methods on both synthetic images and real images, as well as the comparison to some state-of-the-art methods.
This paper proposes a general weighted l 2 - l 0 norms energy minimization model to remove mixed noise such as Gaussian-Gaussian mixture, impulse noise, and Gaussian-impulse noise from the images. ...The approach is built upon maximum likelihood estimation framework and sparse representations over a trained dictionary. Rather than optimizing the likelihood functional derived from a mixture distribution, we present a new weighting data fidelity function, which has the same minimizer as the original likelihood functional but is much easier to optimize. The weighting function in the model can be determined by the algorithm itself, and it plays a role of noise detection in terms of the different estimated noise parameters. By incorporating the sparse regularization of small image patches, the proposed method can efficiently remove a variety of mixed or single noise while preserving the image textures well. In addition, a modified K-SVD algorithm is designed to address the weighted rank-one approximation. The experimental results demonstrate its better performance compared with some existing methods.
In this paper, we propose an interactive color natural image segmentation method. The method integrates color feature with multiscale nonlinear structure tensor texture (MSNST) feature and then uses ...GrabCut method to obtain the segmentations. The MSNST feature is used to describe the texture feature of an image and integrated into GrabCut framework to overcome the problem of the scale difference of textured images. In addition, we extend the Gaussian Mixture Model (GMM) to MSNST feature and GMM based on MSNST is constructed to describe the energy function so that the texture feature can be suitably integrated into GrabCut framework and fused with the color feature to achieve the more superior image segmentation performance than the original GrabCut method. For easier implementation and more efficient computation, the symmetric KL divergence is chosen to produce the estimates of the tensor statistics instead of the Riemannian structure of the space of tensor. The Conjugate norm was employed using Locality Preserving Projections (LPP) technique as the distance measure in the color space for more discriminating power. An adaptive fusing strategy is presented to effectively adjust the mixing factor so that the color and MSNST texture features are efficiently integrated to achieve more robust segmentation performance. Last, an iteration convergence criterion is proposed to reduce the time of the iteration of GrabCut algorithm dramatically with satisfied segmentation accuracy. Experiments using synthesis texture images and real natural scene images demonstrate the superior performance of our proposed method.
In practice, the objects of interest have some shape priors, which would be destroyed by occlusions, distortions and noises. Therefore, the characterization of the shape priors attracts increasing ...attention. This paper is devoted to characterization of convexity prior and its applications in objects segmentation in two-dimensional (2D) spaces using level set function. The shape convexity can be characterized by the Laplacian nonnegativity of the associated signed distance function on the whole image domain, zero-sublevel set and zero-superlevel set. This result is extended to characterization for multiple convex objects and ring shape object with outer, inner and both convex boundaries. One of the advantages of this method is that only one signed distance function is needed to characterize a single object, multiple objects and ring shape with boundary(ies) convexity prior. The characterization methods are incorporated into image segmentation model. In addition, some labels on the foreground and background and landmarks on the boundary of the object(s) can be taken into account as constraints to improve the accuracy of segmentation. A general and efficient numerical framework is developed to solve the proposed models using alternative direction method. Experiments on various images validated the effectiveness and efficiency of the proposed models and algorithms.
PDE Based Algorithms for Smooth Watersheds Hodneland, Erlend; Xue-Cheng Tai; Kalisch, Henrik
IEEE transactions on medical imaging,
2016-April, 2016-Apr, 2016-4-00, 20160401, Letnik:
35, Številka:
4
Journal Article
Odprti dostop
Watershed segmentation is useful for a number of image segmentation problems with a wide range of practical applications. Traditionally, the tracking of the immersion front is done by applying a fast ...sorting algorithm. In this work, we explore a continuous approach based on a geometric description of the immersion front which gives rise to a partial differential equation. The main advantage of using a partial differential equation to track the immersion front is that the method becomes versatile and may easily be stabilized by introducing regularization terms. Coupling the geometric approach with a proper "merging strategy" creates a robust algorithm which minimizes over- and under-segmentation even without predefined markers. Since reliable markers defined prior to segmentation can be difficult to construct automatically for various reasons, being able to treat marker-free situations is a major advantage of the proposed method over earlier watershed formulations. The motivation for the methods developed in this paper is taken from high-throughput screening of cells. A fully automated segmentation of single cells enables the extraction of cell properties from large data sets, which can provide substantial insight into a biological model system. Applying smoothing to the boundaries can improve the accuracy in many image analysis tasks requiring a precise delineation of the plasma membrane of the cell. The proposed segmentation method is applied to real images containing fluorescently labeled cells, and the experimental results show that our implementation is robust and reliable for a variety of challenging segmentation tasks.
We introduce a new method for image smoothing based on a fourth-order PDE model. The method is tested on a broad range of real medical magnetic resonance images, both in space and time, as well as on ...nonmedical synthesized test images. Our algorithm demonstrates good noise suppression without destruction of important anatomical or functional detail, even at poor signal-to-noise ratio. We have also compared our method with related PDE models.
We propose and study novel max-flow models in the continuous setting, which directly map the discrete graph-based max-flow problem to its continuous optimization formulation. We show such a ...continuous max-flow model leads to an equivalent min-cut problem in a natural way, as the corresponding dual model. In this regard, we revisit basic conceptions used in discrete max-flow / min-cut models and give their new explanations from a variational perspective. We also propose corresponding continuous max-flow and min-cut models constrained by priori supervised information and apply them to interactive image segmentation/labeling problems. We prove that the proposed continuous max-flow and min-cut models, with or without supervised constraints, give rise to a series of global binary solutions λ*(x) ϵ {0,1}, which globally solves the original nonconvex image partitioning problems. In addition, we propose novel and reliable multiplier-based max-flow algorithms. Their convergence is guaranteed by classical optimization theories. Experiments on image segmentation, unsupervised and supervised, validate the effectiveness of the discussed continuous max-flow and min-cut models and suggested max-flow based algorithms.
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