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Variational level set method has become a powerful tool in image segmentation due to its ability to handle complex topological changes and maintain continuity and smoothness in the process of evolution. However its evolution process can be unstable, which results in over flatted or over sharpened contours and segmentation failure. To improve the accuracy and stability of evolution, we propose a high-order level set variational segmentation method integrated with molecular beam epitaxy (MBE) equation regularization. This method uses the crystal growth in the MBE process to limit the evolution of the level set function. Thus can avoid the re-initialization in the evolution process and regulate the smoothness of the segmented curve and keep the segmentation results independent of the initial curve selection. It also works for noisy images with intensity inhomogeneity, which is a challenge in image segmentation. To solve the variational model, we derive the gradient flow and design a scalar auxiliary variable scheme, which can significantly improve the computational efficiency compared with the traditional semi-implicit and semi-explicit scheme. Numerical experiments show that the proposed method can generate smooth segmentation curves, preserve segmentation details and obtain robust segmentation results of small objects. Compared to existing level set methods, this model is state-of-the-art in both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This paper proposes an entropy-weighted local intensity clustering-based model for segmenting intensity inhomogeneous images caused by the bias field. The variational model minimizes an energy functional consisting of a regularization term of the total length of object boundaries and a data-fitting term partitioning the image. Specifically, the total length is approximated by the convolution of the heat kernel with the characteristic functions of the segmented regions of interest. The data-fitting term is derived from the multiplicative bias field resulting in a local intensity clustering property and further weighted by the local entropy. One of the most advantageous features of the proposed model is that it can simultaneously segment the image and estimate the bias field for intensity inhomogeneity correction. Moreover, a simple and efficient iterative convolution-thresholding scheme can be applied to realize the model, exhibiting the energy-decaying property. Finally, numerical simulations are carried out to validate the superior performance of the approach. [ABSTRACT FROM AUTHOR]

The paper deals with the multichannel curve segmentation of planar point clouds, scanned by a terrestrial laser scanner (TLS), which usually represent walls of buildings. Information derived from the point cloud can be used for quality check of a building (e.g. wall flatness or mutual perpendicularity of walls) or creation of virtual models of buildings. Therefore, segmentation of the planar point cloud into subsets representing the surface of the wall and other structures (e.g. door, electrical outlets) is desired. We describe a mathematical model of evolving planar curves, which is used for the segmentation of the point cloud. The evolution of curves is controlled by the properties of the scanned walls, such as colour and intensity. We discretize the model using the finite-volume method and the semi-implicit Inflow-Implicit/Outflow-Explicit (IIOE) scheme. We demonstrate the functionality of segmentation on real data. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a novel segmentation method for 4D images based on surface evolution governed by a nonlinear partial differential equation, the generalized subjective surface equation. The new method uses 4D digital image information and information from a thresholded 4D image in a local neighborhood. Thus, the 4D image segmentation is accomplished by defining the edge detector function's input as the weighted sum of the norm of gradients of presmoothed 4D image and norm of presmoothed thresholded 4D image in a local neighborhood. Additionally, we design and study a numerical method based on the finite volume approach for solving the new model. The reduced diamond cell approach is used for approximating the gradient of the solution. We use a semi-implicit finite volume scheme for the numerical discretization and show that our numerical scheme is unconditionally stable. The new 4D method was tested on artificial data and applied to real data representing 3D+time microscopy images of cell nuclei within the zebrafish pectoral fin and hind-brain. In a real application, processing 3D+time microscopy images amounts to solving a linear system with several billion unknowns and requires over 1000 GB of memory; thus, it may not be possible to process these images on a serial machine without parallel implementation utilizing the MPI. Consequently, we develop and present in the paper OpenMP and MPI parallel implementation of designed algorithms. Finally, we include cell tracking results to show how our new method serves as a basis for finding trajectories of cells during embryogenesis. [ABSTRACT FROM AUTHOR]

Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image segmentation is the process of dividing an image into non-overlapping regions. These regions, which may correspond, e.g., to different objects, are fundamental for the correct interpretation and classification of the scene represented by the image. The division into regions is not unique, but it depends on the application, i.e., it must be driven by the final goal of the segmentation and hence by the most significant features with respect to that goal. Thus, image segmentation can be regarded as a strongly ill-posed problem. A classical approach to deal with ill posedness consists in incorporating in the model a-priori information about the solution, e.g., in the form of penalty terms. In this work we provide a brief overview of basic computational models for image segmentation, focusing on edge-based and region-based variational models, as well as on statistical and machine-learning approaches. We also sketch numerical methods that are applied in computing solutions to these models. In our opinion, our view can help the readers identify suitable classes of methods for solving their specific problems. [ABSTRACT FROM AUTHOR]

Assignment flows denote a class of dynamical models for contextual data labelling (classification) on graphs. We derive a novel parametrisation of assignment flows that reveals how the underlying information geometry induces two processes for assignment regularisation and for gradually enforcing unambiguous decisions, respectively, that seamlessly interact when solving for the flow. Our result enables to characterise the dominant part of the assignment flow as a Riemannian gradient flow with respect to the underlying information geometry. We consider a continuous-domain formulation of the corresponding potential and develop a novel algorithm in terms of solving a sequence of linear elliptic partial differential equations (PDEs) subject to a simple convex constraint. Our result provides a basis for addressing learning problems by controlling such PDEs in future work. [ABSTRACT FROM AUTHOR]

Signals and images with discontinuities appear in many problems in such diverse areas as biology, medicine, mechanics and electrical engineering. The concrete data are often discrete, indirect and noisy measurements of some quantities describing the signal under consideration. A frequent task is to find the segments of the signal or image which corresponds to finding the discontinuities or jumps in the data. Methods based on minimizing the piecewise constant Mumford–Shah functional—whose discretized version is known as Potts energy—are advantageous in this scenario, in particular, in connection with segmentation. However, due to their non-convexity, minimization of such energies is challenging. In this paper, we propose a new iterative minimization strategy for the multivariate Potts energy dealing with indirect, noisy measurements. We provide a convergence analysis and underpin our findings with numerical experiments. [ABSTRACT FROM AUTHOR]

One important task in image segmentation is to find a region of interest, which is, in general, a solution of a nonlinear and nonconvex problem. The authors of Chan and Esedoglu (Aspects of total variation regularized L 1 function approximation. SIAM J. Appl. Math. 2005;65:1817–1837) proposed a convex T V − L 1 problem for finding such a region Σ and proved that when a binary input f is given, a solution u ∗ to the convex problem gives rise to other solutions 1 { u ∗ ≥ μ } for a.e. μ ∈ (0 , 1) from which they raised a question of whether or not u ∗ must be binary. The same is to ask if the two-phase Mumford–Shah model in image processing has a unique solution with a binary input. In this paper, we will discuss how to construct a non-binary solution that provides a negative answer to the question through a connection of two ideas, one from the two-phase Mumford–Shah model in image segmentation and the other from mean curvature motions discussed in some geometric problems (e.g. Alter, Caselles, Chambolle. A characterization of convex calibrable sets in R N . Math. Ann. 2005;322:329–366; Chambolle. An algorithm for mean curvature motion. Interfaces Free Boundaries 2004;6:195–218) revealing the nature of non-uniqueness in image segmentation. [ABSTRACT FROM AUTHOR]

Histopathological lung cancer segmentation using region of interest is one of the emerging research area in the field of health monitoring system. In this paper, the histopathological images were collected from the database Stanford Tissue Microarray Database (TMAD). After image collection, pre-processing was performed using a normalization technique, which enhances the quality of the histopathological image by eliminating unwanted noise. After pre-processing, segmentation was carried out using the modified kernel-based fuzzy c-means clustering (KFCM) approach along with the edge bridge and fill technique (EBFT). It was a flexible high-level machine learning technique to localize the object in a complex template. The experimental result shows that the proposed approach segments the normal and abnormal cancer regions by means of precision, recall, specificity, accuracy, and Jaccard coefficient. The proposed methodology improved the classification accuracy in lung cancer segmentation up to 2.5–5% compared to the existing methods deep convolutional neural network (DCNN) and diffusion-weighted approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel model for image segmentation by using the Cahn–Hilliard equation. An interesting feature of this model lies in its ability of interpolating missing contours along wide gaps in order to form meaningful object boundaries, which is often achieved by curvature dependent models in the literature. To solve the associated equation, we employ a recently developed technique, that is, the tailored-finite-point method, which helps preserve sharp jumps and thus helps locate segmentation contours more exactly. Numerical experiments are presented to demonstrate the effectiveness of the proposed model and its features. In addition, analytical results on the existence and uniqueness of the associated equation are also provided. [ABSTRACT FROM AUTHOR]

Tensor is a multi-way representation of an entity that is widely used in many applications of mathematics and physics. The wide range of tensor algebra operations attract the researchers of graphical and vision field to identify unique methods for various applications such as segmentation, compression, indexing and so on. In this paper, low multi-linear rank approximation of a tensor is used for decomposition so as to perform compression on a video that is represented as a 4D tensor. Thus, the encoder has blocks for (1) multilinear rank approximation method so as to aid decomposition, (2) sparsity removal of residual data to reduce the required memory storage to a small level, (3) quantization on the sparse less residual data and (4) LZ77 dictionary coding for the video. The decoder uses a tensor reconstruction block along with residual error correction block that reduces loss/error in the reconstructed video. The size of core tensor is an important factor in rank approximation. It is identified at run time depending on the video contents. This size is determined adaptively using Tikhonov’s regularization method. The best value of core tensor size is identified with the corner of L-curve which preserves the video contents from heavy loss/error. Experimental results of the proposed work on comparison with H.264/AVC compression method indicate that the proposed method achieves up to 10% improvement in compression ratio with the least amount of loss and a maximum signal to noise ratio of 0.14. The proposed system gives better compression ratio than H.265 for videos with more number of frames without compromising quality. [ABSTRACT FROM AUTHOR]

This article introduces a new normalized nonlocal hybrid level set method for image segmentation. Due to intensity overlapping, blurred edges with complex backgrounds, simple intensity and texture information, such kind of image segmentation is still a challenging task. The proposed method uses both the region and boundary information to achieve accurate segmentation results. The region information can help to identify rough region of interest and prevent the boundary leakage problem. It makes use of normalized nonlocal comparisons between pairs of patches in each region, and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation. The boundary information can help to detect the precise location of the target object, it makes use of the geodesic active contour model to obtain the target boundary. The corresponding variational segmentation problem is implemented by a level set formulation. We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function. At last, experimental results on synthetic images and real images are shown in the paper with promising results. [ABSTRACT FROM AUTHOR]

Image segmentation is a key and fundamental problem in image processing, computer graphics, and computer vision. Level set based method for image segmentation is used widely for its topology flexibility and proper mathematical formulation. However, poor performance of existing level set models on noisy images and weak boundary limit its application in image segmentation. In this paper, we present a region consistency constraint term to measure the regional consistency on both sides of the boundary, this term defines the boundary of the image within a range, and hence increases the stability of the level set model. The term can make existing level set models significantly improve the efficiency of the algorithms on segmenting images with noise and weak boundary. Furthermore, this constraint term can make edge-based level set model overcome the defect of sensitivity to the initial contour. The experimental results show that our algorithm is efficient for image segmentation and outperform the existing state-of-art methods regarding images with noise and weak boundary. [ABSTRACT FROM AUTHOR]

Decomposing multidimensional signals, such as images, into spatially compact, potentially overlapping modes of essentially wavelike nature makes these components accessible for further downstream analysis. This decomposition enables space-frequency analysis, demodulation, estimation of local orientation, edge and corner detection, texture analysis, denoising, inpainting, or curvature estimation. Our model decomposes the input signal into modes with narrow Fourier bandwidth; to cope with sharp region boundaries, incompatible with narrow bandwidth, we introduce binary support functions that act as masks on the narrow-band mode for image recomposition. $$L^1$$ and TV terms promote sparsity and spatial compactness. Constraining the support functions to partitions of the signal domain, we effectively get an image segmentation model based on spectral homogeneity. By coupling several submodes together with a single support function, we are able to decompose an image into several crystal grains. Our efficient algorithm is based on variable splitting and alternate direction optimization; we employ Merriman-Bence-Osher-like threshold dynamics to handle efficiently the motion by mean curvature of the support function boundaries under the sparsity promoting terms. The versatility and effectiveness of our proposed model is demonstrated on a broad variety of example images from different modalities. These demonstrations include the decomposition of images into overlapping modes with smooth or sharp boundaries, segmentation of images of crystal grains, and inpainting of damaged image regions through artifact detection. [ABSTRACT FROM AUTHOR]

In this paper, a novel active contours method, which combines with the Student's-t mixture model via Expectaton-Maximizaton (EM) algorithm, is proposed to segment complicated two-phase images. Firstly, we rewrite the cost function and derive a novel updating of level set function based on probabilistic principles. Secondly, we put forward two novel geometric priors from the level-set-based curve evolution; and both of them have advantages, the suitable one is selected by personalized need to obtain level set function in EM framework with the aim of reducing the computational cost. Therefore, the level set function is derived from latent variables and served as a feedback to the estimation of the latent variables in next iteration. Finally, in order to enhance the robustness to the outliers, Student's-t mixture model with heavy tail has been applied in our algorithm. Experimental results obtained by employing the proposed method on many synthetic, medical and real-world images to demonstrate its robustness, accuracy and effectiveness. [ABSTRACT FROM AUTHOR]

Volume constrained image segmentation aims at improving the quality of image reconstruction via incorporating physical information for the underline object of interest into the mathematical modeling of the segmentation problem. In this paper, we develop a general framework for 3D 2-phase image segmentation, based on constrained ℓ 2 minimization of a non-local regularizer, the Euler–Lagrange derivative of which is the discrete graph-Laplacian of a weighted graph, associated with the image voxels. It involves a convenient change of basis in the image domain, for which the optimization function is decomposed element-wise. Using univariate polynomial approximation techniques, we show that the transformation matrix does not need to be explicitly computed and its action is well approximated by a suitable matrix polynomial. The error is independent of the domain size, thus our approach is applicable to high resolution data. The model allows for adding arbitrary linear terms into the optimization function in order to increase the control on the output, in particular to add its scalar product with another, already known, segmentation vector. Such a “hybrid” process may significantly improve on the individual quality of each of the involved segmentations. [ABSTRACT FROM AUTHOR]

In this paper, a novel and robust rotation and scale invariant structuring elements based descriptor (RSSED) for pedestrian classification in infrared (IR) images is proposed. In addition, a segmentation method using difference of Gaussian (DoG) and horizontal intensity projection is proposed. The three major steps are moving object segmentation, feature extraction and classification of objects as pedestrian or non-pedestrian. The segmentation result is used to extract the RSSED feature descriptor. To extract features, the segmentation result is encoded using local directional pattern (LDP). This helps in the identification of local textural patterns. The LDP encoded image is further quantized adaptively to four levels. Finally the proposed RSSED is used to formalize the descriptor from the quantized image. Support vector machine is employed for classification of the moving objects in a given IR image into pedestrian and non-pedestrian classes. The segmentation results shows the robustness in extracting the moving objects. The classification results obtained from SVM classifier shows the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

An abdominal aortic aneurysm (AAA) is a pathological dilation of the abdominal aorta that may lead to a rupture with fatal consequences. Endovascular aneurysm repair (EVAR) is a minimally invasive surgical procedure consisting of the deployment and fixation of a stent–graft that isolates the damaged vessel wall from blood circulation. The technique requires adequate endovascular device sizing, which may be performed by vascular analysis and quantification on Computerized Tomography Angiography (CTA) scans. This paper presents a novel 3D CTA image-based software for AAA inspection and EVAR sizing, eVida Vascular , which allows fast and accurate 3D endograft sizing for standard and fenestrated endografts. We provide a description of the system and its innovations, including the underlying vascular image analysis and visualization technology, functional modules and user interaction. Furthermore, an experimental validation of the tool is described, assessing the degree of agreement with a commercial, clinically validated software, when comparing measurements obtained for standard endograft sizing in a group of 14 patients. [ABSTRACT FROM AUTHOR]

Some problems in image analysis require considering an order on space partitions: in image filtering the partition of image zones must grow, while in image segmentation one maximizes the partition into image objects. In the classical refinement order, the growth of a partition is achieved through the merging of blocks. We generalize this operation into block apportioning: some blocks in a partial partition may be split, and their parts are merged with some remaining blocks; this includes the possibility of a block being merged with another without being split. We study this operation in detail; we obtain then the apportioning order, which extends the refinement order. For partial partitions, the standard order combines the merging of blocks with the growth of existing blocks and the creation of new blocks. Combining these operations with block apportioning leads to the apportioning-inflating and extended orders; the latter contains the standard order. Our analysis rests on a study of Serra's building order on partial partitions, which intervenes in the above new orders. Except the building order, all these orders are graded, with a compound grading for the apportioning-inflating and extended orders; this gives the number of elementary operations involved in a growth of a partial partition. [ABSTRACT FROM AUTHOR]

We investigate the application of the nonmonotone spectral projected gradient (SPG) method to a region-based variational model for image segmentation. We consider a 'discretize-then-optimize' approach and solve the resulting nonlinear optimization problem by an alternating minimization procedure that exploits the SPG2 algorithm by Birgin et al. (SIAM J Optim 10(4):1196-1211, ). We provide a convergence analysis and perform numerical experiments on several images, showing the effectiveness of this procedure. [ABSTRACT FROM AUTHOR]

The automatization of the analysis of Indirect Immunofluorescence (IIF) images is of paramount importance for the diagnosis of autoimmune diseases. This paper proposes a solution to one of the most challenging steps of this process, the segmentation of HEp-2 cells, through an adaptive marker-controlled watershed approach. Our algorithm automatically conforms the marker selection pipeline to the peculiar characteristics of the input image, hence it is able to cope with different fluorescent intensities and staining patterns without any a priori knowledge. Furthermore, it shows a reduced sensitivity to over-segmentation errors and uneven illumination, that are typical issues of IIF imaging. [ABSTRACT FROM AUTHOR]

Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective. [ABSTRACT FROM AUTHOR]

Extraction of lane markings is still a challenge due to the poor quality of lane markings and interferences from external circumstances. In this paper, we utilize line segments as low-level features to detect lane markings on structured road scenes. Our novel algorithm can be highlighted in four items as follows. Firstly, a road surface region is reasonably located using adaptive segmentation method, and then most of the interferences from the external circumstances are eliminated by Laplacian filter. Secondly, the line segments detected by the line segment detector are applied to represent the structural information of lanes. Thirdly, non-lane candidate markings are removed through orientation and vanishing point constraints. Finally, the lanes are accurately extracted from the remaining candidate lane marking. Experimental results on complex structured road scenarios in urban streets are shown and the effectiveness and robustness of our novel algorithm are underpinned by the experimental results. [ABSTRACT FROM PUBLISHER]

In this work, we provide a novel variational level-set based object contour tracking approach. Thus, a mathematically rigorous variant of the Chan-Vese algorithm for image segmentation via geometric active contour model is proposed here. With respect to the original contour detection algorithm, the level set function ϕ(t) defining the evolving contourSt = {x; ϕ(t,x) = 0} is iteratively computed from a nonlinear parabolic boundary value problem that is well posed in the space of functions with bounded variations. We provide a robust mathematical justification of the proposed level-set model. [ABSTRACT FROM PUBLISHER]

Total variation (TV) minimization-based nonlinear models have been proven to be very useful and successful in image processing. A lot of effort has been devoted to overcome the nonlinearity of the model and at the same time to obtain fast numerical schemes. In this paper, we propose a restarted iterative homotopy analysis method (HAM) to improve the computational efficiency for the TV models and will show by experiments that this method demonstrates great potential for recovering the noise and with great speed in both image denoising and image segmentation models. The method modifies the existing HAM and makes it suitable to potentially solve other nonlinear partial differential equations arising from image processing models. In our examples, we will demonstrate the validity of a restarted HAM and that this method is efficient and robust even for images with large ratios of noise and with much less CPU time than other methods. [ABSTRACT FROM AUTHOR]

Ear is a relatively new biometric among others. Many methods have been used for ear recognition to improve the performance of ear recognition systems. In continuation of these efforts, we propose a new ear recognition method based on curvelet transform. Features of the ear are computed by applying Fast Discrete Curvelet Transform via the wrapping technique. Feature vector of each image is composed of an approximate curvelet coefficient and second coarsest level curvelet coefficients at eight different angles. k-NN (k-nearest neighbour) is utilized as a classifier. The proposed method is experimented on two ear databases from IIT Delhi. Results achieved using the proposed method on publicly available ear database are up to 97.77% which show encouraging performance. [ABSTRACT FROM AUTHOR]

Variational image-processing models offer high-quality processing capabilities for imaging. They have been widely developed and used in the last two decades, enriching the fields of mathematics as well as information science. Mathematically, several tools are needed: energy optimization, regularization, partial differential equations, level set functions, and numerical algorithms. This special issue presents readers with nine excellent research papers covering topics from research work intovariational image-processing models, algorithms and applications, including image denoising, image deblurring, image segmentation, image reconstruction, restoration of mixed noise types and three-dimensional surface restoration. [ABSTRACT FROM PUBLISHER]

We propose a novel geodesic-active-contour-based (GAC-based) variational model that uses two level-set functions to segment the right and left ventricles and the epicardium in short-axis magnetic resonance (MR) images. For the right ventricle, the myocardial wall is typically very thin and hard to identify using the resolution of existing MR scanners. We propose to use two level sets to identify both the endocardial wall by pushing away one level-set function from another, in the setting of the edge-driven GAC model with a new edge detection function. Existing edge detection functions have strict restrictions on the location of initial contours. We develop a new edge detection function that relaxes this restriction and propose an iterative method that uses a sequence of edge detection functions to minimize the energy of our model successively. Experimental results are presented to validate the effectiveness of the proposed model. [ABSTRACT FROM PUBLISHER]

We transpose an optimal control technique to the image segmentation problem. The idea is to consider image segmentation as a parameter estimation problem. The parameter to estimate is the colour of the pixels of the image. We use the adaptive parameterization technique which builds iteratively an optimal representation of the parameter into uniform regions that form a partition of the domain, hence corresponding to a segmentation of the image. We minimize an error function during the iterations, and the partition of the image into regions is optimally driven by the gradient of this error. The resulting segmentation algorithm inherits desirable properties from its optimal control origin: soundness, robustness and flexibility. [ABSTRACT FROM AUTHOR]