Shah Model Research Articles

Segmentation in Measure Spaces

We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most well-studied variational models in image processing: the Rudin–Osher–Fatemi model for image denoising (ROF) and the Mumford–Shah model for image segmentation (MS). We show the linkage between the ROF model and the two phases piecewise constant case of MS in perimeter measure spaces. We show applications of our results to nonlocal image segmentation, via discrete weighted graphs, and to multiclass classification on high dimensional spaces.

Multilevel thresholding image segmentation algorithm based on Mumford–Shah model

Abstract Image segmentation is one of the important tasks of computer vision and computer image processing, and the purpose of image segmentation is to achieve the extraction and recognition of the target image region. The classical Mumford–Shah (MSh) image segmentation model is used to achieve the segmentation of images. With the goal to get the best segmentation effect on images by minimizing the MSh energy generalization function, a level set strategy is developed, and a model with global information infinite curve evolution is utilized. However, considering the low efficiency of this model for processing level set curves and the general quality of image segmentation. A multi-layer threshold search scheme is proposed to achieve rapid convergence of the target image level set curve. The experimental results showed that the multi-level thresholding image segmentation algorithm based on the MSh model can significantly improve the segmentation effect of images and reduce the segmentation time. The suggested MSK method outperforms the MPO algorithm, SSA algorithm, and EMO algorithm in the picture segmentation convergence time test, respectively, in terms of runtime efficiency by 356, 289, and 71%. Additionally, it performs superbly in both threshold searches and picture quality tests. The research topic has significant reference value for the study of contemporary computer vision imaging technologies.

Further development and verification of the model for evaporation from pools

The author’s model for evaporation from water pools is further developed and verified. Further development includes the determination of wind velocity in application to outdoor pools. A value for this height at which wind velocity is to be determined is proposed and verified through analysis of test data. Furthermore, a method for calculating the velocity at this height from measurements at other heights is proposed and verified by analysis of test data. The air velocity above indoor pools is discussed and recommendations are made for the velocity to be used in calculations. The model is further verified with new data that include those for an outdoor swimming pool (there were none before) and data for air at temperatures up to 269 °C, with the maximum temperature in previous data analysis being 200 °C. All data were also compared to 20 other prediction methods. The Shah model had a mean absolute deviation of 15.9% for 537 data points from 29 sources. All others had much larger deviations.

Feature-preserving Mumford–Shah mesh processing via nonsmooth nonconvex regularization

Motivated by the success in image processing, the Mumford–Shah functional has attracted extensive attentions in geometry processing. Existing methods, mainly focusing on discretizations on the triangulated mesh, either over-smooth sharp features or are sensitive to noises or outliers. In this paper, we first introduce a nonsmooth nonconvex Mumford–Shah model for a feature-preserving filtering of face normal field to ameliorate the staircasing artifacts that appear in the original Mumford–Shah total variation (MSTV) and develop an alternating minimization scheme based on alternating direction method of multipliers to realize the proposed model. After restoring the face normal field, vertex updating is then employed by incorporating the oriented normal constraints and discontinuities to achieve a detail-preserving reconstruction of mesh geometry. Extensive experimental results demonstrate the effectiveness of the above shape optimization routine for various geometry processing applications such as mesh denoising, mesh inpainting and mesh segmentation.

K-Means image segmentation using Mumford–Shah model

k-Means (KM) is well known for its ease of implementation as a clustering technique. It has been applied for color quantization in RGB, YUV, hyperspectral image, Lab, and other spaces, but this leads to fragmented segments as the pixels are clustered only in the color space without considering connectivity. The problem has been attacked by adding connectivity constraints, or using joint color and spatial features (r, g, b, x, y), which prevent fragmented and nonconvex segments. However, it does not take into account the complexity of the shape itself. The Mumford–Shah model has been earlier used to overcome this problem but with slow and complex mathematical optimization algorithms. We integrate Mumford–Shah model directly into KM context and construct a fast and simple implementation of the algorithm. The proposed approach uses standard KM algorithm with distance function derived from Mumford–Shah model so that it optimizes both the content and the shape of the segments jointly. We demonstrate by experiments that the proposed algorithm provides better results than comparative methods when compared using various error evaluation criteria. The algorithm is applied on 100 images in the Weizmann dataset and two remote sensing images.

On a Variational and Convex Model of the Blake-Zisserman Type for Segmentation of Low-Contrast and Piecewise Smooth Images.

This paper proposes a new variational model for segmentation of low-contrast and piecewise smooth images. The model is motivated by the two-stage image segmentation work of Cai–Chan–Zeng (2013) for the Mumford–Shah model. To deal with low-contrast images more effectively, especially in treating higher-order discontinuities, we follow the idea of the Blake–Zisserman model instead of the Mumford–Shah. Two practical ideas are introduced here: first, a convex relaxation idea is used to derive an implementable formulation, and second, a game reformulation is proposed to reduce the strong dependence of coupling parameters. The proposed model is then analysed for existence and further solved by an ADMM solver. Numerical experiments can show that the new model outperforms the current state-of-the-art models for some challenging and low-contrast images.

Unsupervised Object Segmentation Based on Bi-Partitioning Image Model Integrated with Classification

The development of convolutional neural networks for deep learning has significantly contributed to image classification and segmentation areas. For high performance in supervised image segmentation, we need many ground-truth data. However, high costs are required to make these data, so unsupervised manners are actively being studied. The Mumford–Shah and Chan–Vese models are well-known unsupervised image segmentation models. However, the Mumford–Shah model and the Chan–Vese model cannot separate the foreground and background of the image because they are based on pixel intensities. In this paper, we propose a weakly supervised model for image segmentation based on the segmentation models (Mumford–Shah model and Chan–Vese model) and classification. The segmentation model (i.e., Mumford–Shah model or Chan–Vese model) is to find a base image mask for classification, and the classification network uses the mask from the segmentation models. With the classifcation network, the output mask of the segmentation model changes in the direction of increasing the performance of the classification network. In addition, the mask can distinguish the foreground and background of images naturally. Our experiment shows that our segmentation model, integrated with a classifier, can segment the input image to the foreground and the background only with the image’s class label, which is the image-level label.

Uncertainty Quantification in Image Segmentation Using the Ambrosio\u2013Tortorelli Approximation of the Mumford\u2013Shah Energy

The quantification of uncertainties in image segmentation based on the Mumford–Shah model is studied. The aim is to address the error propagation of noise and other error types in the original image to the restoration result and especially the reconstructed edges (sharp image contrasts). Analytically, we rely on the Ambrosio–Tortorelli approximation and discuss the existence of measurable selections of its solutions as well as sampling-based methods and the limitations of other popular methods. Numerical examples illustrate the theoretical findings.

Bed-to-tube heat transfer characteristics with an immersed horizontal tube in the pressurized fluidized bed at high temperature

High-temperature and high-pressure conditions have great effects on the heat transfer characteristics of the immersed horizontal tube and understanding them will provide an industrial reference for the arrangement and optimization of heat exchanger in the pressurized fluidized bed furnace. In this study, the pressurized fluidized bed apparatus was developed to investigate the effects of factors such as pressure, temperature, particle size and gas velocity on the local and average heat transfer coefficients of the immersed horizontal tube. The experimental results showed the improved heat transfer at elevated pressure and high temperature. When the bed temperature increased from 400 °C to 800 °C, the proportion of the radiative heat transfer increased significantly, but it did not exceed 15%. The maximum heat transfer coefficients in the process of increasing the fluidization number were also measured in this study and fit well with the prediction results of the Shah model. The distribution of circumferential local heat transfer coefficients showed differences at low fluidization numbers and high fluidization numbers. The model proposed for the immersed horizontal tubes in the pressurized fluidized bed predicted the experimental data points from this study and other different sources well with the absolute average deviation of 11.86%.

Comparison of various zero‐dimensional models to analyze the brachial artery blood flow of an arterio‐venous fistula during hemodialysis procedure

AbstractOne of the most recommended vascular accesses for hemodialysis is an autogenous arterio‐venous fistula (AVF), which is a surgically created conduit between an artery and a vein. AVFs can be compromised by stenosis‐induced arterial or venous thrombosis. An effective and efficient mathematical fluid mechanical model can provide insight into the mechanisms for stenosis and thrombosis. In an earlier paper, a laminar entry flow model (Shah) was applied to a fifth order lumped parameter zero dimensional (0D) model to predict the inlet flow rate in the brachial artery of an AVF. ODE45, a built in MATLAB ordinary differential equation (ODE) solver, was used to produce the solution. The Shah model showed closer correlation with a computational fluid dynamics model, performed in COMSOL, than did the Poiseuille flow model. In this study, an outlet flow rate in the brachial artery of an AVF is generated with third, fourth, and fifth order lumped parameter zero dimensional models with laminar and turbulent flow conditions within different arterial segments. Butcher's sixth order Runge‐Kutta (RK) method was used as an ODE solver and the results were compared with the MATLAB ODE solvers (ODE45 and ODE113). The lumped parameter model solved with Butcher's sixth order RK method generated less oscillation with a more stable and consistent outlet flow rate in comparison to the other solvers. Brachial artery blood flow, modeled with Shah's entry flow equation in the inlet segment and Blasius turbulent equation modeled at the outlet segment prior to the beginning of the anastomosis, generated an average outlet flow rate similar to that of clinical data. The dependence of brachial artery on the flow equations indicates the importance of wisely selecting flow resistance models and the effect of blood pressure and peripheral resistance on fistula maturation. The average and peak flow rate also depended on the ODE solver. Third and fourth order lumped parameter models generated results similar to the fifth order model only at normal peripheral resistance. Therefore, this study can help to understand the AVF performance in vitro and guide the application of an appropriate lumped parameter model for blood flow prediction.

Two-stage image segmentation based on nonconvex [formula omitted] approximation and thresholding

Image segmentation is of great importance in image processing. In this paper, we propose a two-stage image segmentation strategy based on the nonconvex ℓ2−ℓp approximation of the Mumford–Shah (MS) model, where we use the nonconvex ℓp (0<p<1) regularizer to approximate the Hausdorff measure and to extract more boundary information. In the first stage, we solve the nonconvex variant of the MS model efficiently via the split-Bregman algorithm. Moreover, we use a closed-form p-shrinkage operator to deal with the ℓp quasi-norm subproblem, which is easy to implement. The second stage is segmenting the u obtained in the first stage into different phases with thresholds determined by the K-means clustering method. We compare our method with several state-of-the-art methods both qualitatively and quantitatively to demonstrate the effectiveness and advantages of our strategy.

Automation of hemocompatibility analysis using image segmentation and supervised classification

The hemocompatibility of blood-contacting medical devices remains one of the major challenges in biomedical engineering and makes research in the field of new and improved materials inevitable. However, current in-vitro test and analysis methods are still lacking standardization and comparability, which impedes advances in material design. For example, the optical platelet analysis of material in-vitro hemocompatibility tests is carried out manually or semi-manually by each research group individually.As a step towards standardization, this paper proposes an automation approach for the optical platelet count and analysis. To this end, fluorescence images are segmented using Zach’s convexification of the multiphase-phase piecewise constant Mumford–Shah model. The non-background components then need to be classified as platelet or no platelet. For this purpose, a supervised random forest is applied to feature vectors derived from the components using features like area, perimeter and circularity. With an overall high accuracy (>93%) and low error rates (≤ 5%), the random forest achieves reliable results. This is supported by high areas under the receiver–operator characteristic curve (≥ 0.94) and the prediction–recall curve (≥ 0.77), respectively.We developed a novel method for a fast, user-independent and reproducible analysis of material hemocompatibility tests. The automatized analysis method overcomes the current obstacles in the way of standardized in-vitro material testing and is therefore a unique and powerful tool for advances in biomaterial research.

Mesh Denoising via a Novel Mumford–Shah Framework

In this paper, we introduce a Mumford–Shah framework to restore the face normal field on the triangulated surface. To effectively discretize Γ-convergence approximation of the Mumford–Shah model, we first define an edge function space and its associated differential operators. They are helpful for directly diffusing the discontinuity function over mesh edges instead of computing the approximated discontinuity function via pointwise diffusion in existing discretizations. Then, by using the operators in the proposed function space, two Mumford–Shah-based denoising methods are presented, which can produce denoised results with neat geometric features and locate geometric discontinuities exactly. Our Mumford–Shah framework overcomes the limitations of existing techniques that blur the discontinuity function, be less able to preserve geometric features, be sensitive to surface sampling, and require a postprocessing to form feature curves from located discontinuity vertices. Intensive experimental results on a variety of surfaces show the superiority of our denoising methods qualitatively and quantitatively.

A two-stage method for spectral–spatial classification of hyperspectral images

We propose a novel two-stage method for the classification of hyperspectral images. Pixel-wise classifiers, such as the classical support vector machine (SVM), consider spectral information only. As spatial information is not utilized, the classification results are not optimal and the classified image may appear noisy. Many existing methods, such as morphological profiles, superpixel segmentation, and composite kernels, exploit the spatial information. In this paper, we propose a two-stage approach inspired by image denoising and segmentation to incorporate the spatial information. In the first stage, SVMs are used to estimate the class probability for each pixel. In the second stage, a convex variant of the Mumford–Shah model is applied to each probability map to denoise and segment the image into different classes. Our proposed method effectively utilizes both spectral and spatial information of the data sets and is fast as only convex minimization is needed in addition to the SVMs. Experimental results on three widely utilized real hyperspectral data sets indicate that our method is very competitive in accuracy, timing, and the number of parameters when compared with current state-of-the-art methods, especially when the inter-class spectra are similar or the percentage of training pixels is reasonably high.

A Three-Stage Variational Image Segmentation Framework Incorporating Intensity Inhomogeneity Information

In this paper, we propose a new three-stage segmentation framework based on a convex variant of the Mumford--Shah model and the intensity inhomogeneity information of an image. The first stage in o...

An Algorithm for Second Order Mumford--Shah Models Based on a Taylor Jet Formulation

Mumford--Shah models are well-established and powerful variational tools for the regularization of noisy data. In the case of images this includes regularizing both the edge set as well as the image values itself. Thus, these models may be used as a basis for a segmentation pipeline or for smoothing the data. In this paper we consider higher order Mumford--Shah functionals which penalize the deviation from piecewise polynomials instead of piecewise constant functions as first order Mumford--Shah functionals do. Minimizing Mumford--Shah functionals, which are nonsmooth and nonconvex functionals, are NP hard problems. Compared with first order Mumford--Shah functionals, numerically solving higher order models is even more challenging, and in contrast to work on more theoretical aspects there are only very few works dealing with the algorithmic side. In this paper, we propose a new algorithmic framework for second order Mumford--Shah regularization. It is based on a proposed reformulation of higher order Mumford--Shah problems in terms of Taylor jets and a corresponding discretization. Using an ADMM approach, we split the discrete jet-based problem into subproblems which we can solve efficiently, noniteratively, and exactly. We derive numerically stable and fast solvers for these subproblems. In summary, we obtain an efficient overall algorithm. Our method requires a priori knowledge on neither the gray or color levels nor the shape of the discontinuity set of a solution. We demonstrate the applicability of the proposed methods in various numerical experiments. In particular, we quantitatively and qualitatively compare the proposed scheme with the algorithms proposed in the literature.

Semi-Linearized Proximal Alternating Minimization for a Discrete Mumford-Shah Model.

The Mumford-Shah model is a standard model in image segmentation, and due to its difficulty, many approximations have been proposed. The major interest of this functional is to enable joint image restoration and contour detection. In this work, we propose a general formulation of the discrete counterpart of the Mumford-Shah functional, adapted to nonsmooth penalizations, fitting the assumptions required by the Proximal Alternating Linearized Minimization (PALM), with convergence guarantees. A second contribution aims to relax some assumptions on the involved functionals and derive a novel Semi-Linearized Proximal Alternated Minimization (SL-PAM) algorithm, with proved convergence. We compare the performances of the algorithm with several nonsmooth penalizations, for Gaussian and Poisson denoising, image restoration and RGB-color denoising. We compare the results with state-of-the-art convex relaxations of the Mumford-Shah functional, and a discrete version of the Ambrosio-Tortorelli functional. We show that the SL-PAM algorithm is faster than the original PALM algorithm, and leads to competitive denoising, restoration and segmentation results.

Experimental Investigation on the Interfacial Debonding between FRP Sheet and Concrete under Medium Strain Rate

Fiber-reinforced polymer (FRP) composites have been widely used to strengthen the existing reinforced concrete (RC) structures to against static and dynamic loads. During the past decades, the interfacial bond behavior between FRP and the concrete substrate under static load has been systematically investigated by experimental and numerical approaches. In contrast, the interfacial bond performance under dynamic loads, e.g., impact and explosive loading, is still far away from well known, especially taking the strain rate effect into account. In this contribution, the single-lap shear test is conducted to sixty specimens at the medium strain rate between 1.0E−4/s and 5.0E−3/s. The effects of various system parameters, including the strain rate, concrete strength, type of FRP and adhesive, on the interfacial fracture energy, peak shear stress, FRP strain distribution, interfacial shear stress, and effective bond length, are thoroughly investigated. It has been revealed that the strain rate and concrete strength can significantly affect the interfacial fracture energy and peak shear stress. The specimen with CFRP sheet possesses higher interfacial shear stress but lower fracture energy than that with BFRP sheet. The adhesive with lower elastic modulus is helpful to improve interfacial energy dissipation under dynamic load. The effective bond length decreases with concrete strength and strain rate, mainly between 75 mm and 90 mm, which is significantly shorter than that under static load. Inspired from the Kulkarni and Shah model, a new model is proposed to evaluate the interfacial fracture energy and peak shear stress with respect to the strain rate, and the estimated values agree well with the experiments.

Automatic prior shape selection for image edge detection with modified Mumford–Shah model

Edge detection plays an important role in the field of image processing. In this paper, we propose a novel variational model to automatically and adaptively detect one or more prior shapes from the given dictionary to guide the edge detection process. In that way, we can effectively detect the shapes of interest from the test image. Moreover, an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) is proposed to solve this model with guaranteed convergence. A variety of numerical experiments show that the proposed method has achieved ideal performance for edge detection in images with missing information, various types of noise and complicated background, and even multiple objects.

A novel model of feature extraction for lung cysts detection in CT image using Minutiae based Mumford and Shah functional model

ABSTRACTLung cancer is one of the commonly occurring and most hazardous diseases to cure which increases the death rate day by day. In order to reduce the death rate, it is necessary to detect the lung cancer in its initial stages and thereby to assist the surgeons to clear away the portion of lung for the treatment of lung cancer, and tumours. This paper concentrates at developing a Computer-Aided Diagnosis (CAD) system for detecting lung cancer by analysing the Computed Tomography (CT) images of lungs. And it is carried out with filtering, binarization, image segmentation based on the Mumford and Shah model, Image enhancement including binarization and thinning, Minutiae Extraction using Termination and Bifurcation, Removal of False Minutiae Points and finally feature Extraction using grey level co-occurrence matrix (GLCM). Also, the system removes 98% of false minutiae and thus, is more efficient than other algorithms which achieve 80% to 90%. In addition, the image quality is analysed using various assessment Metrics. Finally, a comparative and robustness analyses are carried out with the existing self-learning approach in terms extracted values. The results of the proposed system show that there is significant improvement in PSNR value compared to the existing method.