An image segmentation method based on Mumford–Shah model with mask factor and neighborhood factor

Pattern Analysis and Applications - A novel image segmentation model is proposed to improve the stability of existing segmentation methods. In the proposed model, we introduce two factors into the...     

A local region-based Chan–Vese model for image segmentation

In this paper, a new region-based active contour model, namely local region-based Chan–Vese (LRCV) model, is proposed for image segmentation. By considering the image local characteristics, the proposed model can effectively and efficiently segment images with intensity inhomogeneity. To reduce the dependency on manual initialization in many active contour models and for an automatic segmentation, a degraded CV model is proposed, whose segmentation result can be taken as the initial contour of the LRCV model. In addition, we regularize the level set function by using Gaussian filtering to keep it smooth in the evolution process. Experimental results on synthetic and real images show the advantages of our method in terms of both effectiveness and robustness. Compared with the well-know local binary fitting (LBF) model, our method is much more computationally efficient and much less sensitive to the initial contour.     

Mumford–Shah and Potts Regularization for Manifold-Valued Data

Mumford–Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving denoising and segmentation. Being both non-smooth and non-convex, they are computationally challenging even for scalar data. For manifold-valued data, the problem becomes even more involved since typical features of vector spaces are not available. In this paper, we propose algorithms for Mumford–Shah and for Potts regularization of manifold-valued signals and images. For the univariate problems, we derive solvers based on dynamic programming combined with (convex) optimization techniques for manifold-valued data. For the class of Cartan–Hadamard manifolds (which includes the data space in diffusion tensor imaging (DTI)), we show that our algorithms compute global minimizers for any starting point. For the multivariate Mumford–Shah and Potts problems (for image regularization), we propose a splitting into suitable subproblems which we can solve exactly using the techniques developed for the corresponding univariate problems. Our method does not require any priori restrictions on the edge set and we do not have to discretize the data space. We apply our method to DTI as well as Q-ball imaging. Using the DTI model, we obtain a segmentation of the corpus callosum on real data.     

Combinatorial Optimization of the Discretized Multiphase Mumford–Shah Functional

The Mumford–Shah model has been one of the most influential models in image segmentation and denoising. The optimization of the multiphase Mumford–Shah energy functional has been performed using level sets methods that optimize the Mumford–Shah energy by evolving the level sets via the gradient descent. These methods are very slow and prone to getting stuck in local optima due to the use of gradient descent. After the reformulation of the 2-phase Mumford–Shah functional on a graph, several groups investigated the hierarchical extension of the graph representation to multi class. The discrete hierarchical approaches are more effective than hierarchical (or direct) multiphase formulation using level sets. However, they provide approximate solutions and can diverge away from the optimal solution. In this paper, we present a discrete alternating optimization for the discretized Vese–Chan approximation of the piecewise constant multiphase Mumford–Shah functional that directly minimizes the multiphase functional without recursive bisection on the labels. Our approach handles the nonsubmodularity of the multiphase energy function and provides a global optimum if the image estimation data term is known apriori.     

Hidden Markov random field model and Broyden–Fletcher–Goldfarb–Shanno algorithm for brain image segmentation

Abstract

Many routine medical examinations produce images of patients suffering from various pathologies. With the huge number of medical images, the manual analysis and interpretation became a tedious task. Thus, automatic image segmentation became essential for diagnosis assistance. Segmentation consists in dividing the image into homogeneous and significant regions. We focus on hidden Markov random fields referred to as HMRF to model the problem of segmentation. This modelisation leads to a classical function minimisation problem. Broyden–Fletcher–Goldfarb–Shanno algorithm referred to as BFGS is one of the most powerful methods to solve unconstrained optimisation problem. In this paper, we investigate the combination of HMRF and BFGS algorithm to perform the segmentation operation. The proposed method shows very good segmentation results comparing with well-known approaches. The tests are conducted on brain magnetic resonance image databases (BrainWeb and IBSR) largely used to objectively confront the results obtained. The well-known Dice coefficient (DC) was used as similarity metric. The experimental results show that, in many cases, our proposed method approaches the perfect segmentation with a Dice Coefficient above .9. Moreover, it generally outperforms other methods in the tests conducted.     

A framework for development of fuzzy GOMS model for human‐computer interaction

The objective of this study was to examine usefulness of fuzzy methodologies in the analysis and design of human‐computer interaction. A framework for generalization of the Goals‐Operators‐Methods‐Selection Rules (GOMS) model, and its fuzzy version was proposed. An experimental verification of the fuzzy GOMS model was also provided. A total of six subjects participated in two laboratory experiments. These experiments were performed in order to validate the proposed fuzzy GOMS model for the text editing task described in information processing terms. The subjects were not familiar with the text files to be edited, and the task was performed from the subject's own office and desk. All subjects were familiar with and regularly used the VI screen editor. The experiments consisted of the following steps: (1) the subject performed a familiar text editing task using a screen editor (VI); (2) the methods by which the subject achieved his goals (word location) as well as selection rules were elicited; (3) several compatibility functions for fuzzy terms used by the subject were derived; and (4) once all the rules, methods, and corresponding membership functions have been elicited, the theory of possibility was used to model the expert's rule selection process. For this purpose, each of the potential rules was assigned a possibility measure equal to the membership value(s) derived during the elicitation phase of experiment Finally, the selected methods were compared to non‐fuzzy predictions and actual experimental data. It was shown that overall, across all subjects and trials of the main editing task, the fuzzy‐based COMS model predicted significantly more of the subject responses, than did the non‐fuzzy COMS model.     

Fuzzy segmentation for object‐based image classification

This Letter proposes an object‐based image classification procedure which is based on fuzzy image‐regions instead of crisp image‐objects. The approach has three stages: (a) fuzzification in which fuzzy image‐regions are developed, resulting in a set of images whose digital values express the degree of membership of each pixel to target land‐cover classes; (b) feature analysis in which contextual properties of fuzzy image‐regions are quantified; and (c) defuzzification in which fuzzy image‐regions are allocated to target land‐cover classes. The proposed procedure is implemented using automated statistical techniques that require very little user interaction. The results indicate that fuzzy segmentation‐based methods produce acceptable thematic accuracy and could represent a viable alternative to current crisp image segmentation approaches.     

Uncertainty Quantification in Image Segmentation Using the Ambrosio–Tortorelli Approximation of the Mumford–Shah 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.

     

Dynamical behavior of a general reaction–diffusion–advection model for two competing species

It is well known that the studies of the evolution of biased movement along a resource gradient could create very interesting phenomena. This paper deals with a general two-species Lotka–Volterra competition model for the same resources in an advective nonhomogeneous environment, where the individuals are exposed to unidirectional flow (advection) but no individuals are lost through the boundary. It is assumed that the two species have the same population dynamics but different diffusion and advection rates. It is shown that at least five scenarios can occur (i) If one with a very strong biased movement relative to diffusion and the other with a more balanced approach, the species with much larger advection dispersal rate is driven to extinction; (ii) If one with a very strong biased movement and the other is smaller compare to its diffusion, the two species can coexist since one species mainly pursues resources at places of locally most favorable environments while the other relies on resources from other parts of the habitat; (iii) If both of the species random dispersal rates are sufficiently large (respectively small), two competing species coexist; (iv) If one with a sufficiently large random dispersal rate and the other with a sufficiently small one, two competing species still coexist; (v) If one with a sufficiently small random dispersal rate and the other with a suitable diffusion, which causes the extinction of the species with smaller random movement. Where (iii), (iv) and (v) show the global dynamics of (5) when both of the species dispersal rates are sufficiently large or sufficiently small. These results provide a new mechanism for the coexistence of competing species, and they also imply that selection is against excessive advection along environmental gradients (respectively, random dispersal rate), and an intermediate biased movement rate (respectively, random dispersal rate) may evolve. Finally, we also apply a perturbation argument to illustrate the evolution of these rates.     

A separation–aggregation network for image denoising

Image denoising is the problem that aims at recovering a clean image from a noisy counterpart. A promising solution for image denoising is to employ an appropriate deep neural network to learn a hierarchical mapping function from the noisy image to its clean counterpart. This mapping function, however, is generally difficult to learn since the potential feature space of the noisy patterns can be huge. To overcome this difficulty, we propose a separation–aggregation strategy to decompose the noisy image into multiple bands, each of which exhibits one kind of pattern. Then a deep mapping function is learned for each band and the mapping results are ultimately assembled to the clean image. By doing so, the network only needs to deal with the compositing components of the noisy image, thus makes it easier to learn an effective mapping function. Moreover, as any image can be viewed as a composition of some basic patterns, our strategy is expected to better generalize to unseen images. Inspired by this idea, we develop a separation–aggregation network. The proposed network consists of three blocks, namely a convolutional separation block that decomposes the input into multiple bands, a deep mapping block that learns the mapping function for each band, and a band aggregation block that assembles the mapping results. Experimental results demonstrate the superiority of our strategy over counterparts without image decomposition.     

A perception-based model for EDI adoption in small businesses using a technology–organization–environment framework

The wide adoption of electronic data interchange (EDI) has been argued to be important for the success of the technology. Past studies on EDI have focused mainly on large firms, as they were the major users at the time. With the advance of technology, however, EDI applications that used to require mainframe computers can be used on PCs at a much lower cost. At a result, small businesses are now able to enjoy the benefits of EDI. Using a technology–organization–environment framework, this study proposes a perception-based small business EDI adoption model that is tested against data collected from 575 small firms in Hong Kong. Six factors are tested using logistic regression and five are found to be significant in distinguishing adopter firms from non-adopter firms. The results suggest the perception-based model using a technology–organization–environment framework is a useful approach for examining factors affecting the adoption decision. For small businesses, while direct benefits are perceived to be higher by adopter firms than by non-adopter firms, indirect benefits are not perceived differently by either adopter firms or non-adopter firms, contrary to the findings in studies on large business. In addition, adopter firms perceive lower financial costs and higher technical competence than non-adopter firms do. Also, adopter firms perceive higher government pressure but lower industry pressure than non-adopter firms do. Implications of the findings and future research areas are discussed.     

A general “geometric” thermodynamic model for multicomponent solutions

Several “geometric” models have been proposed for estimating thermodynamic properties of a ternary solution from optimized data for its binary subsystems. The most common are the Kohler, Muggianu, Kohler/Toop, and Muggianu/Toop models. The latter two are “asymmetric” in that one component is singled out, whereas the first two are “symmetric”. The use of a symmetric model when an asymetric model is more appropriate can often give rise to errors. There are 64 possible simple geometric models for a ternary system. Equations are developed to calculate the thermodynamic properties of an N-component solution (N>3) in a rational manner while permitting complete flexibility to choose any of the 64 possible geometric models for any ternary subsystem. An improved general functional form for “ternary terms” in the excess Gibbs energy expression is also proposed.     

A CPU–GPU framework for optimizing the quality of large meshes

The automatic generation of 3D finite element meshes (FEM) is still a bottleneck for the simulation of large fluid dynamic problems. Although today there are several algorithms that can generate good meshes without user intervention, in cases where the geometry changes during the calculation and thousands of meshes must be constructed, the computational cost of this process can exceed the cost of the FEM. There has been a lot of work in FEM parallelization and the algorithms work well in different parallel architectures, but at present there has not been much success in the parallelization of mesh generation methods. This paper will present a massive parallelization scheme for re-meshing with tetrahedral elements using the local modification algorithm. This method is frequently used to improve the quality of elements once the mesh has been generated, but we will show it can also be applied as a regeneration process, starting with the distorted and invalid mesh of the previous step. The parallelization is carried out using OpenCL and OpenMP in order to test the method in a multiple CPU architecture and also in Graphics Processing Units (GPUs). Finally we present the speedup and quality results obtained in meshes with hundreds of thousands of elements and different parallel APIs.     

Active spline model: A shape based model—interactive segmentation

We propose to formulate point distribution model in terms of centripetal-parameterized Catmull–Rom spline, so that the model-based segmentation is augmented to permit quick edit, and the consequent shape is independent of scale. We train the model in a fashion similar to active shape model, but with fewer salient/landmark points. We use gradient vector flow field as the external force field to drive the segmentation, but we did not adopt the procedures panned out by Cootes et al. to update a shape. Instead, we transform the shape back and forth between model scale and image scale to get the shape converged to the object of interest. To test the method, we turned the solution into an automated algorithm to segment lung on chest radiographs, and achieved an average overlap of 0.879. With edit, the average overlap increased to 0.945, with a minimum of 0.925. The method can be applied on a variety of images, as illustrated in Appendix C. The source code of the algorithm and the demo video can be located at http://jenh.co/2014/01/09/active-spline-models/.     

A feature-oriented forward–backward diffusion model for intensity image restoration based on level set motion

In this paper, a new enhancing and smoothing partial differential equation coupled with time-delay regularization is presented, which is based on local geometric properties desired for image restoration. To reverse the process of image deterioration, a newly defined shock filter for edge enhancing is combined with a level set motion-based regularization equation. The balance between the backward process and the forward process is carried out by a weighting function coupled with time-delay regularization helping to identify boundary areas and homogeneous regions in a given image. The proposed model is well-posed in terms of viscosity solutions – the existence and uniqueness of periodic viscosity solution to the initial value problem of the equation is established. Numerical results for some kinds of grey-level images are demonstrated to confirm our anticipation.     

An image geometry model for METEOSAT†

METEOSAT is a spin-stabilized geostationary satellite which takes Earth images in three spectral channels, infrared, visible and water vapour absorption band. The time-dependent deviations of the satellite from nominal position, attitude and spin speed are described by an image geometry model. A new iterative procedure for refined attitude determination is used. The attitude is derived from northern and southern polar horizon scan limits which are extracted from infrared image data. The geometry model provides a deformation vector field which relates the ideal reference image to the actual image. The actual image is then mapped to the reference image by the nearest-neighbour rectification process.     

Castelnuovo–Mumford regularity of initial ideals

A bound is given for the Castelnuovo–Mumford regularity of initial ideals of a homogeneous ideal in a polynomial ring over an infinite field of any characteristic. The bound depends neither on term orders nor on the coordinates. If the ideal is perfect, then a much better bound is also provided.     

Unsupervised segmentation of medical image based on difference of mutual information

Image segmentation is a very important research field in the scope of image process- ing. It has extensive application and involves almost all fields such as image understand- ing, pattern recognition and image encoding, etc. Furthermore, research of imag…     

Grayscale image segmentation by spatially variant mixture model with student’s t-distribution

A spatially variant finite mixture model with Student’s t-distribution component function is proposed for grayscale image segmentation. This model employs a new weight function which contains the information along the different spatial directions indicating the relationship of the pixels in the neighborhood. The label probability proportions are explicitly represented as probability vectors in the model. Gradient descend method is used to update the unknown parameters. The proposed model contains fewer parameters and it is easy to be implemented compare with the Markov random field (MRF) models. Comprehensive experiments on synthetic and natural images are carried out to demonstrate that the proposed model outperforms some other related ones.     

A neural model for eye–head–arm coordination

The coordinated movement of the eyes, the head and the arm is an important ability in both animals and humanoid robots. To achieve this, the brain and the robot control system need to be able to perform complex non-linear sensory-motor transformations in the forward and inverse directions between many degrees of freedom. In this article, we apply an omnidirectional basis function neural network to this task. The proposed network can perform 3-D coordinated gaze shifts and 3-D arm reaching movements to a visual target. Particularly, it can perform direct sensory-motor transformations to shift gaze and to execute arm reach movements and can also perform inverse sensory-motor transformations in order to shift gaze to view the hand.