基于方向多尺度变换和统计建模的纹理分类方法

纹理是图像分析和识别中经常使用的关键特征, 而小波变换则是图像纹理表示和分类中的常用工具. 然而, 基于小波变换的纹理分类方法常常忽略了小波低频子带信息, 并且无法提取图像纹理的块状奇异信息. 本文提出小波子带系数的局部能量直方图建模方法、轮廓波特征的Poisson 混合模型建模方法和基于轮廓波子带系数聚类的特征提取方法, 并将其应用于图像纹理分类上. 基于局部能量直方图的纹理分类方法解决了小波低频子带的建模难题, 基于Poisson 混合模型的纹理分类方法则首次将Poisson 混合模型用于轮廓子带特征的建模, 而基于轮廓波域聚类的纹理分类方法是一种快速的分类方法. 实验结果显示, 本文所提出的三类方法都超过了当前典型的纹理分类方法.     

MgNet: A unified framework of multigrid and convolutional neural network

We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks(CNN) for image classification and multigrid(MG) methods for solving discretized partial differential equations(PDEs). This model is based on close connections that we have observed and uncovered between the CNN and MG methodologies. For example, pooling operation and feature extraction in CNN correspond directly to restriction operation and iterative smoothers in MG, respectively. As the solution space is often the dual of the data space in PDEs, the analogous concept of feature space and data space(which are dual to each other) is introduced in CNN. With such connections and new concept in the unified model, the function of various convolution operations and pooling used in CNN can be better understood. As a result,modified CNN models(with fewer weights and hyperparameters) are developed that exhibit competitive and sometimes better performance in comparison with existing CNN models when applied to both CIFAR-10 and CIFAR-100 data sets.     

A new modified panoramic UAV image stitching model based on the GA-SIFT and adaptive threshold method

This paper presents panoramic unmanned aerial vehicle (UAV) image stitching techniques based on an optimal Scale Invariant Feature Transform (SIFT) method. The image stitching representation associates a transformation matrix with each input image. In this study, we formulate stitching as a multi-image matching problem, and use invariant local features to find matches between the images. An improved Geometric Algebra (GA-SIFT) algorithm is proposed to realize fast feature extraction and feature matching work for the scanned images. The proposed GA-SIFT method can locate more feature points with greater accurately than the traditional SIFT method. The adaptive threshold value method proposed solves the limitation problem of high computation load and high cost of stitching time by greater feature points extraction and stitching work. The modified random sample consensus method is proposed to estimate the image transformation parameters and to determine the solution with the best consensus for the data. The experimental results demonstrate that the proposed image stitching method greatly increases the speed of the image alignment process and produces a satisfactory image stitching result. The proposed image stitching model for aerial images has good distinctiveness and robustness, and can save considerable time for large UAV image stitching.     

On a New Diffeomorphic Multi-Modality Image Registration Model and Its Convergent Gauss-Newton Solver

In this work, we propose a new variational model for multi-modal image registration and present an efficient numerical implementation. The model minimizes a new functional based on using reformulated normalized gradients of the images as the fidelity term and higher-order derivatives as the regularizer. A key feature of the model is its ability of guaranteeing a diffeomorphic transformation which is achieved by a control term motivated by the quasi-conformal map and Beltrami coefficient. The existence of the solution of this model is established. To solve the model numerically, we design a Gauss-Newton method to solve the resulting discrete optimization problem and prove its convergence; a multilevel technique is employed to speed up the initialization and avoid likely local minima of the underlying functional. Finally, numerical experiments demonstrate that this new model can deliver good performances for multi-modal image registration and simultaneously generate an accurate diffeomorphic transformation.     

Local histograms and image occlusion models

The local histogram transform of an image is a data cube that consists of the histograms of the pixel values that lie within a fixed neighborhood of any given pixel location. Such transforms are useful in image processing applications such as classification and segmentation, especially when dealing with textures that can be distinguished by the distributions of their pixel intensities and colors. We, in particular, use them to identify and delineate biological tissues found in histology images obtained via digital microscopy. In this paper, we introduce a mathematical formalism that rigorously justifies the use of local histograms for such purposes. We begin by discussing how local histograms can be computed as systems of convolutions. We then introduce probabilistic image models that can emulate textures one routinely encounters in histology images. These models are rooted in the concept of image occlusion. A simple model may, for example, generate textures by randomly speckling opaque blobs of one color on top of blobs of another. Under certain conditions, we show that, on average, the local histograms of such model-generated-textures are convex combinations of more basic distributions. We further provide several methods for creating models that meet these conditions; the textures generated by some of these models resemble those found in histology images. Taken together, these results suggest that histology textures can be analyzed by decomposing their local histograms into more basic components. We conclude with a proof-of-concept segmentation-and-classification algorithm based on these ideas, supported by numerical experimentation.     

Multi-Label Markov Random Fields as an Efficient and Effective Tool for Image Segmentation,Total Variations and Regularization

One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. This model is a discrete optimization problem, which is shown here to formulate many continuous models used in image segmentation. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the non-effectiveness is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm. Worse still, heuristics do not link directly the input functions and parameters to the output thus obscuring what would be ideal choices of parameters and functions which are to be selected by users in each particular application context.We describe here how MRF can model and solve efficiently several known continuous models for image segmentation and describe briefly a very efficient polynomial time algorithm, which is provably fastest possible, to solve optimally the MRF problem. The MRF algorithm is enhanced here compared to the algorithm in Hochbaum (2001) by allowing the set of assigned labels to be any discrete set. Other enhancements include dynamic features that permit adjustments to the input parameters and solves optimally for these changes with minimal computation time. Several new theoretical results on the properties of the algorithm are proved here and are demonstrated for images in the context of medical and biological imaging. An interactive implementation tool for MRF is described, and its performance and flexibility in practice are demonstrated via computational experiments.We conclude that many continuous models common in image segmentation have discrete analogs to various special cases of MRF and as such are solved optimally and efficiently, rather than with the use of continuous techniques, such as PDE methods, which restrict the type of functions used and furthermore, can only guarantee convergence to a local minimum.     

Adaptive Segmentation Model for Images with Intensity Inhomogeneity based on Local Neighborhood Contrast

Segmentation of images with intensity inhomogeneity is a significant task in the field of image processing, especially in medical image processing and analysis. Some local region-based models work well on handling intensity inhomogeneity, but they are always sensitive to contour initialization and high noise. In this paper, we present an adaptive segmentation model for images with intensity inhomogeneity in the form of partial differential equation. Firstly, a global intensity fitting term and a local intensity fitting term are constructed by employing the global and local image information, respectively. Secondly, a tradeoff function is defined to adjust adaptively the weight between two fitting terms, which is based on the neighborhood contrast of image pixel. Finally, a weighted regularization term related to local entropy is used to ensure the smoothness of evolution curve. Meanwhile, a distance regularization term is added for stable level set evolution. Experimental results show that the proposed model without initial contour can segment inhomogeneous images stably and effectively, which thereby avoiding the influence of contour initialization on segmentation results. Besides, the proposed model works better on noise images comparing with two relevant segmentation models.     

Bifurcation analysis of a population model and the resulting SIS epidemic model with delay

This paper deals with the model for matured population growth proposed in Cooke et al. [Interaction of matiration delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39 (1999) 332–352] and the resulting SIS epidemic model. The dynamics of these two models are still largely undetermined, and in this paper, we perform some bifurcation analysis to the models. By applying the global bifurcation theory for functional differential equations, we are able to show that the population model allows multiple periodic solutions. For the SIS model, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution.     

A new nonlocal model for the restoration of textured images

In this paper, we focus on the mathematical and numerical study of a new nonlocal reaction-diffusion system for image denoising. This model is motivated by involving the decomposition approach of $H^{-1}$ norm suggested by Meyer [25] which is more appropriate to represent the oscillatory patterns and small details in the textured image. Based on Schaeffer''s fixed point theorem, we prove the existence and uniqueness of solution of the proposed model. To illustrate the efficiency and effectiveness of our model, we test the denoising experimental results as well we compare with some existing models in the literature.     

A compromised multi-objective solution using fuzzy mixed integer goal programming for market-based short-term unit commitment problem

When implementing, the solution of single-objective unit commitment models may be dissatisfactory or inapplicable. This might mainly be due to not considering the secondary conflicting objectives from the policy-making in internal/external environment of generation companies in the developed models. To attain a practical compromised multi-objective solution for the short-term unit commitment in the deregulated hybrid markets, a novel fuzzy mixed integer linear goal programme is developed in which several complementary objectives with lower relative importances are also incorporated. Non-linear characteristic curves of the generating units are approximated through the piece-wise linear functions. The fuzzy approach is proposed to handle the imprecise nature of the goals’ target levels and priorities as well as some critical data. The critical aspects of power systems are considered in the model. The efficiency of the proposed approach is demonstrated using the experimental results inspired by a real case. The applicable nice feature of our model is that it can easily and efficiently be matched with a various line of unit commitment problems.