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This paper presents an unsupervised and semi-automatic image segmentation approach where we formulate the segmentation as an inference problem based on unary and pairwise assignment probabilities computed using low-level image cues. The inference is solved via a probabilistic graph matching scheme, which allows rigorous incorporation of low-level image cues and automatic tuning of parameters. The proposed scheme is experimentally shown to compare favorably with contemporary semi-supervised and unsupervised image segmentation schemes, when applied to contemporary state-of-the-art image sets.

A new image measurement method for obtaining time-mean velocity field is proposed. The so-called time-averaged contrast is a statistical parameter of image data. Its characteristics are examined in detail with a simple mathematical model for particle images. It is found that the variance of image data gives the time-averaged contrast in time. Numerical simulation shows the possibility of practical measurement.

Aiming at the problems of low image data retrieval accuracy and slow retrieval speed in the existing image database retrieval algorithms, this paper designs a clothing image database retrieval algorithm based on wavelet transform. Firstly, it represents the color consistency vector of clothing image, reflects the composition and distribution of image color through color histogram, quantifies the visual features of clothing image, aggregates them into a fixed size representation vector, and uses the Fair Value (FV) model to complete the collection of clothing image data. Then, the size of the clothing image is adjusted by using the size transformation technology, and the clothing pattern is divided into four moments with the same size. On this basis, the clothing image is discretized with the help of Hu invariant moment to complete the preprocessing of clothing image data. Finally, the generating function of wavelet transform is determined, and a cluster of functions is obtained through translation and expansion. The wavelet filter is decomposed into basic modules, and then, the wavelet transform is studied step by step. The clothing image data are regarded as a signal, split, predicted, and updated and input into the wavelet model, and the retrieval research of clothing image database is completed. The experimental results show that the design of the retrieval algorithm is reasonable, the retrieval data accuracy is high, and the retrieval speed is fast.

The segmentation and extraction of brain tissue in magnetic resonance imaging (MRI) is a meaningful task because it provides a diagnosis and treatment basis for observing brain tissue development, delineating lesions, and planning surgery. However, MRI images are often damaged by factors such as noise, low contrast and intensity brightness, which seriously affect the accuracy of segmentation. A non-local fuzzy c-means clustering framework incorporating the Markov random field for brain tissue segmentation is proposed in this paper. Firstly, according to the statistical characteristics that MRF can effectively describe the local spatial correlation of an image, a new distance metric with neighborhood constraints is constructed by combining probabilistic statistical information. Secondly, a non-local regularization term is integrated into the objective function to utilize the global structure feature of the image, so that both the local and global information of the image can be taken into account. In addition, a linear model of inhomogeneous intensity is also built to estimate the bias field in brain MRI, which has achieved the goal of overcoming the intensity inhomogeneity. The proposed model fully considers the randomness and fuzziness in the image segmentation problem, and obtains the prior knowledge of the image reasonably, which reduces the influence of low contrast in the MRI images. Then the experimental results demonstrate that the proposed method can eliminate the noise and intensity inhomogeneity of the MRI image and effectively improve the image segmentation accuracy.

International audience; A hyperspectral image sequence can be obtained at different time in the same region from a hyperspectral sensor. The environmental change usually leads to variation in endmember reflectance, which has an important influence on unmixing process. In this article, a Bayesian unmixing model considering spectral variability for hyperspectral sequence is proposed, in which composite prior distributions of abundance and endmember variability are developed. The abundance priors consider the continuity of abundance in the temporal and spatial domains, simultaneously. Specifically, in the spatial domain, a data-adaptive variance of the abundance prior distribution is put forward based on local spatial difference. Moreover, the priors of endmember variability in temporal continuity and spectral smoothness are also exploited. Finally, a joint posterior distribution is obtained by the likelihood function and the parameter prior distributions, which can be calculated by the Markov chain Monte Carlo (MCMC) algorithm. Experiments on synthetic and real data sets demonstrate the effectiveness of the proposed approach in terms of abundance, endmember, and its variability estimation accuracy.

Markov random fields (MRFs) are well studied during the past 50 years. Their success are mainly due to their flexibility and to the fact that they gives raise to stochastic image models. In this work, we will consider a stochastic differential equation (SDE) driven by Lévy noise. We will show that the solution $ X_v $ of the SDE is a MRF satisfying the Markov property. We will prove that the Gibbs distribution of the process $ X_v $ can be represented graphically through Feynman graphs, which are defined as a set of cliques, then we will provide applications of MRFs in image processing where the image intensity at a particular location depends only on a neighborhood of pixels.

The low-rank representation (LRR) method has recently gained enormous popularity due to its robust approach in solving the subspace segmentation problem, particularly those concerning corrupted data. In this paper, the recursive sample scaling low-rank representation (RSS-LRR) method is proposed. The advantage of RSS-LRR over traditional LRR is that a cosine scaling factor is further introduced, which imposes a penalty on each sample to minimize noise and outlier influence better. Specifically, the cosine scaling factor is a similarity measure learned to extract each sample’s relationship with the low-rank representation’s principal components in the feature space. In order words, the smaller the angle between an individual data sample and the low-rank representation’s principal components, the more likely it is that the data sample is clean. Thus, the proposed method can then effectively obtain a good low-rank representation influenced mainly by clean data. Several experiments are performed with varying levels of corruption on ORL, CMU PIE, COIL20, COIL100, and LFW in order to evaluate RSS-LRR’s effectiveness over state-of-the-art low-rank methods. The experimental results show that RSS-LRR consistently performs better than the compared methods in image clustering and classification tasks.

The segmentation of weak boundary is still a difficult problem, especially sensitive to noise, which leads to the failure of segmentation. Based on the previous works, by adding the boundary indicator function with L 2,1 norm, a new convergent variational model is proposed. A novel strategy for the weak boundary image is presented. The existence of the minimizer for our model is given, by using the alternating direction method of multipliers (ADMMs) to solve the model. The experiments show that our new method is robust in segmentation of objects in a range of images with noise, low contrast, and direction.

The defect detection of 3D image of nano CT under different interference has the phenomenon of prominent dislocation. Therefore, an adaptive detection method of 3D image defect of nano CT based on wavelet decomposition is proposed. Analyze the noise of three-dimensional image of nano CT, determine the mixed filtering of image sequence according to the different noise properties, evaluate the mixed filtering of image sequence, complete the preprocessing of three-dimensional image of nano CT, fuse the three-dimensional image of nano CT decomposed by wavelet after preprocessing, enhance the image after decomposition, and realize the defect adaptive detection through the characteristics of wavelet decomposition. The experimental results show that the design method can effectively detect the interference and solve the problems of traditional methods.

We present a sufficient condition for recovering unique texture and viewpoints from unknown orthographic projections of a flat texture process. We show that four observations are sufficient in general, and we characterize the ambiguous cases. The results are applicable to shape from texture and texture-based structure from motion.

To contribute to the area of infra soft topology, we introduce one of the generalizations of infra soft open sets called infra soft semiopen sets. We establish some characterizations of them and study their main properties. We determine under what condition this class is closed under finite intersection and show that this class is preserved under infra soft continuous mappings and finite product of soft spaces. Then, we present the concepts of infra semi-interior, infra semiclosure, infra semilimit, and infra semiboundary soft points of a soft set and elucidate the relationships between them. Finally, we exploit infra soft semiopen and infra soft semiclosed sets to define new types of soft mappings. We characterize each one of these soft mappings and explore main features.

This paper introduces families of bilateral filters for image denoising and sharpness enhancements, JPEG deblocking, and texture filtering. While the Gaussian distribution dictates the application of the bilateral filters, we introduce a wide variety of kernels based on Riemann-Lebesgue’s theorem. The derivation of the bilateral filters are established in both adaptive and non-adaptive approaches. The adaptation of the filters is adjusted via computing the variances (inflection points) using different methods based on applications. For image denoising and sharpness, the variance estimated using Laplacian-of-Gaussian filter followed by affine mapping. The variance is computed as a proportion of intensity differences across the boundary in JPEG deblocking. In texture filtering, the variance is calculated form modified relative variations. We carry out extensive experiments in three different applications and compare the results using different bilateral filters. The proposed filters are giving better results, compared with standard bilateral and adaptive bilateral filters.

Many metrics such as accuracy rate (ACC), area under curve (AUC), Jaccard index (JI), and Cohen's kappa coefficient are available to measure the success of the system in pattern recognition and machine/deep learning systems. However, the superiority of one system to one other cannot be determined based on the mentioned metrics. This is because such a system can be successful using one metric, but not the other ones. Moreover, such metrics are insufficient when the number of samples in the classes is unequal (imbalanced data). In this case, naturally, by using these metrics, a sensible comparison cannot be made between two given systems. In the present study, the comprehensive, fair, and accurate Roza (Roza means rose in Persian. When different permutations of the metrics used are superimposed in a polygon format, it looks like a flower, so we named it Roza.) metric is introduced for evaluating classification systems. This metric, which facilitates the comparison of systems, expresses the summary of many metrics with a single value. To verify the stability and validity of the metric and to conduct a comprehensive, fair, and accurate comparison between the systems, the Roza metric of the systems tested under the same conditions are calculated and comparisons are made. For this, systems tested with three different strategies on three different datasets are considered. The results show that the performance of the system can be summarized by a single value and the Roza metric can be used in all systems that include classification processes, as a powerful metric.

The problem of parallel segmentation of halftone images by brightness for implementation on the basis of programmable logic integrated circuits is considered. Segmentation divides an image into regions formed from pixels with approximately the same brightness, and is a computationally complex operation due to multiple checks of the value of each pixel for the possibility of joining an adjacent region. To speed up segmentation, parallel algorithms for growing areas have been developed, in which processing begins from the neighborhoods of preselected initial growth pixels. The condition of joining an adjacent pixel to an area takes into account the average brightness of the area to limit the variance of its pixel values. Therefore, when each new pixel is added to the area, its average brightness is recalculated. This leads to high time complexity. In some parallel algorithms, the sample mean is calculated in a small window, which makes it possible to slightly reduce the time complexity when matching the window size with the segment sizes. To significantly reduce the temporal complexity, the article proposes a model for the parallel growth of image regions based on a simplified condition for joining adjacent pixels to a region, taking into account the sample average value of the region's brightness along the growth route connecting the boundary pixel of the region and the initial growth pixel through a sequence of pixels used to attach the considered boundary pixel to area. A significant decrease in the temporal complexity of the proposed model of parallel growing of image regions in comparison with the known models is achieved due to a slight increase in the spatial complexity.

The mean curvature-based image deblurring model is widely used to enhance the quality of the deblurred images. However, the discretization of the associated Euler-Lagrange equations produce a nonlinear ill-conditioned system which affect the convergence of the numerical algorithms like Krylov subspace methods. To overcome this difficulty, in this paper, we present two new symmetric positive definite (SPD) preconditioners. An efficient algorithm is presented for the mean curvature-based image deblurring problem which combines a fixed point iteration (FPI) with new preconditioned matrices to handle the nonlinearity and ill-conditioned nature of the large system. The eigenvalues analysis is also presented in the paper. Fast convergence has shown in the numerical results by using the proposed new preconditioners.

We propose a new algorithm to compute the X-ray transform of an image represented by unit (pixel/voxel) basis functions. The fundamental task is equivalently calculating the intersection lengths of...

This research work models two methods together to provide maximum information about a study area. The quantification of image texture is performed using the “grey level co-occurrence matrix (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{GLCM}$$\end{document}GLCM)” technique. Image classification-based “object-based change detection (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{OBCD}$$\end{document}OBCD)” methods are used to visually represent the developed transformation in the study area. Pre-COVID and post-COVID (during lockdown) panchromatic images of Connaught Place, New Delhi, are investigated in this research work to develop a model for the study area. Texture classification of the study area is performed based on visual texture features for eight distances and four orientations. Six different image classification methodologies are used for mapping the study area. These methodologies are “Parallelepiped classification (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{PC}$$\end{document}PC),” “Minimum distance classification (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{MDC}$$\end{document}MDC),” “Maximum likelihood classification (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{MLC}$$\end{document}MLC),” “Spectral angle mapper (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SAM}$$\end{document}SAM),” “Spectral information divergence (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SID}$$\end{document}SID)” and “Support vector machine (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{SVM}$$\end{document}SVM).” \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{GLCM}$$\end{document}GLCM calculations have provided a pattern in texture features contrast, correlation, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ASM}$$\end{document}ASM, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{IDM}$$\end{document}IDM. Maximum classification accuracy of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$83.68\%$$\end{document}83.68% and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$73.65\%$$\end{document}73.65% are obtained for pre-COVID and post-COVID image data through \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{MLC}$$\end{document}MLC classification technique. Finally, a model is presented to analyze before and after COVID images to get complete information about the study area numerically and visually.

The object of the present paper is to study the notion of quasi-bi-slant submanifolds of almost contact metric manifolds as a generalization of slant, semi-slant, hemi-slant, bi-slant, and quasi-hemi-slant submanifolds. We study and characterize quasi-bi-slant submanifolds of Sasakian manifolds and provide non-trivial examples to signify that the structure presented in this paper is valid. Furthermore, the integrability of distributions and geometry of foliations are researched. Moreover, we characterize quasi-bi-slant submanifolds with parallel canonical structures.

In conventional approaches to Growth Mixture Modeling (GMM), a trajectory is first estimated using latent growth curve modeling that serves as a baseline trajectory for the GMM. In this approach, t...

In this paper, an extension of the bilateral Laplace transform on infinite-dimensional Banach spaces is introduced. In order to develop the concept of an analytic bilateral Laplace–Feynman transfor...

In 2016 Hakeem A. Othman and Md. Hanif Page introduced a new notion of set in general topology called an infra -α- open set and investigated its fundamental properties and studied the relationship between infra -α- open set and other topological sets. The objective of this paper is to introduce the new concepts called infra -α- compact space, countably infra -α- compact space, infra -α- Lindelof space, almost infra -α- compact space, mildly infra -α- compact space and infra -α- connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.

We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and quaternary Hermitian LCD codes, which improve the previously known lower bound on the largest minimum weights., Comment: 25 pages

For three-dimensional (3-D) measurement of dynamic objects, a new three-part phase unwrapping algorithm is proposed. First, a novel fringe modulation degree threshold estimation method is proposed. Then, the unwrapped phase can be obtained by three segments. The first-segment is calculated by 2-D spacial phase unwrapping algorithm while the fringe modulation degree is within the threshold. The second-segment is calculated between two frames when their fringe modulation degree difference is within the threshold. The third-segment is calculated by a estimation method of $2\pi $ jump order. This method only need one wrapped phase to calculate the unwrapped phase. Simulations and experiments have proved the effectiveness of the proposed method.

Fused Lasso is one of extensions of Lasso to shrink differences of parameters. We focus on a general form of it called generalized fused Lasso (GFL). The optimization problem for GFL can be came do...

Infra soft topology is one of the recent generalizations of soft topology which is closed under finite intersection. Herein, we contribute to this structure by presenting two kinds of soft covering properties, namely, infra soft compact and infra soft Lindelöf spaces. We describe them using a family of infra soft closed sets and display their main properties. With the assistance of examples, we mention some classical topological properties that are invalid in the frame of infra soft topology and determine under which condition they are valid. We focus on studying the “transmission” of these concepts between infra soft topology and classical infra topology which helps us to discover the behaviours of these concepts in infra soft topology using their counterparts in classical infra topology and vice versa. Among the obtained results, these concepts are closed under infra soft homeomorphisms and finite product of soft spaces. Finally, we introduce the concept of fixed soft points and reveal main characterizations, especially those induced from infra soft compact spaces.

In this paper, a novel weighted anisotropic total variational (WATV) model is proposed for image restoration. In this model, a weight function is defined to process degraded images, which is introduced into the $$\ell _{1}$$ norm-based regularization. In order to efficiently compute the restored images, the alternating direction method of multipliers (ADMM) is explored and the according convergence is analyzed briefly. The proposed model is applied to recover images with blurring and noise. Compared experiments of deblurring, denoising as well as restoration are conducted to show the effectiveness and efficiency of the proposed WATV model.

The aim of this paper is to investigate the flexibility of the skew-normal distribution to classify the pixels of a remotely sensed satellite image. In the most of remote sensing packages, for example ENVI and ERDAS, it is assumed that populations are distributed as a multivariate normal. Then linear discriminant function (LDF) or quadratic discriminant function (QDF) is used to classify the pixels, when the covariance matrix of populations are assumed equal or unequal, respectively. However, the data was obtained from the satellite or airplane images suffer from non-normality. In this case, skew-normal discriminant function (SDF) is one of techniques to obtain more accurate image. In this study, we compare the SDF with LDF and QDF using simulation for different scenarios. The results show that ignoring the skewness of the data increases the misclassification probability and consequently we get wrong image. An application is provided to identify the effect of wrong assumptions on the image accuracy.

Local Binary Pattern (LBP) are considered as a classical descriptor for texture analysis, it has mostly been used in pattern recognition and computer vision applications. However, the LBP gets information from a restricted number of local neighbors which is not enough to describe texture information, and the other descriptors that get a large number of local neighbors suffer from a large dimensionality and consume much time. In this regard, we propose a novel descriptor for texture classification known as Circular Parts Local Binary Pattern (CPLBP) which is designed to enhance LBP by extending the area of neighborhood from one to a region of neighbors using polar coordinates that permit to capture more discriminating relationships that exists amongst the pixels in the local neighborhood which increase efficiency in extracting features. Firstly, the circle is divided into regions with a specific radius and angle. After that, we calculate the average gray-level value of each part. Finally, the value of the center pixel is compared with these average values. The relevance of the proposed idea is validate in databases Outex 10 and 12. A complete evaluation on benchmark data sets reveals CPLBP's high performance. CPLBP generates the score of 99.95 with SVM classification.

Dual-pol Shannon Entropy captures the dynamic crop growth parameters. It was used to evaluate biophysical parameters of important crops using Sentinel-1 data. Improved phenology information is vita...

In this paper, the problem of segmentation of halftone images is considered, in which areas of local maxima and minima (extrema) are distinguished with a monotonic change in the brightness of pixels from local extrema to the boundaries of areas. To solve this problem, a mathematical model is proposed and a segmentation algorithm is developed on the basis of counter-wave growing of local extremum regions. The developed algorithm differs from the known segmentation algorithms by using a set of brightness thresholds (by the number of regions), varying by one in each cycle, starting from the values of local extrema, taking into account the increase or decrease in brightness to select adjacent pixels that are attached to the regions formed from these local extrema. The algorithm provides a greater deviation of pixel brightness from the average value within the region compared to known segmentation algorithms. This does not allow evaluating its efficiency using known indicators based on the variance of the brightness within the region. In this regard, estimates of the monotonicity of changes in the brightness of regions are proposed based on a) the shortest distances from each pixel of the region to the corresponding local extremum along the routes determined by the maximum increase (for the region of the local maximum) or decrease (for the region of the local minimum) the brightness of pixels and b) taking into account the number pixels that break the monotony of the segment brightness change. Using these estimates, it is shown that the proposed algorithm provides segmentation of artificial and natural grayscale images with a monotonic change in the brightness of pixels in the areas of local extrema. These properties allow us to consider the developed algorithm as a basis for the selection of texels, spots, low-contrast objects in images.

The paper proposes a histogram estimate of the probability density based on fuzzy data belonging to a grouping interval. A methodology for constructing a histogram estimate using a histogram smoothing filter is presented. The technique of constructing such a filter is described. The main filter parameter is established – the coefficient of the statistical relationship between the amount of data falling into the grouping interval for a single inclusion function and when approaching to use the membership function. The use of an iterative procedure for a histogram filter allows for a greater “smoothness” of the histogram. The simulation results show the effectiveness of using a histogram filter for different data volumes. At the same time, the choice of the number of grouping intervals for the “correct” recognition of probability density becomes not critical. The histogram filter is a simple tool that can easily be built into any algorithm for constructing histogram estimates.

Magnetic Resonance Fingerprinting (MRF) is a novel technique that simultaneously estimates multiple tissue-related parameters, such as the longitudinal relaxation time T1, the transverse relaxation time T2, off resonance frequency B0 and proton density, from a scanned object in just tens of seconds. However, the MRF method suffers from aliasing artifacts because it significantly undersamples the k-space data. In this work, we propose a compressed sensing (CS) framework for simultaneously estimating multiple tissue-related parameters based on the MRF method. It is more robust to low sampling ratio and is therefore more efficient in estimating MR parameters for all voxels of an object. Furthermore, the MRF method requires identifying the nearest atoms of the query fingerprints from the MR-signal-evolution dictionary with the L2 distance. However, we observed that the L2 distance is not always a proper metric to measure the similarities between MR Fingerprints. Adaptively learning a distance metric from the undersampled training data can significantly improve the matching accuracy of the query fingerprints. Numerical results on extensive simulated cases show that our method substantially outperforms state-of-the-art methods in terms of accuracy of parameter estimation.

We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.

In this paper, we propose a variational method for restoring images corrupted by multiplicative noise. Computationally, we employ the alternating minimization method to solve our minimization problem. We also study the existence and uniqueness of the proposed problem. Finally, experimental results are provided to demonstrate the superiority of our proposed hybrid model and algorithm for image denoising in comparison with state-of-the-art methods.

In this study, we propose a new gray model called “normalized beta function gray model”. Its main idea is to use the normalized beta function to optimize the linear gray action quantity into a nonl...

The Radon transform is a major integral transform in computed tomography and a widely applied technique in computer vision and image analysis which is used to detect linear structures and regular textures. Its application is based on the property of the integrals of the direct problem to accumulate the image brightness along the contours under study. The back-projection operation, one of the main components of tomographic algorithms, results in ridge functions having the directions in which they participated in the direct operator. In the present paper, we examine the ridge functions and their orientation as the features for describing the anisotropy of regular textures. These features are involved in the regular texture model as a sum of ridge functions. Many textures are visually perceived as a superposition of linear structures and are therefore examined using the Radon transform. The paper presents a computational scheme for the singular value decomposition of a regular texture into a sum of informative ridge functions. The results are given of numerical experiments with the textures of industrial fabrics. The algorithm can be used in processing the visual data in computer vision systems, textile industry, robotics, and crystallography.

Retinex theory shows that the color of a scene perceived by human visual system is only dependent on the intrinsic reflectance and unrelated to the illumination. For images recorded by digital cameras, the intensities are the product of the scene reflectance and illumination. Image intensities are different when taken under different illuminations. The aim of image retinex problem is to decompose the reflectance from the image intensities. In this paper, we propose a variational model for image retinex problem. The model can be reduced to a linear complementarity problem and a modulus-based multigrid method is applied to solve it. A pointwise coupled modulus-based Gauss-Seidel iteration scheme is used as a smoother of the multigrid method. The smoothing factor of the smoother is analyzed by using the local Fourier analysis. Both theoretical analyses and numerical results show the efficiency of the proposed method for image retinex problem.

Researches and studies on compressing digital images are aiming to make it easier to deal with networks, communications and Internet by reducing the size of the multimedia files transferred, and reducing the execution time and transmission time. In this research, the lossy compression method was adopted as one of the solutions that reduce the size of the data required to compress the image, through the process of compression of digital image data using Discrete Wavelet Transform algorithms using Haar filter, and Contourlet. Using Laplace and Directional Filter, Curvelet transformation using FDCT- Wrapping Technology .The performance of the algorithms used in the proposed research is also evaluated using a Ratio Compression (RC) scale, As well as the Peak signal to noise ratio (PSNR) scale, the mean sequence error (MSE) scale, the signal to noise ratio (SNR) scale, and finally, the Normalization correlation (NC) scale. Correspondence between the original image and the recovered image after compression, in order to choose the best algorithm that achieves the best compression ratio of the image and maintains the parameters of the recovered image based on the standards (MSE, PSNR, SNR, COR and CR) used with the three algorithms, and the results showed that the Curvelet transformation algorithm achieved : best compression ratio, but at the expense of image quality.

The paper shows that the moment invariants proposed recently in this journal by Hjouji et al. (J Math Imaging Vis 62:606–624, 2020) are incomplete, which leads to a limited discriminability. We prove this by means of circular projection of the image. In a broader context, we demonstrate that completeness of the invariants leads to a better recognition power.

The mean curvature (MC)-based image denoising and image deblurring models are used to enhance the quality of the denoised images and deblurred images respectively. These models are very efficient i...

Image denoising is a very important problem in image processing field. In order to improve denoising effects and meanwhile keep image structures, a novel weighted total variation (WTV) model is proposed in this paper. The WTV model consists of data fidelity and ℓ1 norm based regularisation terms. In the WTV model, a weight function w in exponential form is incorporated into the regularisation term, which only depends on the given image itself without extra parameters. The nonlinearly monotone formulation of w helps to increase gaps between lower and higher frequencies of images, which is effective to highlight edges and keep textures. For solving the proposed model, the alternating direction method of multipliers is explored and the according convergence is analysed. Compared experiments of TV, HOTV, ATV and TVp models are conducted and the results show the effectiveness and efficiency of the proposed model.

In this paper, we establish some inequalities for rational functions with prescribed poles and restricted zeros which generalize and refine the results of Aziz and Shah.

Threshlod image segmentation is a classic method of color image segmentation. In this paper, we propose a hybrid equilibrium optimizer algorithm for multi-level image segmentation. When multi-level threshold method calculates the neighborhood mean and median of color image, it takes huge challenge to find the optimal threshold. We use the proposed method to optimize the multi-level threshold method and get the optimal threshold from the color image. In order to test the performance of the proposed method, we select the CEC2015 dataset as the benchmark function. The result shows that the proposed method improves the optimization ability of the original algorithm. And then, the classic images and wood fiber images are taken as experimental objects to analyze the segmentation result. The experimental results show that the proposed method has a good performance in Uniformity measure, Peak Signal-to-Noise Ratio and Feature Similarity Index and CPU time.

Made available in DSpace on 2021-07-14T10:21:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-06-25. Added 1 bitstream(s) on 2021-07-14T11:27:56Z : No. of bitstreams: 1 S0100-69162021000300319.pdf: 915553 bytes, checksum: 032aa323077110649b223df7fe9ee77a (MD5) In order to estimate the response of biometric variables in different irrigation depths in radish crop, as well as their relations in the development of the crop, a fuzzy mathematical analysis was carried out from irrigation with depths of different percentages of the crop evapotranspiration (ETc), using Gaussian pertinence functions for the input variable and triangular for the biometric output variables. Validations were performed using neural network models, smoothing splines and polynomial regression. The relation among the biometric variables was measured applying the Pearson correlation coefficient. The results showed that the fuzzy modeling presented superiority in the crop development estimate over the quadratic polynomial regression model, neural network and smoothing splines, because it achieved an average reduction of errors among the biometric variables, of 7.8% 94.6% and 9.2% for the RMSE in the respective models, as well as a better adjustment of the data with average R2 of the variables. The modeling with neural network showed inadequate agronomic behavior in data representation. Regarding biometric variables, the length and diameter of the tuberous root are inversely correlated, and the fresh phytomass of the tuberous root is correlated only with the fresh phytomass of the root. São Paulo State University, School of Agriculture São Paulo State University, School of Sciences and Engineering São Paulo State University, School of Agriculture São Paulo State University, School of Sciences and Engineering

Linear complementary dual (LCD) codes are linear codes whose intersections with their duals are trivial. In this paper, characterizations of LCD codes with respect to the symplectic inner product, i.e. symplectic LCD codes, over finite fields are given. Some methods for constructing symplectic LCD codes and symplectic LCD MDS codes are presented. As an application, a class of symplectic LCD MDS codes is constructed by employing Vandermonde matrices, and the corresponding MDS maximal entanglement entanglement-assisted quantum error-correcting codes (EAQECCs) are constructed.

With the advancements of computer technology, image recognition technology has been more and more widely applied and feature extraction is a core problem of image recognition. In study, image recognition classifies the processed image and identifies the category it belongs to. By selecting the feature to be extracted, it measures the necessary parameters and classifies according to the result. For better recognition, it needs to conduct structural analysis and image description of the entire image and enhance image understanding through multi-object structural relationship. The essence of Radon transform is to reconstruct the original N-dimensional image in N-dimensional space according to the N-1 dimensional projection data of N-dimensional image in different directions. The Radon transform of image is to extract the feature in the transform domain and map the image space to the parameter space. This paper study the inverse problem of Radon transform of the upper semicircular curve with compact support and continuous in the support. When the center and radius of a circular curve change in a certain range, the inversion problem is unique when the Radon transform along the upper semicircle curve is known. In order to further improve the robustness and discrimination of the features extracted, given the image translation or proportional scaling and the removal of impact caused by translation and proportion, this paper has proposed an image similarity invariant feature extraction method based on Radon transform, constructed Radon moment invariant and shown the description capacity of shape feature extraction method on shape feature by getting intra-class ratio. The experiment result has shown that the method of this paper has overcome the flaws of cracks, overlapping, fuzziness and fake edges which exist when extracting features alone, it can accurately extract the corners of the digital image and has good robustness to noise. It has effectively improved the accuracy and continuity of complex image feature extraction.

Fuzzy c-means with regularization by K–L information (KLFCM) is an objective function method for clustering, which is regarded as a fuzzy counterpart of Gaussian mixture models (GMMs) with EM algor...

The quantity of information in images can be evaluated by means of the Shannon entropy. When dealing with natural images with a large scale of gray levels, as well as with images containing textures or suffering some degradation such as noise or blurring, this measure tends to saturate. That is, it reaches high values due to a large amount of irrelevant information, making it useless for measuring significant information. In this paper we present a new information measure, the clustered entropy. This information measure, based on clustering local histograms, has a zero value for quasi-homogeneous regions and reaches high values for regions containing edges. The clustered entropy is used in this paper as an edge detector, by centering a sliding window on every pixel of an image, and calculating the clustered entropy of the corresponding histogram. A search for local maxima throughout the resulting matrix of entropies provides the final image of edges. The mathematical properties of clustered entropy are studied, a comparison between the clustered and the normal entropy is done, and some comparative experiments of edge detection are shown in this paper.

Three-dimensional (3D) sparse reconstruction of landslide topography based on unmanned aerial vehicle (UAV) images has been widely used for landslide monitoring and geomorphological analysis. In order to solve the isolated island phenomenon caused by multi-scale image matching, which means that there is no connection between the images of different scales, we herein propose a method that selects UAV image pairs based on image retrieval. In this method, sparse reconstruction was obtained via the sequential structure-from-motion (SfM) pipeline. First, principal component analysis (PCA) was used to reduce high-dimensional features to low-dimensional features to improve the efficiency of retrieval vocabulary construction. Second, by calculating the query depth threshold and discarding the invalid image pairs, we improved the efficiency of image matching. Third, the connected network of the dataset was constructed based on the initial matching of image pairs. The lost multi-scale image pairs were identified and matched through the image query between the connection components, which further improved the integrity of image matching. Our experimental results show that, compared with the traditional image retrieval method, the efficiency of the proposed method is improved by 25.9%.

In this paper, a crystal image analysis method is presented to measure and predict crystal sizes, based on cooling crystallization of β-form L-glutamic acid (LGA) by using an in-situ non-invasive imaging system. The proposed method consists of image restoration, image segmentation, crystal size measurement, and size prediction. To cope with the effects of noise pollution, uneven illumination and movement blurring, the image processing method is conducted for segmenting crystal images captured from the stirring reactor. Thus, the crystal size distribution for crystal population is obtained by using a probability density function. In addition, a short-term prediction method is given for crystal sizes. An experimental study on the cooling crystallization process of β-form LGA is shown to demonstrate the effectiveness of the proposed method.