Space-time fractional Zener wave equation

Space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analyzed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented

Measure of similarity between GMMs by embedding of the parameter space that preserves KL divergence

In this work, we deliver a novel measure of similarity between Gaussian mixture models (GMMs) by neighborhood preserving embedding (NPE) of the parameter space, that projects components of GMMs, which by our assumption lie close to lower dimensional manifold. By doing so, we obtain a transformation from the original high-dimensional parameter space, into a much lower-dimensional resulting parameter space. Therefore, resolving the distance between two GMMs is reduced to (taking the account of the corresponding weights) calculating the distance between sets of lower-dimensional Euclidean vectors. Much better trade-off between the recognition accuracy and the computational complexity is achieved in comparison to measures utilizing distances between Gaussian components evaluated in the original parameter space. The proposed measure is much more efficient in machine learning tasks that operate on large data sets, as in such tasks, the required number of overall Gaussian components is always large. Artificial, as well as real-world experiments are conducted, showing much better trade-off between recognition accuracy and computational complexity of the proposed measure, in comparison to all baseline measures of similarity between GMMs tested in this paper.Web of Science99art. no. 95

Semiautomatic epicardial fat segmentation based on fuzzy c-means clustering and geometric ellipse fitting

Automatic segmentation of particular heart parts plays an important role in recognition tasks, which is utilized for diagnosis and treatment. One particularly important application is segmentation of epicardial fat (surrounds the heart), which is shown by various studies to indicate risk level for developing various cardiovascular diseases as well as to predict progression of certain diseases. Quantification of epicardial fat from CT images requires advance image segmentation methods. The problem of the state-of-the-art methods for epicardial fat segmentation is their high dependency on user interaction, resulting in low reproducibility of studies and time-consuming analysis. We propose in this paper a novel semiautomatic approach for segmentation and quantification of epicardial fat from 3D CT images. Our method is a semisupervised slice-by-slice segmentation approach based on local adaptive morphology and fuzzy c-means clustering. Additionally, we use a geometric ellipse prior to filter out undesired parts of the target cluster. The validation of the proposed methodology shows good correspondence between the segmentation results and the manual segmentation performed by physicians

Image denoising by a direct variational minimization

<p>Abstract</p> <p>In this article we introduce a novel method for the image de-noising which combines a mathematically well-posdenes of the variational modeling with the efficiency of a patch-based approach in the field of image processing. It based on a direct minimization of an energy functional containing a minimal surface regularizer that uses fractional gradient. The minimization is obtained on every predefined patch of the image, independently. By doing so, we avoid the use of an artificial time PDE model with its inherent problems of finding optimal stopping time, as well as the optimal time step. Moreover, we control the level of image smoothing on each patch (and thus on the whole image) by adapting the Lagrange multiplier using the information on the level of discontinuities on a particular patch, which we obtain by pre-processing. In order to reduce the average number of vectors in the approximation generator and still to obtain the minimal degradation, we combine a Ritz variational method for the actual minimization on a patch, and a complementary fractional variational principle. Thus, the proposed method becomes computationally feasible and applicable for practical purposes. We confirm our claims with experimental results, by comparing the proposed method with a couple of PDE-based methods, where we get significantly better denoising results specially on the oscillatory regions.</p

Bootstrapped SSL CycleGAN for Asymmetric Domain Transfer

Most CycleGAN domain transfer architectures require a large amount of data belonging to domains on which the domain transfer task is to be applied. Nevertheless, in many real-world applications one of the domains is reduced, i.e., scarce. This means that it has much less training data available in comparison to the other domain, which is fully observable. In order to tackle the problem of using CycleGAN framework in such unfavorable application scenarios, we propose and invoke a novel Bootstrapped SSL CycleGAN architecture (BTS-SSL), where the mentioned problem is overcome using two strategies. Firstly, by using a relatively small percentage of available labelled training data from the reduced or scarce domain and a Semi-Supervised Learning (SSL) approach, we prevent overfitting of the discriminator belonging to the reduced domain, which would otherwise occur during initial training iterations due to the small amount of available training data in the scarce domain. Secondly, after initial learning guided by the described SSL strategy, additional bootstrapping (BTS) of the reduced data domain is performed by inserting artifically generated training examples into the training poll of the data discriminator belonging to the scarce domain. Bootstrapped samples are generated by the already trained neural network that performs transferring from the fully observable to the scarce domain. The described procedure is periodically repeated during the training process several times and results in significantly improved performance of the final model in comparison to the original unsupervised CycleGAN approach. The same also holds in comparison to the solutions that are exclusively based either on the described SSL, or on the bootstrapping strategy, i.e., when these are applied separately. Moreover, in the considered scarce scenarios it also shows competitive results in comparison to the fully supervised solution based on the pix2pix method. In that sense, it is directly applicable to many domain transfer tasks that are relying on the CycleGAN architecture

Bootstrapped SSL CycleGAN for Asymmetric Domain Transfer

Most CycleGAN domain transfer architectures require a large amount of data belonging to domains on which the domain transfer task is to be applied. Nevertheless, in many real-world applications one of the domains is reduced, i.e., scarce. This means that it has much less training data available in comparison to the other domain, which is fully observable. In order to tackle the problem of using CycleGAN framework in such unfavorable application scenarios, we propose and invoke a novel Bootstrapped SSL CycleGAN architecture (BTS-SSL), where the mentioned problem is overcome using two strategies. Firstly, by using a relatively small percentage of available labelled training data from the reduced or scarce domain and a Semi-Supervised Learning (SSL) approach, we prevent overfitting of the discriminator belonging to the reduced domain, which would otherwise occur during initial training iterations due to the small amount of available training data in the scarce domain. Secondly, after initial learning guided by the described SSL strategy, additional bootstrapping (BTS) of the reduced data domain is performed by inserting artifically generated training examples into the training poll of the data discriminator belonging to the scarce domain. Bootstrapped samples are generated by the already trained neural network that performs transferring from the fully observable to the scarce domain. The described procedure is periodically repeated during the training process several times and results in significantly improved performance of the final model in comparison to the original unsupervised CycleGAN approach. The same also holds in comparison to the solutions that are exclusively based either on the described SSL, or on the bootstrapping strategy, i.e., when these are applied separately. Moreover, in the considered scarce scenarios it also shows competitive results in comparison to the fully supervised solution based on the pix2pix method. In that sense, it is directly applicable to many domain transfer tasks that are relying on the CycleGAN architecture

Feature Map Regularized CycleGAN for Domain Transfer

CycleGAN domain transfer architectures use cycle consistency loss mechanisms to enforce the bijectivity of highly underconstrained domain transfer mapping. In this paper, in order to further constrain the mapping problem and reinforce the cycle consistency between two domains, we also introduce a novel regularization method based on the alignment of feature maps probability distributions. This type of optimization constraint, expressed via an additional loss function, allows for further reducing the size of the regions that are mapped from the source domain into the same image in the target domain, which leads to mapping closer to the bijective and thus better performance. By selecting feature maps of the network layers with the same depth d in the encoder of the direct generative adversarial networks (GANs), and the decoder of the inverse GAN, it is possible to describe their d-dimensional probability distributions and, through novel regularization term, enforce similarity between representations of the same image in both domains during the mapping cycle. We introduce several ground distances between Gaussian distributions of the corresponding feature maps used in the regularization. In the experiments conducted on several real datasets, we achieved better performance in the unsupervised image transfer task in comparison to the baseline CycleGAN, and obtained results that were much closer to the fully supervised pix2pix method for all used datasets. The PSNR measure of the proposed method was, on average, 4.7% closer to the results of the pix2pix method in comparison to the baseline CycleGAN over all datasets. This also held for SSIM, where the described percentage was 8.3% on average over all datasets

Survey on Big Data Applications

The goal of this chapter is to shed light on different types of big data applications needed in various industries including healthcare, transportation, energy, banking and insurance, digital media and e-commerce, environment, safety and security, telecommunications, and manufacturing. In response to the problems of analyzing large-scale data, different tools, techniques, and technologies have bee developed and are available for experimentation. In our analysis, we focused on literature (review articles) accessible via the Elsevier ScienceDirect service and the Springer Link service from more recent years, mainly from the last two decades. For the selected industries, this chapter also discusses challenges that can be addressed and overcome using the semantic processing approaches and knowledge reasoning approaches discussed in this book