Integral representations for Padé-type operators

The main purpose of this paper is to consider an explicit form of the Padé-type operators. To do so, we consider the representation of Padé-type approximants to the Fourier series of the harmonic functions in the open disk and of the L p-functions on the circle by means of integral formulas, and, then we define the corresponding Padé-type operators. We are also oncerned with the properties of these integral operators and, in this connection, we prove some convergence results

Existence domains for holomorphic Lp functions

If $\Omega$ is a domain of holomorphy in $\Bbb C^n$, having a compact topological closure into another domain of holomorphy $U\subset \Bbb C^n$ such that $(\Omega,U)$ is a Runge pair, we construct a function $F$ holomorphic in $\Omega$ which is singular at every boundary point of $\Omega$ and such that $F$ is in $L^p(\Omega)$, for any $p\in (0,+\infty)$

Non-linear Convolution Filters for CNN-based Learning

During the last years, Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance in image classification. Their architectures have largely drawn inspiration by models of the primate visual system. However, while recent research results of neuroscience prove the existence of non-linear operations in the response of complex visual cells, little effort has been devoted to extend the convolution technique to non-linear forms. Typical convolutional layers are linear systems, hence their expressiveness is limited. To overcome this, various non-linearities have been used as activation functions inside CNNs, while also many pooling strategies have been applied. We address the issue of developing a convolution method in the context of a computational model of the visual cortex, exploring quadratic forms through the Volterra kernels. Such forms, constituting a more rich function space, are used as approximations of the response profile of visual cells. Our proposed second-order convolution is tested on CIFAR-10 and CIFAR-100. We show that a network which combines linear and non-linear filters in its convolutional layers, can outperform networks that use standard linear filters with the same architecture, yielding results competitive with the state-of-the-art on these datasets.Comment: 9 pages, 5 figures, code link, ICCV 201

Comprehensive Comparison of Deep Learning Models for Lung and COVID-19 Lesion Segmentation in CT scans

Recently there has been an explosion in the use of Deep Learning (DL) methods for medical image segmentation. However the field's reliability is hindered by the lack of a common base of reference for accuracy/performance evaluation and the fact that previous research uses different datasets for evaluation. In this paper, an extensive comparison of DL models for lung and COVID-19 lesion segmentation in Computerized Tomography (CT) scans is presented, which can also be used as a benchmark for testing medical image segmentation models. Four DL architectures (Unet, Linknet, FPN, PSPNet) are combined with 25 randomly initialized and pretrained encoders (variations of VGG, DenseNet, ResNet, ResNext, DPN, MobileNet, Xception, Inception-v4, EfficientNet), to construct 200 tested models. Three experimental setups are conducted for lung segmentation, lesion segmentation and lesion segmentation using the original lung masks. A public COVID-19 dataset with 100 CT scan images (80 for train, 20 for validation) is used for training/validation and a different public dataset consisting of 829 images from 9 CT scan volumes for testing. Multiple findings are provided including the best architecture-encoder models for each experiment as well as mean Dice results for each experiment, architecture and encoder independently. Finally, the upper bounds improvements when using lung masks as a preprocessing step or when using pretrained models are quantified. The source code and 600 pretrained models for the three experiments are provided, suitable for fine-tuning in experimental setups without GPU capabilities.Comment: 10 pages, 8 figures, 2 table

Using Tobit Kalman filtering in order to improve the Motion recorded by Microsoft Kinect

In this paper, we analyze data from Microsoft Kinect v2 camera using Kalman Tobit and Kalman filters so as to minimize noise. The data concern three-dimensional spatial coordinates recording movements of a persons’A joints, which are subject to measurement errors. The noise variances of the process and the measurements are estimated using the maximum likelihood function. In order to include into the model restrictive conditions based on anthropometric data (e.g. the distances between various joints) we apply the Tobit Kalman Filter. Additionally, restrictions for the joints displacements per fame based on real data can be used in order to get better results. Finally simulations of skeleton before and after using Kalman filtering are presented