Discretization schemes and numerical approximations of PDE impainting models and a comparative evaluation on novel real world MRI reconstruction applications

While various PDE models are in discussion since the last ten years and are widely applied nowadays in image processing and computer vision tasks, including restoration, filtering, segmentation and object tracking, the perspective adopted in the majority of the relevant reports is the view of applied mathematician, attempting to prove the existence theorems and devise exact numerical methods for solving them. Unfortunately, such solutions are exact for the continuous PDEs but due to the discrete approximations involved in image processing, the results yielded might be quite unsatisfactory. The major contribution of This work is, therefore, to present, from an engineering perspective, the application of PDE models in image processing analysis, from the algorithmic point of view, the discretization and numerical approximation schemes used for solving them. It is of course impossible to tackle all PDE models applied in image processing in this report from the computational point of view. It is, therefore, focused on image impainting PDE models, that is on PDEs, including anisotropic diffusion PDEs, higher order non-linear PDEs, variational PDEs and other constrained/regularized and unconstrained models, applied to image interpolation/ reconstruction. Apart from this novel computational critical overview and presentation of the PDE image impainting models numerical analysis, the second major contribution of This work is to evaluate, especially the anisotropic diffusion PDEs, in novel real world image impainting applications related to MRI

Bounding the search space for global optimization of neural networks learning error: an interval analysis approach

Training a multilayer perceptron (MLP) with algorithms employing global search strategies has been an important research direction in the field of neural networks. Despite a number of significant results, an important matter concerning the bounds of the search region---typically defined as a box---where a global optimization method has to search for a potential global minimizer seems to be unresolved. The approach presented in this paper builds on interval analysis and attempts to define guaranteed bounds in the search space prior to applying a global search algorithm for training an MLP. These bounds depend on the machine precision and the term guaranteed denotes that the region defined surely encloses weight sets that are global minimizers of the neural network's error function. Although the solution set to the bounding problem for an MLP is in general non-convex, the paper presents the theoretical results that help deriving a box which is a convex set. This box is an outer approximation of the algebraic solutions to the interval equations resulting from the function implemented by the network nodes. An experimental study using well known benchmarks is presented in accordance with the theoretical results

Solving the linear interval tolerance problem for weight initialization of neural networks

Determining good initial conditions for an algorithm used to train a neural network is considered a parameter estimation problem dealing with uncertainty about the initial weights. Interval Analysis approaches model uncertainty in parameter estimation problems using intervals and formulating tolerance problems. Solving a tolerance problem is defining lower and upper bounds of the intervals so that the system functionality is guaranteed within predefined limits. The aim of this paper is to show how the problem of determining the initial weight intervals of a neural network can be defined in terms of solving a linear interval tolerance problem. The proposed Linear Interval Tolerance Approach copes with uncertainty about the initial weights without any previous knowledge or specific assumptions on the input data as required by approaches such as fuzzy sets or rough sets. The proposed method is tested on a number of well known benchmarks for neural networks trained with the back-propagation family of algorithms. Its efficiency is evaluated with regards to standard performance measures and the results obtained are compared against results of a number of well known and established initialization methods. These results provide credible evidence that the proposed method outperforms classical weight initialization methods

Reliable estimation of a neural network’s domain of validity through interval analysis based inversion

Reliable estimation of a neural network’s domain of validity is important for a number of reasons such as assessing its ability to cope with a given problem, evaluating the consistency of its generalization etc. In this paper we introduce a new approach to estimate the domain of validity of a neural network based on Set Inversion Via Interval Analysis (SIVIA), the methodology established by Jaulin andWalter [1]. This approach was originally introduced in order to solve nonlinear parameter estimation problems in a bounded error context and proved to be effective in tackling several types of problems dealing with nonlinear systems analysis. The dependence of a neural network output on the pattern data is a nonlinear function and hence derivation of the impact of the input data to the neural network function can be addressed as a nonlinear parameter estimation problem that can be tackled by SIVIA. We present concrete application examples and show how the proposed method allows to delimit the domain of validity of a trained neural network. We discuss advantages, pitfalls and potential improvements offered to neural networks

An efficient multi-agent modelling scheme of wireless sensor networks (Wsn) towards improved performance evaluation

The simulation of a Wireless Sensor Network (WSN) is a large and diverse set of tasks which, ideally, are spread in (logical) time and (memory) space. Although in the literature many research attempts have introduced simulation platforms for Wireless Sensor Networks design, nearly all are focused in limited layers of abstraction not including the physical and communications layer. Moreover, scheduling of events is not considered carefully. In this paper, Coordination mechanisms invoked to execute these tasks in a timely accurate manner towards precision are shown and at machine level similar mechanisms are considered and invoked to manage multiple threads (in Central Processing Units (CPUs), Graphics Processing Units (GPUs) and combinations) towards improved performance. These mechanisms are illustrated in the proposed multiagent simulation system, which transform the concepts of a multi agent system (in this case Wireless Sensor Network motes), communication schemes and environment abstractions to a set of individual tasks as threads, executed in groups depending on the underlying machine. The contribution of this paper lies in the development of a suitable multiagent simulation system model for Wireless Sensor Networks, modelling all main real world abstractions taking place in such a system. Moreover, a study of the overhead management regarding this multithreading design is considered illustrating an affordable overhead even in case of very large systems simulation. © 2020 Praise Worthy Prize S.r.l.-All rights reserved

New PDE-based methods for image enhancement using SOM and Bayesian inference in various discretization schemes

A novel approach is presented in this paper for improving anisotropic diffusion PDE models, based on the Perona–Malik equation. A solution is proposed from an engineering perspective to adaptively estimate the parameters of the regularizing function in this equation. The goal of such a new adaptive diffusion scheme is to better preserve edges when the anisotropic diffusion PDE models are applied to image enhancement tasks. The proposed adaptive parameter estimation in the anisotropic diffusion PDE model involves self-organizing maps and Bayesian inference to define edge probabilities accurately. The proposed modifications attempt to capture not only simple edges but also difficult textural edges and incorporate their probability in the anisotropic diffusion model. In the context of the application of PDE models to image processing such adaptive schemes are closely related to the discrete image representation problem and the investigation of more suitable discretization algorithms using constraints derived from image processing theory. The proposed adaptive anisotropic diffusion model illustrates these concepts when it is numerically approximated by various discretization schemes in a database of magnetic resonance images (MRI), where it is shown to be efficient in image filtering and restoration applications

Neural Network Training and Simulation Using a Multidimensional Optimization System

A new approach is presented to neural network simulation and training that is based on the use of general purpose optimization software. This approach requires that the training problem should be formulated as the minimization of a cost function of the network weights. This cost function is a user written code called by the optimization system, which in turn provides the user with a variety of minimization procedures that can be combined via user programmable minimization strategies. Experimental results concerning several learning paradigms indicate that the approach is very convenient and effective and leads to the discovery of efficient training strategies. 1 Introduction The increased interest in neural network research has led to the development of many software simulators that provide the experimentation means for training and testing the variety of the existing models. These simulators can be classified into the following categories. 1. Network specific simulators. They are spe..

Neural network based textural labeling of images in multimedia applications

In this paper the use of multilayer perceptron type neural networks in the characterization of images by texture content is investigated. The paper is focused on the effects of textural feature extraction methods on the network architecture, training performance and generalization capability when applied to indexing of images in multimedia image databases. An in depth experimental study is conducted comparing several well known textural feature extraction techniques along with a novel discrete wavelet transform based methodology. It is demonstrated that the proposed technique leads to the design and selection of multilayer perceptron architectures with the best texture classification accuracy