Regularization of descriptor systems

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.

Robust State-Derivative Feedback LMI-Based Designs for Linear Descriptor Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Improving image classification through descriptor combination

The efficiency in image classification tasks can be improved using combined information provided by several sources, such as shape, color, and texture visual properties. Although many works proposed to combine different feature vectors, we model the descriptor combination as an optimization problem to be addressed by evolutionary-based techniques, which compute distances between samples that maximize their separability in the feature space. The robustness of the proposed technique is assessed by the Optimum-Path Forest classifier. Experiments showed that the proposed methodology can outperform individual information provided by single descriptors in well-known public datasets. © 2012 IEEE.

HTS: A new shape descriptor based on Hough Transform

In this paper we propose a novel method for shape analysis called HTS (Hough Transform Statistics), which uses statistics from Hough Transform space in order to characterize the shape of objects in digital images. Experimental results showed that the HTS descriptor is robust and presents better accuracy than some traditional shape description methods. Furthermore, HTS algorithm has linear complexity, which is an important requirement for content based image retrieval from large databases. © 2013 IEEE.

Swarm-based descriptor combination and its application for image classification

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Breast imaging: is the sonographic descriptor of orientation valid for magnetic resonance imaging?

Purpose: To evaluate if the Breast Imaging Reporting and Data System (BI-RADS) ultrasound descriptor of orientation can be used in magnetic resonance imaging (MRI). Materials and Methods: We conducted a retrospective study to evaluate breast mass lesions identified by MRI from 2008 to 2010 who had ultrasound (US) and histopathologic confirmation. Lesions were measured in the craniocaudal (CC), anteroposterior (AP), and transverse (T) axes and classified as having a nonparallel orientation, longest axis perpendicular to Cooper's ligaments, or in a parallel orientation when the longest axis is parallel to Cooper's ligaments. The MR image data were correlated with the US orientation according to BI-RADS and histopathological diagnosis. Results: We evaluated 71 lesions in 64 patients. On MRI, 27 lesions (38.0%) were nonparallel (8 benign and 19 malignant), and 44 lesions (62.0%) were parallel (33 benign and 11 malignant). There was significant agreement between the lesion orientation on US and MRI (kappa value = 0.901). The positive predictive values (PPV) for parallel orientation malignancy on MR and US imaging were 70.4% and 73.1%, respectively. Conclusion: A descriptor of orientation for breast lesions can be used on MRI with PPV for malignant lesions similar to US. J. Magn. Reson. Imaging 2012; 36:13831388. (C) 2012 Wiley Periodicals, Inc.

Texture descriptor based on partially self-avoiding deterministic walker on networks

Texture image analysis is an important field of investigation that has attracted the attention from computer vision community in the last decades. In this paper, a novel approach for texture image analysis is proposed by using a combination of graph theory and partially self-avoiding deterministic walks. From the image, we build a regular graph where each vertex represents a pixel and it is connected to neighboring pixels (pixels whose spatial distance is less than a given radius). Transformations on the regular graph are applied to emphasize different image features. To characterize the transformed graphs, partially self-avoiding deterministic walks are performed to compose the feature vector. Experimental results on three databases indicate that the proposed method significantly improves correct classification rate compared to the state-of-the-art, e.g. from 89.37% (original tourist walk) to 94.32% on the Brodatz database, from 84.86% (Gabor filter) to 85.07% on the Vistex database and from 92.60% (original tourist walk) to 98.00% on the plant leaves database. In view of these results, it is expected that this method could provide good results in other applications such as texture synthesis and texture segmentation. (C) 2012 Elsevier Ltd. All rights reserved.

A Logical Descriptor for Regular Languages via Stone Duality

In this paper we introduce a class of descriptors for regular languages arising from an application of the Stone duality between finite Boolean algebras and finite sets. These descriptors, called classical fortresses, are object specified in classical propositional logic and capable to accept exactly regular languages. To prove this, we show that the languages accepted by classical fortresses and deterministic finite automata coincide. Classical fortresses, besides being propositional descriptors for regular languages, also turn out to be an efficient tool for providing alternative and intuitive proofs for the closure properties of regular languages.